Solène Bernard
email: solene.bernard@centrale.centralelille.fr

Patrick Bas
email: patrick.bas@centralelille.fr

John Klein
email: john.klein@univ-lille.fr

Tomáš Pevný
email: tomas.pevny@fel.cvut.cz

Optimizing Additive Approximations of Non-Additive Distortion Functions

The progress in steganography is hampered by a gap between nonadditive distortion functions, which capture well complex dependencies in natural images, and their additive counterparts, which are efficient for data embedding. This paper proposes a theoretically justified method to approximate the former by the latter. The proposed method, called Backpack (for BACKPropagable AttaCK), combines new results in the approximation of gradients of discrete distributions with a gradient of implicit functions in order to derive a gradient w.r.t. the distortion of each JPEG coefficient. Backpack combined with the min max iterative protocol leads to a very secure steganographic algorithm. For example, the error rate of XuNet on 512 × 512 JPEG images, compressed with quality factor 100 and a payload of 0.4 bits per non-zero AC coefficient is 37.3% with Backpack, compared to a 26.5% error rate using ADV-EMB with min max protocol (considered state of the art in this work) and a 16.9% error rate with J-UNIWARD.

INTRODUCTION

Steganography by cover modification hides data into an innocuous looking content, such that the mere fact of a payload being hidden cannot be reliably detected. A counterpart of steganography is steganalysis, aiming to detect contents with hidden data. Antagonist goals of steganographers versus steganalysts force them to play a cat-and-mouse game (called steganographic game below) commonly found in security fields. This paper takes a step forward in removing humans from playing this game by proposing an automatic way to design attacks and counter-attacks.

State of the art steganographic algorithms rely on the principle of minimizing a distortion function, which needs to be additive for practical reasons. Before hiding the message (embedding), a steganographic algorithm assigns to each modifiable coefficient (e.g. a pixel or DCT coefficient if the cover object is an image) an embedding cost. The message is then hidden by syndrome trellis codes [START_REF] Filler | Minimizing embedding impact in steganography using trellis-coded quantization[END_REF], which minimizes the additive distortion function under the constraint of communicating a message. For research purposes, the act of embedding a concrete message is skipped in favor of a mere simulation [START_REF] Fridrich | Practical methods for minimizing embedding impact in steganography[END_REF][START_REF] Kin | Simulating Suboptimal Steganographic Embedding[END_REF]. Presently, the design of new steganographic algorithms therefore boils down to defining the embedding costs.

Note that the construction of costs falls into two (and half) categories. Heuristics are used in UNIWARD [START_REF] Holub | Universal distortion function for steganography in an arbitrary domain[END_REF], HILL [START_REF] Li | A new cost function for spatial image steganography[END_REF] or UERD [START_REF] Guo | Using statistical image model for JPEG steganography: Uniform embedding revisited[END_REF], where costs promote preservation of properties in natural images that steganography might violate, as for example smoothness. An alternative, in our view more sophisticated, approach [START_REF] Giboulot | Detectability-based JPEG steganography modeling the processing pipeline: the noise-content tradeoff[END_REF][START_REF] Pevny | Using High-Dimensional Image Models to Perform Highly Undetectable Steganography[END_REF][START_REF] Sedighi | Content-adaptive steganography by minimizing statistical detectability[END_REF] calculates the cost to minimize detectability of a specific steganalyzer (also called detection function or detector). Note that this detection function (typically modeling the noise extracted from one cover image) is different from that used by real steganalytic detectors (built from numerous cover and stego images), since its direct minimization may be complicated in practice [START_REF] Pevny | Exploring non-additive distortion in steganography[END_REF].

An evolution is to automate the design of detection functions. The very first attempt known to us was ASO [START_REF] Kouider | Adaptive steganography by oracle (ASO)[END_REF], which convergence issues prevented a wider adoption and success. More recent approaches relied on generative adversarial networks (GAN) [START_REF] Tang | Automatic Steganographic Distortion Learning Using a Generative Adversarial Network[END_REF][START_REF] Yang | An Embedding Cost Learning Framework Using GAN[END_REF] which simultaneously optimize a neural network predicting embedding costs and another neural network as steganalyzer. It is known that under some assumptions, GANs converge to the Nash equilibrium [START_REF] Frans A Oliehoek | GANGs: Generative adversarial network games[END_REF] of a steganographic game, with actions defined by spaces parametrized by chosen models. Yet, the convergence of GANs is difficult to achieve in practice. An alternative to GANs is [START_REF] Bernard | Exploiting adversarial embeddings for better steganography[END_REF] which does not use the fixed estimator of embedding changes. Instead, the distortions associated to each DCT sample are optimized by means of adversarial embedding (ADV-EMB) [START_REF] Tang | CNN-Based Adversarial Embedding for Image Steganography[END_REF] for a given image and steganalyzer. The main contribution of [START_REF] Bernard | Exploiting adversarial embeddings for better steganography[END_REF] and [START_REF] Bernard | Explicit optimization of min max steganographic game[END_REF] was to show, how to construct iteratively steganalyzers without suffering from the convergence issues of ASO.

The set of steganalyzers created by the min max protocol in [START_REF] Bernard | Exploiting adversarial embeddings for better steganography[END_REF] plays the role of non-additive distortion functions, as they measure the detectability of a given image. Indeed the adversaries (here the classifiers) capture mid-range dependencies between DCT coefficients which are by definition non-additive. In order to overcome this issue, the embedding can induce correlations by either using lattices (see section 2.2) and/or by crafting specific non-symmetric additive costs as done here. For example ADV-EMB [START_REF] Tang | CNN-Based Adversarial Embedding for Image Steganography[END_REF] adjusts costs of some symmetric additive distortion function (J-UNIWARD) w.r.t. the gradient of the loss of one steganalyzer by performing only one gradient descent step and by distinguishing costs related to +1 to costs related to -1 w.r.t. the gradient of the detectability function. In Section 2.4 it is shown however that ADV-EMB cannot reliably adjust embedding costs such that the resulting stego object is undetectable by the worst classifier from a set. Moreover, ADV-EMB does not natively take the length of embedded message into account.

This paper proposes a method called Backpack (for BACKPropagable AttaCK) 1 fixing flaws of ADV-EMB by finding embedding costs by gradient descent with constraint on message length included by means of implicit differentiation. To put the proposed method into a wider context, it optimizes parameters of additive distortion function (embedding costs) by challenging a non-additive distortion function (a set of steganalyzers) for a given image and message length. In this sense, the method is general. The experimental evaluation demonstrates its advantages with respect to ADV-EMB by improving the security of a steganographic algorithm found by min max protocol [START_REF] Bernard | Exploiting adversarial embeddings for better steganography[END_REF] by 11% when the distortion function is a deep neural network with a Xu-Net [START_REF] Xu | Deep convolutional neural network to detect J-UNIWARD[END_REF] architecture.

This paper is organized as follows. The next section recalls important prior arts for explaining and framing of the method and also shows the weakness of ADV-EMB algorithm. Section 3 formally defines the problem and shows how to calculate the gradient of a differentiable steganalyzer with respect to embedding costs. Experimental section 4 shows the effect of the proposed scheme on security of the obtained embedding costs.

Notations

In the following, letters in bold are used to represent vectors and matrices, a corresponding non bold letters are used for their elements. Calligraphic letters are used for sets. Cover and stego objects are denoted as vectors and they are respectively denoted as c = (𝑐 𝑖 ) and s = (𝑠 𝑖 ), 𝑖 ∈ {1, . . . , 𝑛} (ranges in sums are dropped if it is clear from context). B denotes the set of allowed embedding changes made to the cover. Subscripts 𝑖 ∈ {1, . . . , 𝑛} denote index of a coefficient, whereas superscripts 𝑗 ∈ B are for embedding directions.

Spaces I, M, and K are respectively the space of all images, messages and keys with appropriate distributions, P • , defined over them.

A steganalyzer (or steganographic detector or detector) is any function 𝑓 (x) : I ↦ → R and x is assigned to stego class if the output is greater than some threshold 𝑡. A steganographic algorithm is any pair of functions ℎ emb (x, 𝑚, 𝑘) : I × M × K → I and 𝑔 ext (x, 𝑘) : I × K → M for which it holds that 𝑔 ext (ℎ emb (x, m, 𝑘), 𝑘) = m for all m ∈ M, 𝑘 ∈ K, and x ∈ I.. 1 The name is derived from methods which inspired the work: backpropagation and adversarial attacks on neural networks.

BACKGROUND 2.1 Distortion minimization principle

Steganography by cover modification maps a cover object c to a stego object s such that it communicates a message m while minimizing a distortion function 𝑓 (s, c). The range of embedding changes b = cs is usually restricted to the set B, which is most of the time small B = {-1, 0, +1}.

For general distortion functions 𝑓 the above problem is NP-hard, therefore practical embedding schemes use an additive 𝑓 (s, c) = Given cover object c, message m,, key 𝑘 and embedding costs 𝝆, the 𝝆-parametrized embedding function ℎ emb (c, m, 𝑘; 𝝆) solving the above optimization problem for additive distortion function is usually implemented by Syndrome Trellis Codes [START_REF] Filler | Minimizing embedding impact in steganography using trellis-coded quantization[END_REF] (STC), which produce stego objects with distortion usually within 5% -7% of that of the optimal embedding.

As shown in [START_REF] Fridrich | Practical methods for minimizing embedding impact in steganography[END_REF], the optimal embedding minimizing an additive distortion function can be simulated by adding random embedding changes b to a cover signal, i.e. s = c + b, where embedding changes b are realizations of a random variable distributed according to

𝑃 b (b|𝝆, 𝜆) = 𝑛 𝑖=1 𝑃 𝑏 𝑖 (𝑏 𝑖 = 𝑗 |𝜌 𝑖 , 𝜆)
where

𝑃 𝑏 𝑖 (𝑏 𝑖 = 𝑗 |𝜌 𝑖 , 𝜆) = 𝑒 -𝜆𝜌 𝑗 𝑖 𝑘 ∈B 𝑒 -𝜆𝜌 𝑘 𝑖 , 𝑖 ∈ {1, . . . , 𝑛}, 𝑗 ∈ B (1)
with a condition that the entropy of the steganographic channel is equal to the length of the message, i.e :

𝐻 (𝑃 b (b|𝝆, 𝜆)) = |m|, (2)
where |m| denotes the length of the message in bits and

𝐻 (p) = -𝑖,𝑗 𝑝 𝑗 𝑖 log 𝑝 𝑗 𝑖 if p = (𝑝 𝑗 𝑖
) is a matrix. The stego object s created by the simulation is random, as it is a realization of a random variable and as the message is not fixed and assumed to be drawn randomly from a uniform distribution. In contrast, in STC, the embedding function is deterministic, since the message is fixed.

Non-additive distortion functions

The above theory is well developed for additive distortion functions, unfortunately many interesting distortion functions, mainly those corresponding to state of the art steganalyzers are non-additive and the above methodology does not apply.

Gibbs construction [START_REF] Filler | Gibbs construction in steganography[END_REF] proposes to solve the problem using Gibbs sampling, which is theoretically correct (albeit not optimal), but prohibitively expensive. A greedy approximation by dynamic programming is proposed in [START_REF] Pevny | Exploring non-additive distortion in steganography[END_REF], but it is also computationally expensive. Other constructions rely on decomposing the image into disjoint lattices in order to synchronize embedding changes [START_REF] Li | A strategy of clustering modification directions in spatial image steganography[END_REF][START_REF] Taburet | JPEG Steganography and Synchronization of DCT Coefficients for a Given Development Pipeline[END_REF]. Contrary to Gibbs sampling, the embedding stops when all the lattice have been visited once.

A completely different approach inspired by the creation of adversarial attacks is offered by adversarial embedding ADV-EMB [START_REF] Tang | CNN-Based Adversarial Embedding for Image Steganography[END_REF].

ADV-EMB heuristically modifies embedding costs 𝝆 of some existing embedding algorithm (J-UNIWARD) to avoid detection by a fixed steganalyzer 𝑓 . Specifically, embedding costs are divided into a common, L 𝑐 , and an adjustable, L 𝑎 , group and they are modified according to

ρ 𝑗 𝑖 = 𝜌 𝑗 𝑖 𝛼 𝑗sign( 𝜕𝑓 (s) 𝜕s 𝑖 ) iff 𝑖 ∈ L 𝑎 , ρ 𝑗 𝑖 = 𝜌 𝑗 𝑖 iff 𝑖 ∈ L 𝑐 , (3)
where ρ denotes new embeddings costs and 𝛼 = 10 is a parameter. Notice that embedding costs of coefficients in the common group are not changed. ADV-EMB uses heuristic to overcome a major hurdle in applying a gradient descend to optimization of embedding costs, which is that the embedding operation is not differentiable. Instead of using a proper gradient (or its estimate), it uses its sign and fixes the step. ADV-EMB has been reported to perform well against a single fixed detector. By an exhaustive search the algorithm minimizes the number of adjusted embedding costs to prevent modifying too many embedding coefficients, which might be easily detectable.

min max protocol

ADV-EMB [START_REF] Tang | CNN-Based Adversarial Embedding for Image Steganography[END_REF] allows efficiently to create a stego object secure with respect to a given differentiable steganalyzer. Although the same reference proposes an iterative algorithm to create a steganalyzer, such that the resulting stego images are secure, the proposed iterative algorithm does not have any theoretical guarantees. A theoretically justified approach proposed in [START_REF] Bernard | Exploiting adversarial embeddings for better steganography[END_REF] is revised below. Security of a practical steganographic scheme ℎ emb with respect to a set of steganalyzers F is defined as the error of the best steganalyzer :

arg min 𝑓 ∈ F 1 2 E 𝑥∼𝑃 c I[𝑓 (x) ≥ 𝑡] + I[𝑓 (ℎ emb (x)) < 𝑡] . ( 4
)
where I is the indicator function, and 𝑡 a decision threshold. Since F is in practice very large it is difficult to create a steganographic algorithm by explicitly optimizing this criteria. Ref. [START_REF] Bernard | Exploiting adversarial embeddings for better steganography[END_REF] decreases the computational complexity by (i) selecting a small but representative subset of F and (ii) using ADV-EMB to create stego images maximally secure with respect to this small subset of F . The subset of F is constructed iteratively starting with an empty set F 0 = ∅. At the 𝑘 th iteration, the protocol consists of the following two steps :

(1) Create a set of stego images S 𝑘 maximally secure with respect to the set of detectors F 𝑘-1 = {𝑓 0 , 𝑓 1 , . . . , 𝑓 𝑘-1 }.

(2) Build a new detector 𝑓 𝑘 detecting stego images produced in step [START_REF] Abadi | Tensorflow: A system for large-scale machine learning[END_REF] and add it to the set F 𝑘-1 , i.e. F 𝑘 = F 𝑘-1 ∪ {𝑓 𝑘 }. Notice that the construction of the small subset explicitly exhibits a cat and mouse game played by the community for decades, where step (1) corresponds to proposing a new steganographic algorithm maximally secure with respect to all known steganalyzers and step (2) corresponds to proposing a new steganalyzer breaking the newly proposed steganographic algorithm.

Flaws of ADV-EMB in min max protocol

During the 𝑘 + 1 th iteration, the min max protocol uses ADV-EMB to create stego images undetectable by all steganalyzers in F 𝑘 . The gradient of the steganalyzer with respect to stego image used in Equation (3) therefore becomes :

𝜕 max 𝑓 ∈ F 𝑘 𝑓 (s) 𝜕s = 𝜕 f (s) 𝜕s ,
where f = arg max 𝑓 ∈ F 𝑘 𝑓 (𝑠). Since ADV-EMB calculates the gradient and adjusts embedding costs just once, the resulting stego image is optimized only with respect to the classifier f and ignoring remaining adversaries F 𝑘 \ f , which means that the resulting stego image created with adjusted embedding costs ρ can be still detectable by them. Moreover, as mentioned before, the use of the gradient in ( 3) is heuristic, and does not reflect the fact that the embedding costs should directly be modified according to the gradient of 𝑓 (.) w.r.t. the costs.

DIFFERENTIABLE STEGANOGRAPHY 3.1 Problem formulation

The problem we solve is for a given cover object x to find an embedding cost map 𝝆 minimizing detectability of a stego object s = c + b by a non-additive distortion function 𝑓 (s) (read steganalyzer), where b ∼ 𝑃 b (b|𝝆, 𝜆) and 𝑓 being almost everywhere differentiable with respect to s. We therefore focus on simulation of embedding changes. The stego object s = c + b is a realization of a random variable and we minimize the expected detectability over all possible stego objects written as :

arg min 𝝆,𝜆 E b∼𝑃 b (b |𝝆,𝜆) [𝑓 (c + b)], (5)
subject to the entropy constraint:

𝐻 (𝑃 b (b|𝝆, 𝜆)) = |m|. (6)
We want to solve the above problem using gradient descend with respect to 𝝆, because it is efficient but its use for this problem is difficult from two reasons: first, the optimization problem contains an implicit constraint on the entropy; second the gradient of the expectation of 𝑓 with respect to 𝝆 does not have an analytical expression and its exact computation (summation over all possible embedding changes) would be prohibitively expensive. The rest of this section first presents how to overcome these two hurdles and then describes an algorithm to efficiently minimize (5).

Estimating the gradient of expectation of a discrete distribution

Let us first focus on the problem of calculating the gradient of:

𝜕 𝜕𝜌 E b∼𝑃 b (b |𝝆,𝜆) [𝑓 (c + b)], (7)
without the entropy constraint (we assume 𝜆 is fixed for now). The exact computation of the expectation (and therefore its gradient) is computationally very expensive. To compute it exactly one would need to sum over the support of all stego images (for a given cover), which has |B| 𝑛 (recall that |B| is the cardinality of embedding changes and 𝑛 is the number of coefficients that can be modified during embedding). The rest of this section therefore focuses on an approximation of (7) that would be sufficiently accurate while being computationally cheap.

To simplify the notation, the calculation of the expected gradient is introduced for a single coefficient. This means that the modification 𝑏 of a coefficient is a scalar with probability distribution described by a vector p of length |B|. Since embedding changes are assumed to be independent (this is required by our constraint on the distortion function to be additive), the generalization to all coefficients of an object is straightforward.

Hardmax

Gumbel. The problem of calculating the gradient of expectation of discrete probability distribution with respect to its parameters is very well studied problem. From the vast prior art, we have chosen the method [START_REF] Jang | Categorical Reparameterization with Gumbel-Softmax[END_REF] relying on the Gumbel distribution. This technique has an advantage of giving a general formula to draw samples according to any discrete distribution, so it can be used without a modification for 𝑛-ary coding, and its theoretical properties are well analyzed.

A discrete distribution defined by a probability vector p = (𝑝 𝑗 ) 𝑗 ∈B , (recall that p specifies probability of changing a single coefficient to values allowed by embedding) can be sampled by dividing also interval [0, 1] into |B| buckets of size p, and then returning index of a bucket to which a random variable with uniform distribution on [0, 1] falls. An alternative approach is to sample the same distribution according to following strategy :

𝑏 = MG(p, g) = arg max 𝑗 ∈B (𝑔 𝑗 + log 𝑝 𝑗 ), (8)
where elements of g are independently sampled from the Gumbel distribution 𝐺 (0, 1

= SG 𝜏 (p, g) = 𝑗 ∈B 𝑗 𝑧 𝑗 , (9)
with z = softmax g + log p 𝜏 , (10)
where g and p are as above. The last Equation ( 9) is easily differentiable with respect to p since the calculation can treat the random numbers g as constants (in machine learning this is called a re-parametrization trick).

The main advantage of re-parametrization this is that the gradient in Equation ( 7) can be now estimated using 𝑘 samples g 1 , . . . , g 𝑘 as 1

𝐾 𝐾 𝑗=1 𝜕𝑓 (c + SG 𝜏 (p, g 𝑗 )) 𝜕p 𝜕p 𝜕𝜌 . ( 11
)
The number 𝐾 of drawn samples g 1 , . . . , g 𝐾 , control the trade-off between variance of the estimate and computational complexity. It is common in to use 𝐾 as small as 𝐾 = 1, i.e. estimating the gradient from a single sample (compare this to complexity |B| 𝑛 of the exact computation in Equation ( 7)). The drawback of this estimator is that it is biased. In experiments presented in this paper, 𝐾 was selected to the highest number which the GPU memory allowed.

Incorporating constraint on entropy

Assuming gradient (7) can be efficiently approximated by Equation [START_REF] Giboulot | Detectability-based JPEG steganography modeling the processing pipeline: the noise-content tradeoff[END_REF], compliance with the constraint on entropy ( 6) is still required. Among other possibilities (e.g. the method of Lagrange multipliers), one can remove constraints by incorporating them into the optimization term through an implicit function. This does not does not change the solution of the optimization but simplifies it. This subsection shows that this is indeed possible in problem [START_REF] Bernard | Exploiting adversarial embeddings for better steganography[END_REF].

Recall that for a given embedding cost 𝝆, the probabilities of changing coefficients 𝑃 b are calculated by Equation (1) for a 𝜆 being solution of an entropy constraint given by Equation [START_REF] Boroumand | Deep residual network for steganalysis of digital images[END_REF]. Thus for a given 𝝆, 𝜆 is a unique solution of some implicitly defined function, which is here denoted as Λ(𝝆, |m|) = 𝜆. Substituting this implicit function Λ(𝝆, |m|) into the Equation (1) for distribution of embedding changes, gradient of Equation ( 7) with respect to embedding costs 𝜌 can be written as :

𝜕 𝜕𝜌 E b∼𝑃 b (b |𝝆,Λ(𝝆, |m |)) [𝑓 (c + b)],
which is free of 𝜆 but contains the implicit function Λ. According to the chain rule of derivatives, this gradient becomes :

𝜕 𝜕p E b∼𝑃 b (b |p) [𝑓 (c + b)] 𝜕p 𝜕𝜌 . ( 12
)
While good approximations of the first term can be obtained as explained in 3.2, computing 𝜕p 𝜕𝜌 is more cumbersome since p depends on both 𝜌 and 𝜆.

Because p = 𝑃 b (b|𝜌, 𝜆), writing the total derivative gives:

𝜕p 𝜕𝜌 = 𝜕𝑃 b 𝜕𝜌 𝜕𝜌 𝜕𝜌 + 𝜕𝑃 b 𝜕𝜆 𝜕Λ(𝜌, |m|)) 𝜕𝜌 . ( 13
)
Although function Λ is implicit, its gradient

𝜕Λ(𝜌, |m |)) 𝜕𝜌
can be computed. Recall that for a given 𝜌, 𝜆 is a solution of an entropy constraint (Equation ( 6)), therefore it holds that

𝐻 (𝑃 b (𝜆, 𝜌)) = 𝐻 (𝑃 b (Λ(𝜌, |m|), 𝜌)) = |m|, (14)
and therefore 𝐻 (𝑃 b (Λ(𝜌, 𝑚), 𝜌)) -|m| = 0. Applying the chain rule to this equation gives :

𝜕 𝜕𝜌 𝐻 (𝑃 b (𝜌, Λ(𝜌, |m|))) = 𝜕𝐻 (𝑃 b ) 𝜕𝜌 𝜕𝜌 𝜕𝜌 + 𝜕𝐻 (𝑃 b ) 𝜕𝜆 𝜕Λ 𝜕𝜌 = 0, ( 15
)
from which the desired gradient of Λ(𝜌, |m|), 𝜌) can be expressed as

𝜕Λ(𝜌, |m|)) 𝜕𝜌 = - 𝜕𝐻 (𝑃 b ) 𝜕𝜆 -1 𝜕𝐻 (𝑃 b ) 𝜕𝜌 . ( 16
)
Combining Equation ( 16) and Equation ( 13) with Equation ( 12) yields to a closed form expression for the gradient :

𝜕 𝜕p E b∼𝑃 b (b |p) [𝑓 (c + b)] 𝜕𝑃 b 𝜕𝜌 - 𝜕𝑃 b 𝜕𝜆 𝜕𝐻 (𝑃 b ) 𝜕𝜆 -1 𝜕𝐻 (𝑃 b ) 𝜕𝜌 (17)

Optimizing embedding costs

Results presented in above sections allows us to efficiently approximate the gradient of Equation ( 7) by estimating a gradient of its smooth approximation with a constraint on the entropy. This allows use to adapt a gradient descend method to minimize detectability with respect to all detectors in a set F 𝑘 as needed in min max protocol.

The proposed algorithm with pseudocode shown in Algorithm 1 uses continuous approximation of discrete embedding changes to optimize the embedding costs 𝜌. In every iteration, it checks if detectability of stego images with discrete embedding costs is below threshold. If yes, the algorithm is terminated, otherwise it continues. If the detectability of stego images with continuous approximation is below a given threshold, the temperature is halved. In practice, there is also a limit on the maximum number of iterations. All expectations in the pseudocode are estimated from a single sample, as described in Section 3.2.1. The threshold on detectability is the detectability of the unmodified cover object.

The progress of the proposed algorithm on minimizing detectability of a single stego object against a single detector is shown in Figure 2. Although the optimization uses continuous approximation of stego objects (blue line), the main goal is to create stego objects with discrete embedding change (orange line). We can observe that in the very beginning, when temperature is high, there is a big difference between detectability of continuous approximations and that of real stego objects. But as the algorithm progresses and temperature decreases, this difference becomes negligible.

The proposed algorithm is iterative, therefore it does not suffer the weakness of ADV-EMB described in Section 2.4 and it is well suited to minimize detectability measured as a maximum over a set of steganalyzers.

Data: A JPEG cover image c, initial embedding costs 𝜌 0 , initial 𝜏 0 Result: An adversarial embedding costs 𝝆 𝝆 ← 𝝆 0 ;

𝜏 ← 𝜏 0 ; õ ← max 𝑖 E b𝜏 ∼𝑃 (𝜆,𝝆) [𝑓 𝑖 (c + b𝜏 ) -𝑓 𝑖 (c)]; 𝑜 ← max 𝑖 E b∼𝑃 (𝜆,𝝆) [𝑓 𝑖 (c + b) -𝑓 𝑖 (c)];
while True do while õ > 0 and 𝑜 > 0 do Update 𝝆 by one step of gradient descend with

𝜕 õ 𝜕𝝆 ; õ ← max 𝑖 E b𝜏 ∼𝑃 (𝜆,𝝆) [𝑓 𝑖 (c + b𝜏 ) -𝑓 𝑖 (c)]; 𝑜 ← max 𝑖 E b∼𝑃 (𝜆,𝝆) [𝑓 𝑖 (c + b) -𝑓 𝑖 (c)]; end if 𝑜 ≤ 0 then Return 𝝆 else while õ ≤ 0 do 𝜏 ← 𝜏 2 ; õ ← max 𝑖 E b𝜏 ∼𝑃 (𝜆,𝝆) [𝑓 𝑖 (c + b𝜏 ) -𝑓 𝑖 (c)]; end end end Algorithm 1:
The proposed algorithm optimizing embedding costs to minimize detectability of a stego object with respect to a set of steganalyzers F 𝑘 .

EXPERIMENTAL EVALUATION

Backpack is below compared to ADV-EMB by each method implementing step 2 in the min max protocol (see Section 2.3). Note that due to the weakness described in Section 2.4 the ADV-EMB algorithm is computationally less expensive, since it is sufficient to optimize it against the last steganalyzer 𝑓 𝑘 , whereas Backpack needs to be optimized with respect to all classifiers 𝑓 ∈ F 𝑘 . [START_REF] Bas | Break Our Steganographic System": The Ins and Outs of Organizing BOSS[END_REF] of size 512 × 512 in grayscale format and compressed with Quality Factor (QF) 100 and 75. All images are embedded using an embedding rate of 0.4 bits per non-zero AC DCT coefficient (bpnzAC) at each iteration of the algorithm.

Steganalysis.

A proper evaluation of min max protocol (and its variants) requires two sets of steganalyzers and their overlap depends on who knows what. The first set of classifiers, F is available to Alice, who is running the min max protocol. In this work, this set contains all classifiers with XuNet architecture [START_REF] Xu | Deep convolutional neural network to detect J-UNIWARD[END_REF] (differing in weights). The second set, F , of classifiers is available to Eve. In our experiments, F contains all classifiers with SrNet and XuNet architectures, classifiers trained with DCTR [START_REF] Holub | Low-complexity features for JPEG steganalysis using undecimated DCT[END_REF] or GFR [START_REF] Song | Steganalysis of adaptive JPEG steganography using 2D Gabor filters[END_REF] features. XuNet and SrNet were implemented in TensorFlow [START_REF] Abadi | Tensorflow: A system for large-scale machine learning[END_REF]. This experimental setup allows to investigate two different setups which practically express the assumptions that whether or not Alice knows which class of steganalyzers Eve uses.

At each iteration of the min max protocol, a new steganalyzer 𝑓 𝑘 is trained by classifying cover objects C and stego objects S 𝑘 created in previous iteration at the second step of the min max protocol. Steganalyzers are trained on full-size images of 512 × 512 coefficients, 2×4000 cover and stego objects for training, 2×1000 for validation set and using remaining 2 × 5000 to estimate error rates.

The training database is shuffled after each epoch. In each batch, we apply data augmentation based on random mirroring and rotation of the batch images by 90 degrees. 280 epochs are used for training using Adam optimizer [START_REF] Diederik | Adam: A method for stochastic optimization[END_REF]. The configuration achieving the best validation accuracy is used as the result of training. XuNet, the classifier is trained starting with randomly initialized weights (zero mean Gaussian with standard deviation 0.01), initial learning rate is set to 0.001 and decreased after each 5000 steps to 0.9 times the current value. Remaining parameters of Adam are kept to default setting. The size of mini-batch is 32 (16 cover-stego pairs). The configuration of SrNet is the one proposed in the paper [START_REF] Boroumand | Deep residual network for steganalysis of digital images[END_REF], except the training uses 280 epochs. The size of mini-batch is 16 (8 coverstego pairs).

Optimization of embedding costs.

Both compared methods requires initialization of embedding costs, for which those of J-UNIWARD [START_REF] Holub | Universal distortion function for steganography in an arbitrary domain[END_REF] were used (this has been done in [START_REF] Tang | CNN-Based Adversarial Embedding for Image Steganography[END_REF]). The ADV-EMB method for adjusting costs is implemented as described in Section 2.2. Backpack uses Adam [START_REF] Diederik | Adam: A method for stochastic optimization[END_REF] with a learning rate of 0.05 to optimize the embedding costs 𝜌 in Algorithm 1. Gradients of expected error (Equation ( 11)) are computed with 𝑘 = 30 samples until fourth iteration of min max protocol, with 𝑘 = 20 samples until its eight iteration, and with 𝑘 = 10 samples. Although a single sample is frequently sufficient, more samples improves the accuracy of predicted gradients and they can be calculated in parallel on the GPU in the same batch. However as min max protocol progresses, the gradient needs to be calculated with increasingly more models, which occupies the memory of GPU and therefore we had to progressively decrease the number of samples. The initial temperature was set to 𝜏 0 = 10. The error of steganalyzers was measured by Equation (4), which is the usual average error on cover and stego objects assuming equal prior probability of their occurrence (denoted as 𝑃 err ). Since the goal of steganography is to be undetectable, higher value is better. 3 at 𝑘 = 0 and 𝑘 = 7 or 𝑘 = 8 for QF 75 or QF 100, for both ADV-EMB and Backpack.

Discussion of results

QF

The main bulk of experimental results are presented in Figure 3 and in Table 1 showing error 𝑃 err of XuNet, SrNet, DCTR, and Optimizing Additive Approximations of Non-Additive Distortion Functions -, -, -GFR steganalyzers on testing data with respect to the iteration of min max protocol. The proposed Backpack method is clearly superior to the ADV-EMB. The 𝑃 err error of a XuNet steganalyzer trained after eight iterations is 37% on images created with the proposed method while it is 26% on those created by ADV-EMB (also after eight iterations) and 16% on those created by J-UNIWARD. This means that if [START_REF] Bernard | Exploiting adversarial embeddings for better steganography[END_REF] is considered by state of the art, the proposed method has improved by 11% (as measured by XuNet for which it has been optimized). These results are for JPEG 100 and in the optimistic case for Alice where she knows which type of steganalyzer Eve will use (but Eve optimizes her steganalyzer on Alice's stego images from her final iteration such that Kerckhoffs' principle is not violated). It is interesting to observe that even though Alice is not explicitly optimizing against SrNet, DCTR, and GFR steganalyzers, she is still improving the security of her steganograhic algorithm with respect to them, although the curve is not as steep as that for XuNet. 3The evolution of 𝑃 err also suggest that GFR steganalyzers relies on a similar type of information as XuNet (on JPEG images with QF 100), but DCTR and SrNet uses different type, as the improvement in the security is not as high.

Experimental results on JPEG images with QF 75 copy those on QF 100. Though there is an interesting difference in behavior of steganalyzer utilizing DCTR features. On QF 100 this steganalyzer is almost insensitive to the improvement in security with respect to XuNet, whereas on QF 75, it reflects the improvement. This suggests that at QF 100, it is detecting artifacts, which are not present at QF 75 and XuNet cannot see these artifacts. This might be caused by rounding artifacts described in [START_REF] Butora | Reverse JPEG compatibility attack[END_REF].

Unlike ADV-EMB, Backpack does not contain any regularization minimizing the number of modified coefficients. It can be trivially added, for example by defining a prior on distribution of embedding changes, but it should be learned from data rather than added explicitly. Moreover, the min max protocol should theoretically correct too detectable embedding changes in subsequent iterations. Nevertheless the steady increase in steganographic security as measured by XuNet steganalyzers do not indicate that such regularization is needed.

CONCLUSION AND OVERVIEW

This paper framed adversarial attacks against steganalyzers into a perspective of the general steganographic problem, which is the minimization of non-additive distortion functions. It has shown that adversarial attacks can be seen as an optimization of an approximation of non-additive distortion function by its additive counterpart defined implicitly by costs of changing embedding coefficients.

The proposed method, called Backpack, relies on the fact that most state of the art steganalyzers, mainly those implemented by convolution neural networks, allow to calculate gradients of their output with respect to the input (by means of back-propagation). Backpack approximates discrete embedding changes by samples from Gumbel-Softmax distribution, which is nowadays a standard approach in machine learning field. It also uses differentiation of implicit function to effectively handle constraints on message length.

The experimental experimentally confirms the theoretical correctness of the approach. A security a steganographic scheme as measured by XuNet on 512 × 512 JPEG images compressed with quality factor 100 with payload of 0.4 bits per non-zero AC coefficient has increased to 37.3% whereas that of the previous state of the art known to authors was 26.5% under the same setting. Interestingly, although the steganographic algorithm was optimized with respect to XuNet steganalyzer, the security with respect to other steganalyzers realized by SrNet, GFR or DCTR features has increases as well.

Backpack's constraint on differentiable distortion functions seems to be limiting at first sight. Yet a line of works on black-box attacks and gradient obfuscation [START_REF] Athalye | Obfuscated gradients give a false sense of security: Circumventing defenses to adversarial examples[END_REF][START_REF] Tramer | On adaptive attacks to adversarial example defenses[END_REF] shows that adversarial attacks can be applied either to a differentiable surrogate of the true adversary, or without directly evaluating the gradient [START_REF] Maho | SurFree: a fast surrogatefree black-box attack[END_REF]. Such approaches are left for future works.

Figure 1 :

 1 Figure1: For a given value of triplet 𝑔 = (𝑔 -1 , 𝑔 0 , 𝑔 +1 ) (where 𝑔 𝑗 ∼ 𝐺 (0, 1) are independently drawn from Gumbel standard distribution), value of the modification b𝜏 = SG(𝑝, 𝑔) is plotted the 𝑧-axis for all possible triplets of probabilities 𝑝 = (𝑝 -1 , 𝑝 0 , 𝑝 +1 ), and for 4 values of 𝜏. The triplets are plotted in the trilinear coordinate system.

Figure 2 :

 2 Figure 2: Effect of decreasing the temperature 𝜏 during optimization of a embedding costs for a given cover image. Is plotted on the left 𝑦-axis the average and variance of detectability (1 for stego class and 0 for cover class) given by classifier 𝑓 0 (for which 𝑓 0 (c) = 0) over 20 sampled simulated continuous stego object (blue plot where s = c+ b𝜏 ) and for 20 sampled simulated discrete stego object (orange plot, where s = c + b), over the 33 steps of optimization on the 𝑥-axis.

2

 2

4. 1

 1 Experimental settings4.1.1 Images. The experiments use the JPEG version of the BossBase database

Figure 3 :

 3 Figure 3: 𝑃 err of test sets w.r.t iterations of the protocol with QF 100 (top line) or QF 75 (bottom line), an embedding rate of 0.4 bpnzAC, cost initialized with J-UNIWARD and applied with our attack (left column) or ADV-EMB attack (right column). Assumed class of detectors is XuNet architecture, and real detectors are XuNet, SrNet, DCTR and GFR.

Table 1 :

 1 Values of 𝑃 err plotted in Figure

		ℎ emb	𝑃 err (%) XuNet SrNet DCTR GFR
		J-UNIWARD (𝑘 = 0)	16.9	13.1	26.6	26.8
	100	ADV-EMB (𝑘 = 8)	26.5	18.9	26.5	32.4
		Backpack (𝑘 = 8)	37.4	25.3	30.7 37.3
		J-UNIWARD (𝑘 = 0)	7.5	6.0	16.2	10.0
	75	ADV-EMB (𝑘 = 7)	22.0	10.7	26.7	25.8
		Backpack (𝑘 = 7)	47.6	15.6	32.9 31.5

Note that due to the max function, it attacks in each iteration of Algorithm 1 a single steganalyzer from the set F 𝑘 , but this single classifier is potentially different at every iteration.

Ref.[START_REF] Bernard | Explicit optimization of min max steganographic game[END_REF] has demonstrated min max protocol to optimize with respect to steganalyzers of different architectures. This optimization is a bit more complicated, as their outputs needs to be carefully calibrated, and also computationally more complex. From these reasons, this experiment was avoided here and left to a future work. Theoretically, we do not see any reason why the proposed method should not work.

ACKNOWLEDGMENTS

This work has been funded in part by the French National Research Agency (ANR-18-ASTR-0009), ALASKA project: https:// alaska.utt.fr, and by the French ANR DEFALS program (ANR-16-DEFA-0003). The authors acknowledge the support of the OP VVV project CZ.02.1.01/0.0/0.0/16_019/0000765 "Research Center for Informatics" and a support by Czech Ministry of Education 19-29680L. This work was granted access to the HPC resources of IDRIS under the allocation 2019-AD011011259 made by GENCI (Grand Equipement National de Calcul Intensif).


Ini Dele-Adedeji

Scarcity in the Study of Boko Haram in Nigeria

Keywords: Boko Haram, ethnography, sources, prison, Nigeria. Résumé

Since the national and subsequent international spotlight has been put on Boko Haram in 2009, the Nigerian sect has piqued the curiosity of the academic and non-academic worlds. The continuous stream of scholarly, media and general audience writings focusing on Boko Haram is testament to this. The skirmishes between Boko Haram fighters and the Nigerian security forces in north-eastern Nigeria in July 2009, leading to the extrajudicial killing of Mohammed Yusuf, the sect's leader, proved to be epochal in shaping and changing the history of the movement-turning it from a fringe radical Islamic sect to an insurgent movement. In the years that have since followed, the multiple narratives that have emerged on various topics relating to Boko Haram have attempted to shape public opinion based on the limited data available on the sect's activities.

Drawing upon an analysis of relevant scholarship and fieldwork data, this article argues that the post-July 2009 policy of the Nigerian government and military has engendered an economy of data scarcity on Boko Haram. This scarcity, which has negatively affected the quality of the outputs disseminated on the sect, can only be addressed through the collection, production and use of more primary data from the field. This article draws upon ethnographic data collected during fieldwork in 2013-2015 in northern Nigeria, and northeastern Nigeria in particular, to make the argument that the absence of a wider stream of ethnographic data on Boko Haram has encouraged the use of derivative data, and in some cases of no data at all. The anthropological sources of data have to be emphasized in order to fill the glaring gaps which the economy of data scarcity is responsible for, thus affecting the study of Boko Haram.

non-académiques. En témoigne le flux continu d'écrits scientifiques, médiatiques et de vulgarisation consacrés à Boko Haram. Les accrochages entre les combattants de Boko Haram et les forces de sécurité nigérianes dans le nord-est du Nigeria en juillet 2009, qui ont conduit à l'exécution extrajudiciaire de Mohammed Yusuf, le chef de la secte, ont constitué une étape décisive dans le façonnage et la transformation de l'histoire du mouvement. Depuis, cette secte islamique radicale et marginale est devenue un mouvement insurgé. Dans les années qui ont suivi, de multiples récits ont émergé sur divers sujets relatifs à Boko Haram. Ils ont contribué à façonner l'opinion publique sur la base des données très limitées dont on dispose sur les activités de la secte.

En s'appuyant sur l'étude de travaux spécialisés et de données collectées sur le terrain, cet article soutient que la politique menée par le gouvernement et l'armée nigérians après juillet 2009 a conduit à une économie de la rareté des données sur Boko Haram. Cette pénurie, qui a un effet négatif sur la qualité des travaux produits sur la secte, ne peut être résolue que par la collecte, la production et l'utilisation de matériaux primaires issus du terrain. En ce sens, cet article s'appuie sur des données ethnographiques collectées lors de missions réalisées entre 2013 et 2015 dans le nord du Nigeria, et le nord-est en particulier. Il montre combien l'absence de production de riches données ethnographiques sur Boko Haram a conduit à l'utilisation de données dérivées, voire à des analyses démunies de données. Il importe de mettre en lumière l'importance des sources anthropologiques des données afin de combler les lacunes flagrantes dont cette économie de la rareté des données est responsable, lesquelles affectent l'étude de Boko Haram. Mots-clés : Boko Haram, ethnographie, sources, prison, Nigéria.

Resumo

Escassez no estudo do Boko Haram na Nigéria: Notas de campo (2013-2016) Desde que os focos dos projectores internacionais se fixaram sobre o Boko Haram em 2009, esta seita nigeriana tem atiçado a curiosidade dos meios universitários assim como não académicos. É disto testemunho o fluxo contínuo de textos científicos mediáticos e de divulgação consagrados ao Boko Haram. Os confrontos entre os combatentes do Boko Haram e as forças de segurança nigerianas no nordeste da Nigéria em Julho de 2009, que levaram à execução extra-judicial de Mohammed Yusuf, chefe da seita, constituíram uma etapa decisiva para a formação e transformação da história do movimento. Desde então esta seita islâmica radical e marginal tornou-se um movimento insurgente. Nos anos que se seguiram, emergiram múltiplas narrativas sobre diversos assuntos relacionados com o Boko Haram. Estes contribuíram para formar a opinião pública com base nos dados muito limitados disponíveis sobre as actividades da seita.

Apoiando-se no estudo de trabalhos especializados e de dados recolhidos no terreno, este artigo defende que a política conduzida pelo governo e exército nigerianos, depois de Julho de 2009, engendrou uma economia de escassez de dados sobre o Boko Haram. Esta penúria, que tem um efeito negativo sobre a qualidade dos trabalhos produzidos sobre a seita, só pode ser resolvida com a recolha, produção e utilização de materiais primários provenientes do terreno. Neste sentido o artigo apoia-se em dados etnográficos recolhidos durante missões realizadas entre 2013 e 2015, no norte da Nigéria, em particular no nordeste. Mostra como a ausência de produção de um amplo fluxo de dados etnográficos sobre Boko Haram conduziu à utilização de dados derivados, isto é, a análises desprovidas de dados. É importante destacar a importância das fontes antropológicas dos dados a fim de colmatar as lacunas flagrantes, de que esta economia de escassez de dados é responsável, o que afecta o estudo do Boko Haram. Palavras-chave: Boko Haram, etnografia, fontes, prisão, Nigéria.

Introduction

In 2009, the Nigerian security forces killed Mohammed Yusuf, the leader of the sect popularly known as Boko Haram based in north-eastern Nigeria. This extrajudicial killing and its spiralling effect in mobilising Mohammed Yusuf's acolytes has, since then, extended the popularity of the sect beyond its initial base in the city of Maiduguri. 1 Between 2010 and early 2016, large swathes of land in the northeast of Nigeria were ceded to the control of Boko Haram members. This went together with frequent attacks in urban centres until 2013 when the security forces, in collaboration with the Civilian Joint Task Force, dislodged most known Boko Haram cells within many cities and towns, forcing members of the sect to emigrate en masse to hinterland areas in the vicinity of the Gwoza Hills, Mandara mountains, and the Lake Chad islands (Mahmood and Ani 2018). In addition, the use of asymmetrical warfare tactics against civilian and non-civilian targets (using women and girls as suicide bombers) and frequent militaristic assaults in failed attempts to gain entry into the city of Maiduguri influenced the sociological management of space and securitisation in the Borno and Yobe States. After 2013, the sect began to launch coordinated attacks, with armed members attempting to gain control of these areas. At the time of publication of this article, the capture of these Boko Haram-controlled territories by the Nigerian army was almost completed, with many Boko Haram factions now hiding out in the Lake Chad axis (Seignobos 2016). However, these former Boko Haram-controlled zones along with other parts of north-eastern Nigeria are still prone to occasional Boko Haram attacks. Some of these zones have been converted to buffer zones by the Nigerian security forces, rendering them inaccessible to most civilians. The transformation of Boko Haram from being an extremist sect to an armed movement has had far-reaching effects on the biographical narrative of the Nigerian state. The current leader of a faction of the sect, Abubakar Shekau, is considered to be one of the most wanted terrorists in the world (Brigaglia 2014). The Nigerian government has increased its security budget exponentially since Boko Haram's insurgency began in 2011 (Onuoha, Nwangwu and Ugwueze 2020), in a bid to squash what was initially considered an insignificant threat. It has also propelled this hitherto fringe movement into the international discourse on terror and collective violence.

In this context, a steadily growing demand has arisen for data across different fields and by various institutions. It has led to a growing field of study on all things concerning Boko Haram and resulted in the production of literature attempting to contribute to the production of knowledge on Boko Haram, with threads linking to various academic disciplines or fields of expertise. The various approaches used to analyse the emergence of Boko Haram and its re-emergence as a violent movement can be credited with the creation of multi-dimensional lenses, themselves commensurate with the multi-faceted aspects of the sect itself. This has given birth to scholarship situated in Islamic studies, international relations theory, gender studies, social movement theory, history, anthropology, and security studies, among others. However, despite the sect's insurgency lasting more than a decade at present, and the continuous production of writings of different forms on various topics relating to Boko Haram, there is still arguably so much that remains unknown about its past all the way to its present. More profoundly, in spite of these new perspectives, one major problem remains, which affects the production of knowledge about this sect: first-hand anthropological data in north-eastern Nigeria remains difficult to collect for most researchers on the region. This is primarily due to the climate of fear and insecurity engendered by more than a decade of insurgency by Boko Haram fighters in the region and its environs. It is within this context that conjectural analyses, derivative data, and unfounded and conspiracy theories emerged and fuelled a large majority of the literature produced on north-eastern Nigeria and the Boko Haram insurgency, in particular. 2 However, as this article illustrates, empirical data is invaluable to unearthing a more nuanced understanding of the insurgency in northeastern Nigeria. In order to achieve this, though, some degree of anthropological research is required. The article argues, based on my own ethnographic fieldwork experience and that of other researchers, that there are methods of navigating around the field, as the human element is of primary importance in collating narratives on the impact of Boko Haram's insurgency in north-eastern Nigeria.

This article attempts to study the economy of information on the sect itself. It draws upon ethnographic data collected during fieldwork in northern Nigeria, and north-eastern Nigeria in particular, to make the argument that the absence of a wider stream of ethnographic data on Boko Haram has encouraged the use of derivative data, and in some cases none at all, in the study of the sect. After analysing how most researchers have conducted research on Boko Haram (section 1), I will reflect on the constraints in which I, myself, conducted fieldwork (section 2). I will thus show how the use of selected material and field notes can shed light on the sect and its dynamics. For the purpose of underscoring the centrality of ethnographic 2. For scholarship that explores the problematic nature of the predominant analytical approach to studying and writing on the Boko Haram insurgency, with specific reference to the controversy surrounding the writing of Jacob Zenn, see Higazi et al. (2014).

203

data to better understand Boko Haram, I have selected two elements from my fieldwork material: first, a letter purported to have been distributed in Kano by Boko Haram prior to the beginning of my research in the region in 2013, which I have in my possession and have translated from Hausa into English. Through this example, I argue that the ethnography of documents produced by Boko Haram can help researchers to limit what I call the "erosion" of sources in the case of the sect (section 3). Secondly, I present a condensed summary of the fieldwork interviews I conducted at Kuje Minimum Security Prison with convicted Boko Haram members and with some workers employed under a European Union-funded deradicalisation programme set-up for the convicts. In a context of unavailability of prime sources of information, researchers can use information provided by former members or sympathizers of the sect (section 4). While advocating for caution where ethical issues are concerned (section 5), I conclude that the anthropological sources of data have to be emphasised in order to fill the glaring gaps responsible for the economy of data scarcity on the study of Boko Haram.

Navigating the Scarcity of Ethnographic Data on Boko Haram:

A Literature Review

The scholarship on Boko Haram is characterised by an impressive number of publications. 3 Yet, only a small minority of those publications is based on original first-hand data. What are the factors responsible for the scarcity of data in the field of study on Boko Haram? How have scholars attempted to navigate the challenges around data collection? The field of study on Boko Haram currently finds itself in a difficult position due to two major informational gaps: the organisational structure of the sect, and the attitude of the Nigerian state.

On the one hand, and even before July 2009, Boko Haram already had a peculiar organisational structure, mostly due to its insular religious ideology of separation from "unbelievers" (Murtada 2013). This has helped to make the sect exclusive and impenetrable, with few outsiders having limited access to its goings-on. In addition to this, whereas before it was considered a marginal sect with its hub based in an urban centre (i.e. Maiduguri), Boko Haram's post-July 2009 factionalisation and migration has seen the sect's members gradually desert urban areas in order to occupy most recently geographically peripheral areas on the banks of the Lake Chad and the Lake Chad islands. This has made access to Boko Haram and data on the sect even more difficult, due to the notoriously inaccessible nature of the Lake Chad zone, a phenomenon that predates the emergence of Boko Haram. As Marielle Debos (2016) pointed out, the Lake Chad axis has a historical reputation as a haven for rebels who were hostile to the former Chadian President Hissène Habré in the early 1980s.

Moreover, the Nigerian government's state policy regarding the Boko Haram insurgency has arguably proven to be counterproductive in bringing about its end.

3. For a history of the sect, see Loimeier (2012); Pérouse de Montclos (2014). This is largely due to the harassment and detention of individuals suspected of being Boko Haram sympathisers, including individuals allegedly pressured by the government to act as intermediaries with the leadership of the sect. Contrary to the state narratives, journalistic reports in the past have alluded to negotiations between Boko Haram and the Nigerian government. The absence of publicly accessible evidence, however, has made these reports difficult to substantiate. Negotiations and agreements between Boko Haram and the Nigerian state hardly ever feature in analyses of the conflict between the two sides. Yet, this is a factor that has shaped the trajectory of important episodes in the timeline of the conflict between the Nigerian state and the sect. It is, however, necessary to chronicle these "unrecorded" engagements in order to avoid a jaundiced narrative of the insurgency. For example, Boko Haram fighters adopted the method of abduction in north-eastern Nigeria as leverage in negotiation deals for the release of their fighters and relatives in the custody of the state, which could explain the Chibok girls kidnapping in April 2014.

During the July 2009 skirmish between Boko Haram and security forces in Maiduguri, the first erosion of the most direct links to Boko Haram began, with the extra-judicial killing of Mohammed Yusuf and some of his acolytes. The next phase of this erosion came in the aftermath of these killings, beginning with the arrest of many Boko Haram identified by the security forces. During this period, several members were also killed in various attempts by the security forces to apprehend them. The indiscriminate arrest and detention of relatives of Boko Haram members followed suit. Many of these relatives-some of them being women and childrenwere allegedly detained in secret locations without trial. Among them were one of Abubakar Shekau's wives and their children, and one of Mohammed Yusuf's widows. 4 Much of the protracted negotiations between factions of Boko Haram and the Nigerian government from 2011 to 2015 were centred on the sect's demand for the release of their detained spouses and children. The subsequent release of Abubakar Shekau's wife, Hassana Yakubu, along with her children, and of other family members of Boko Haram, can be attributed to the Nigerian government's acquiescence to the sect's conditionality, or the desire by the government to resolve the ethical lacuna connected to the detention of relatives of Boko Haram fighters, according to those privy to the negotiations. Regardless of the rationale behind the government's actions, the as-yet unrecorded discussions between the leadership of the Boko Haram sect and the Nigerian government is an indicator of the multiple layers of the insurgency that are still in need of uncovering.

Because of these gaps, the field of study on Boko Haram currently finds itself in a paradox. More than a decade after the sect transformed to an armed movement, the insurgency continues. However, there is still so much that appears to be unknown about various strands of the sect and its biographical narrative. At the same time, the appeal of the topic has led to an overproduction of academic and non-academic or grey literature to satisfy the high demand for more information. Yet, only an infinitesimal amount is based on actual first-hand data, which adds to the recycling of information and further obscuring of the sect and its workings. Most publications hardly bring any actual critical evidence nor diligently explain their methodology that could help verify how they reach their conclusions.

Despite this methodological opaqueness, insight on how to navigate issues of access and accessibility can be gleaned from the works of scholars whose research has proven seminal in this field. These researchers have developed their own methodological mix while facing constraints. Political scientist Marc-Antoine Pérouse de Montclos visited Maiduguri as well as Kano, Zaria, and Abuja several times after July 2009 to conduct interviews. He, however, noted that he was unable to travel to Maiduguri at all between 2013 and 2014, after the closure of the Maiduguri International airport by the military. Although he makes no mention of accessibility difficulties in his research, this can be implied from his writings. Pérouse de Montclos had more success in Niger, where he notes that he was able to interview security officers in Diffa and also conduct interviews with presumed members of Boko Haram in the Koutoukalé and Kollo prisons, at the beginning of 2015 (Pérouse de Montclos 2016, 879). Another case is Adam Higazi's anthropological study on Boko Haram's mobilisation in north-eastern Nigeria. His work is arguably the first piece of research that focuses on the Gwoza region and population within the context of Boko Haram's insurgency. Higazi's fieldwork-reliant study in the hinterland of north-eastern Nigeria relevantly confirms the establishment of Boko Haram's bases within this borderland region, particularly within the Muslim section of the multi-ethnic Gwoza Hills population. It also helps to confound conspiracy theories regarding the supposed seamless acclimatising of transplants from urban areas such as Maiduguri to this rural terrain (Higazi 2015, 346). Higazi was able to accomplish this detailed study of the Gwoza population by having the foresight to travel to Gwoza before the mass migration of Boko Haram members from Maiduguri and other hubs to the north-eastern hinterlands.

Predicting the significance that the killing of several key members of Boko Haram would have on the scarcity of data on the sect, Murray Last, who wrote in 2009, confesses himself to relying on daily or weekly newspapers like Daily Trust, Leadership, Weekly Trust, Amana and local radios. Information he extracted via these sources was supplemented and crossed with information from various other sources in different cities across northern Nigeria (Last 2009, 11). Christian Seignobos, exploring the presence of Boko Haram in the Lake Chad axis in 2015, reveals a similar method of data collection as he relied on media reports and the relaying of information from interviewees and informants living in the Lake Chad axis. He, then, counterbalanced the information received with specific historical situations to bring context to the data (Seignobos 2015, 90). According to political scientist Hilary Matfess, apart from being a relatively new phenomenon, a reason why Boko Haram

has not yet enjoyed the sort of analysis that other insurgencies, social movements, and terrorist groups have had is due to paucity of access. She posits that the reliance on second-hand accounts and newspaper reporting in much of the scholarship on the sect's insurgency in north-eastern Nigeria may decrease if the Nigerian military securitize the region, therefore making fieldwork more feasible (Matfess 2017, 17).

Researching Boko Haram: Constraints of Conducting Ethnographic Fieldwork

As a doctoral candidate, I conducted fieldwork across different cities in northern Nigeria, between October 2013 and December 2015, for a period lasting a total of six months. I faced two major issues: security fears, and reluctance of the inhabitants to share information with me. Before I began my fieldwork research in northern Nigeria, I had actually not considered the possibility of travelling to north-eastern Nigeria because bomb attacks were on-going as well as gunfights between the government forces and the insurgents. Boko Haram cells in Yobe and Borno were also frequent at the time. While the situation was the same in Kano, the city was in my estimation relatively safer than the former two states. However, the gradual realisation, after three months in Kano, that beyond controlled interviews, there was very little to dredge up by way of gaining direct and relatively unfettered access to reliable sources of information on the sect influenced my decision to shift base to Maiduguri, the capital of Borno. By the time I arrived in Maiduguri in July 2014, I came to the conclusion that the paucity of access to first-hand inside knowledge on Boko Haram was not exclusive to regions beyond the northeast, such as Kano, but had affected the north-eastern region most of all. The security situation was arguably worse in Borno than in any other part of the northern region. There was no exact formula for accurately predicting the time range or intended targets of Boko Haram attacks, which meant that residents had to avoid public spaces which attracted crowds. This was not so much the case in Maiduguri due to the rare occurrence of Boko Haram attacks on the city itself over the last five years. This has allowed for a semblance of normalcy to return to the city.

I arrived in Maiduguri on a Saturday in July 2014, three days after a bomb planted by Boko Haram at the Maiduguri Monday market killed scores of people. 5 When I went to this market seven days after, it had been re-opened for business and was heavily re-populated with traders and buyers. As such, while there had been a heavy securitisation and militarisation of public spaces in most of the north-eastern urban centres and especially in Maiduguri, there was no uniformity in the ways in which residents reacted between July 2014 and December 2015, though the governmentimposed curfew on activities in Borno achieved this to some extent. However, as a researcher and visitor to the region, I was primarily concerned with the issues of mobility and security as they could have limiting effects on my work. I needed to travel around to source for data while at the same time reducing the possibility of coming to harm as much as possible.

The first impediment I encountered regarding mobility manifested itself in the choice of commute to Maiduguri. President Goodluck Jonathan had ordered the closure of the Maiduguri international airport in December 2013 to commercial flights 6 , leaving access into the state by road the only option for civilians 7 . This was where, for me, the issues of mobility and security intersected as I got access to reports informing about coordinated attacks by Boko Haram on certain highway routes targeting commercial vehicles transporting passengers within and around the northeast. Despite this travel difficulty, I boarded one of the buses travelling to Maiduguri via Damaturu at the Kano terminus early in the morning in order to avoid being on the road by evening, which would have increased the probability of being waylaid by Boko Haram. This mode of transport did, however, prove to be advantageous to some degree, as my first encounter with the Civilian JTF vigilante group 8 -which also involved watching them in operation-occurred at a road-block between Damaturu and a town on the outskirts of Maiduguri.

I encountered another constraint that hampered access to data: the pervading fear among local residents of both the government security forces and Boko Haram. Initially, during the early phase of my fieldwork in Kano, I was attempting to study Boko Haram mobilisation techniques and reasons for local support in some of the wards where the existence of local cells had been confirmed (Hotoro and Wudil, outside the city, being examples). Although I had always intended to interview imprisoned Boko Haram members, I also wanted to have as broad a category of 6. "Maiduguri International Airport Closed after Boko Haram Raid on Air Force Base." 2013. Sahara Reporters, 2 December. URL: http://saharareporters.com/2013/12/02/maiduguriinternational-airport-closed-after-boko-haram-raid-air-force-base [archive].

7. Ironically, the same airport was opened a week after exclusively for Ali Modu Sheriff, the former governor of Borno, to fly into Borno on the day he formally declared himself a member of the then ruling People's Democratic Party (PDP). Idris, Hamza, and Ibrahim Sawab. 2014. "Nigeria: Govt Reopens Maiduguri Airport for Sheriff." Daily Trust, 15 July. URL: https:// dailytrust.com/fg-reopens-maiduguri-airport-for-ex-gov-sheriff [archive].

8. The "Civilian JTF" is a vigilante group believed to have been mobilised initially in 2013. It earned its appellation from the residents of north-eastern Nigeria who consider that the volunteer members of this group complement the efforts of the Joint Task Force (JTF), that is, the section of the Nigerian army stationed in the northeast. In Hausa, the "Civilian JTF/ CJTF" members are referred to as "Yan kato da gora," which means "the men who hold canes" as they arm themselves with sticks (believed to be laced with charms), machetes and amulets. The relative effectiveness and local legitimacy of the CJTF owes to the fact that its members (who operate in batches within a "sector" in each locality where they have a presence) have a superior knowledge of the local terrain and population than members of the army. Some locals also believe that several CJTF members were previously worshippers at the "Boko Haram mosques," residents of the same wards as some other members, or were even initial members who later became disillusioned at Boko Haram's penchant for wanton killings and destruction, and decided to mobilise themselves against the sect. interviewees as possible. This ethnographic naiveté with which I approached my study quickly dissipated, as I discovered that there was a strong reluctance by local residents to use the "Boko Haram" title, much less engaging unfamiliar persons in conversation about any themes related to the sect. The fear of the police and Boko Haram was a major deterrent towards sharing pertinent materials. Understandably, with respect to the modus operandi of Boko Haram, local residents did not want to fall on the wrong side of the sect by being perceived as colluding with security forces to identify their members. This was more so due to the fact that it was impossible to identify those employed to spy and relay information back to Boko Haram within different wards.

The lack of easy access to insiders or those with first-hand knowledge of the goings-on within Boko Haram also makes it more difficult to sourcing ethnographic data on the sect. Achieving this, or trying to do so, can put researchers at risk. It is also worth noting that the individuals who have been successfully engaged as negotiators between the sect and the Nigerian government have thus far been sanctioned by the top cadres of Boko Haram. The few non-members who have continued to have access to Boko Haram are individuals who have adopted an ostensibly neutral position in refusing to outrightly condemn Boko Haram in its entirety or who have a long-running history of engagement with the sect that precedes 2009. Mohammed Yusuf's use of his Kanuri kinship (coupled with the heavy emphasis placed on expansionist proselytisation by his then religious organisation, the Izala 9 ) to cultivate Boko Haram's network links is also pertinent in understanding the successful propagation of his religious ideology in the northeast and also how he extended it to neighbouring regions in Cameroon, Niger and Chad by also making use of the expansive preaching network of the Izala movement. 10 Consequently, these ethnic and religious markers have been used to accentuate the otherness of non-indigenous researchers seeking to access communities in northeastern Nigeria for their fieldwork.

Moreover, the scorched earth approach adopted by the Nigerian security forces against Boko Haram in the aftermath of the sect's 2009 revolt resulted in the arrest and imprisonment of several non-combatants alleged to have had some connection, whether directly or indirectly, to Boko Haram. In more extreme cases, there have been allegations raised against the army by Boko Haram, who accused soldiers of killing unarmed Boko Haram "emissaries, " thus making it less of an appealing incentive for those with first-hand knowledge of Boko Haram to make themselves known. 11 By destroying the places of worship and residences of alleged Boko Haram members, potential sources through which to retrieve data on the sect have been wiped out. 9. Jama'atu Izalat al-Bid'a wa Iqamat al-Sunna (Arabic: the Society for the Removal of Innovation and the Re-establishment of the Sunna). 10. See Thurston (2016). Another equally revelatory study on the fluid modes of proselytisation adopted by certain Izala actors is: Sounaye (2014).

Interview conducted in December 2015with a liaison in the negotiations between Boko

Haram and the Nigerian Government.

Also, this has reflexively led to the dispersion of potential sources of human data. This is because many of the casualties of this blanket policy which mostly affected those residing at Railway Quarters in Maiduguri-where Mohammed Yusuf's core following were mobilised from in the early years of Boko Haram's formation-were not themselves members of the sect but their relatives to acquaintances, or in some cases had attended the popular sermons of the sect's clerics. 12 There is also an absence of precedent regarding information-sharing between the security agencies and the Nigerian public, which hampered the verification of data. Thus, the government has displayed its ineptitude in the area of intelligence-gathering. For example, in relation to the abduction of around 234 school girls from Chibok in Borno State, the media arm of the Nigerian army delayed the confirmation of the incident only because the government itself had not immediately verified the veracity of the reports. According to former Nigerian President Olusegun Obasanjo who conducted a fact-finding mission in Borno in the aftermath of the Chibok tragedy, it was discovered from the local residents that the abduction of the school girls was an afterthought by Boko Haram members. As has now become the norm since they began to occupy towns and villages outside Maiduguri, Boko Haram raided Chibok in search of foodstuff and other materials to replenish the dwindling supplies at their neighbouring base (Habila 2016). However, on leaving the village, they met with school girls who had stayed overnight at the local secondary school and decided to abduct them. 13 The Borno State government also supported this narrative, with Governor Kashim Shettima placing the blame on the federal government for the delay in taking action to rescue the abductees after he had directly informed President Goodluck Jonathan of the incident. 14 This example highlights the disjuncture in the governmental approach to information gathering.

Conversely, where the government has been able to access certain information, it has in some cases been accused of disinformation as well as of being economical with the information released to the Nigerian public. The bulk of these accusations relate to the control on information about the military campaign against Boko Haram by the Nigerian army. The Nigerian army's media arm has been accused in some quarters of "bending the facts" of its current campaign against Boko Haram in the north-eastern region in a bid to either conceal its tactical ineptitude or to avoid losing the "media war" to the sect. This has culminated in episodes in which the army has made a report only to have it be contradicted by another report. This insistence on controlling the media narrative, whenever Boko Haram's activities are concerned, makes the army an unreliable source of information. In 2015, a member of the Air Force arm of the military from Adamawa was reportedly captured and killed by Boko Haram fighters while on active duty in the northeast. This event was reported by a Nigerian news medium but the army denied it in a statement it released after the breaking of the news. I interviewed a relative of the deceased soldier who confirmed that the military refused to release the news of the death of their kin for months, despite knowing he was dead from the evidence which had been released (his military uniform was shown in a video taken by Boko Haram combatants after they had downed his fighter jet). The interlocutor even denied that their kin was a soldier when images showing him were released by Boko Haram. The army, however, later sent an envoy to confirm the death of the soldier and condole with his family. 15 As I gradually became aware of these constraints on conducting research on Boko Haram, I opted for different strategies in order to gather ethnographic data. First, difficulties of this sort, which I encountered, helped me better understand the utility of relying on a "gate-keeper" when conducting ethnographic research, particularly one which requires entry into a guest culture or community. In the case of Boko Haram, the mode of delivery of warning letters to communities and in some cases to individuals (see section 2) added credence to my hypothesis that these tasks could only have been achieved with stealth by those familiar with the local geography. Also, from my study of the tone assumed by Boko Haram in missives delivered within local communities both in Kano and Borno, which I collected on my fieldwork travels, I perceived what was a deliberate attempt by the respective authors of these notes to convey to their intended audiences their familiarity with them and ease of access to them if they disobeyed their injunctions.

Moreover, I recruited and worked together with a research assistant who was familiar with the area where I conducted fieldwork and also doubled as my Hausa translator. I was able to use him as a liaison to conduct interviews with local residents. As someone indigenous to Kano and with a wide network of acquaintances, my assistant was able to draw from his repertoire of information to direct me, telling me where to go and search the data I needed. He also acted as a safety barometer, of sorts, adjudging which locations we could travel to and the ones in which the level of risk outweighed any potential research value to be gained (this was a period of heavy skirmishes between government forces and Boko Haram fighters who the former were trying to flush out of wards within Kano and the outskirts). 16 The exact role of my research assistant was to accompany me to meet potential 15. Interview conducted in December 2015 with a family member of the deceased soldier. interviewees and help with translating from English to Hausa and vice versa during my interviews with non-English speakers. 17 Finally, I always made sure to let prospective informants know that I would only be using my notebook and pen and that their names would not be appearing in any of my public writings. In such, I borrowed from Wood's template which she used during her fieldwork in El Salvador: she was disguising her notes and refusing to record any names or voices in order to ensure the protection of the identities of the subjects of her study (Wood 2006, 381).

In total, I conducted a 6-month fieldwork in north-eastern Nigeria. Interviews were conducted in fieldwork sites located in Kano, Abuja, and Maiduguri, respectively. I resided in Kano from October to December 2013. There, I conducted semi-structured interviews with prison inmates (some of whom were suspected by the authorities of having been complicit in Boko Haram-related acts of violence) at the Goron Dutse Maximum Security Prison. I also conducted semi-structured interviews with state government officials, particularly officials of the Kano State Hisbah. I resided in Maiduguri from June to August 2014 and also spent the month of December 2015 there. During my time in the city, I conducted semi-structured interviews with residents of Railway Terminus Quarters (Shehuri North ward), individuals who were acquainted with Mohammed Yusuf during the years he spent in Maiduguri establishing Boko Haram, relatives of deceased Boko Haram members, and self-confessed former members of the sect. In December 2015, I conducted interviews with some members of the team employed under the European Union-funded pioneer deradicalisation programme designed to rehabilitate convicted Boko Haram members imprisoned in Maiduguri and Abuja. In the same month, I conducted semi-structured interviews with Boko Haram convicts imprisoned at Kuje Medium Security Prison.

An Ethnography of Boko Haram Documents

One of the issues researchers on Boko Haram face is the "erosion" of sources, by which I mean the inability to access previous human sources and sites for collecting firsthand data, particularly because of population displacement. For example, during the July 2009 skirmish between sect members and security forces in Maiduguri, the first erosion of the most direct links to Boko Haram began, with the killing of Mohammed Yusuf and his acolytes. The next phase of this erosion came about in the aftermath of the July killings, beginning with the arrest of many Boko Haram members identified by the security forces. During this period, several members were also killed in various attempts by the security forces to apprehend them. The indiscriminate arrest and detention of relatives of Boko Haram members followed suit. Many of these relatives, some of whom were women and children, were allegedly detained in secret locations without trial, among whom were one of Abubakar Shekau's 17. For a detailed historical study on anthropological fieldwork assistants, and their centrality to the shaping of their employer's research, see Schumaker (2001).

wives and their children, 18 and one of Mohammed Yusuf's widows. Furthermore, in the course of traversing Maiduguri in 2014 to locate relatives of Boko Haram members or those who might have been morally supportive of the sect at a point, I discovered that those who had been identified by other local residents as being previously frequent attendees of Boko Haram mosques, being members of the sect or in certain cases having been close relations of known Boko Haram members faced stigmatisation within their locales. Many among them emigrated out of Borno. Those who remained, some of whom I encountered, were hostile to having their past affiliation with Boko Haram recalled. 19 To counterbalance the gradual disappearance or inaccessibility of human sources and also retrace Boko Haram's emergence and activities, I turned to material artefacts produced by the sect. I had also grown frustrated with the recycling of mostlyconjectural analyses, whereas I used and kept references to videos of sermons by Boko Haram clerics, letters distributed by the sect's members, and a book by Mohammed Yusuf titled Hādhihi 'Aqīdatunā wa-Manhaj Da'watunā. 20 My attempt at engaging with actors familiar with Boko Haram's ideology was thus aimed to gain access to written materials by the sect, which in my opinion offer insight into Boko Haram's collective and ideological self-perception.

A number of narratives have emerged from different parts of northern Nigeria over the years corroborating claims that Boko Haram was using locally-distributed letters to pass across messages to specific demographics. 21 The image above is a letter purported to have been composed by Boko Haram. Printed on a white sheet of paper, written in capital letters and unsigned, it was distributed to residents in the Sharada ward of Kano prior to an attack between 2011 and 2012. The letter was given to me via my research assistant at the time, a resident of the locale where the letter was purported to have been distributed. The residents I interviewed in Kano and Maiduguri neighbourhoods corroborated that Boko Haram had used such letters locally, mostly where and when attacks were impending. As can be deduced from the translated version of this letter in Hausa, several complex layers intertwine and require dissection in order to understand the motivations behind certain attacks, instead of resorting to unfounded claims and conspiracy theories which dominate the field of study on the sect. This particular letter, for instance, has no appended signature to prove the identity of its composer(s). This omission can be interpreted 18. Interview conducted with a "middleman" in the negotiations between Boko Haram and the Nigerian government, in December 2015. The interviewee confirmed the arrest of one of Shekau's wives and her children, but alleges that they were later released.

19. Interviews conducted in July 2014 with residents of Maiduguri and "Civilian JTF" members. 20. Arabic: This is our faith and our method of proselytisation. Another text known as "Guduma" has also been discovered in the possession of some "post-2009 Boko Haram members," with its authorship yet to be ascertained at the time of writing this article. 21. See, for example, "Boko Haram Warns Residents not to Vote." 2015. Pulse, 14 February. URL: http://pulse.ng/local/in-gombe-boko-haram-warns-residents-not-to-vote-id3484010.html [archive].

in a number of ways. It could be argued that opportunists made it, attempting to instrumentalise the Boko Haram name to achieve some personal objectives. Another interpretation could highlight the then-existing relationship of "trust" between Boko Haram fighters and local communities, since at the time both were enmeshed to some degree. This could explain why some locals believed that Boko Haram was responsible for the delivery of the letter.

A letter purportedly distributed by Boko Haram members specifically to residents of a particular locale in Kano Translation (from Hausa): "Peace be upon you, people. We will be coming to Sabon Titin (New Street), Jaen (Sharada Local Government Area), to execute Allah's work, but we have no business with the rest of the people. When we are going about our work, everyone should avoid the place. Our quarrel is with the security forces. We are fighting with them to protect our religion and our business, and to claim our right."

Copy in author's possession.

Unfortunately, such documents have proven very difficult to access. Individuals were both reluctant to talk about Boko Haram beyond generic responses and to present tangible materials-such as letters, pamphlets, audio-visual cassettes, books, etc.-produced by the sect. Some explained that after 2009 the security forces began arresting anyone found to be in possession of Boko Haram-related materials. Consequently, many discarded theirs or hid them away. This counter-propaganda strategy by the Nigerian security forces has, to a large extent, contributed to the lack of empirical sources that could be used for a more nuanced understanding of Boko Haram, its functioning and its belief system. The security forces' policy of arresting those found in possession of the sect's materials forced people to either destroy or hide them from public view. Not only has this made it difficult for scholars to easily access these materials, but it also set in motion what could be described as a further gradual erosion of data on the Boko Haram sect.

Affiliating with Boko Haram: Interviews with Former Members

As it mostly remained impossible to gather information from Boko Haram sympathizers, I resorted to interviewing people who had or claimed to have been affiliated to the sect in the past, but had later distanced themselves. Later in 2014, during my time in Borno, I was, for example, able to interview different young men who hailed from the Shehuri axis within Maiduguri and claimed to have been involved with Boko Haram at several points in their lives. One particular interview was pertinent to my hypothesis that the fear of Boko Haram was a deterrent to speaking about the sect. B.S., my interviewee, explained to me how he was recruited by Boko Haram members who knew him from the neighbourhood when he was around the age of thirteen. B.S. claimed to have been induced into joining the sect due to the monetary incentives they had offered to him, at the time. Although he refused to confide in me as to the breadth of his involvement during his time as a member and if he joined in in acts of violence, he did explain to me that he operated primarily as a "spotter" for higher-ups who he reported to. His higher-ups, according to him, would give him a list of names of people, periodically, and his task was to follow them around without being seen, with the objective to find out the addresses of these potential targets and their daily schedules and then report back. He opined that due to his youthfulness, he was able to operate efficiently because his movements never aroused suspicion. 22 Moreover, I gathered some ethnographic data from interviews with officers and participants in the deradicalisation programme set up to rehabilitate Boko Haram imprisoned in Maiduguri and Abuja. In December 2015 I met with one of the project's workers, Malam Baba Kura, 23 who provided me with some insight into the framework of the programme before I made a trip to Abuja to interview some of the enlisted convicts. Baba Kura explained to me that, in December 2015, there were between 30 to 40 Boko Haram members enrolled on a European Union-funded deradicalisation programme in Kuje Minimum Security Prison in Abuja. He told me that the enlisted were those who had signed up voluntarily, as registration was not compulsory. Asked how he was able to have members of the sect sign up to the programme, he explained that he began by reaching out to the "leaders" of Boko Haram within the prison. He was able to gradually convince them of the textual 22. Interview conducted in Maiduguri (Shehuri North ward), in November 2013.

23. Interview with Malam Baba Kura (not his real name). Maiduguri, Borno. 12 December 2015. errors in their application and interpretation of Islamic scriptures, after time and effort. Once the high-ranking Boko Haram members joined the programme, they were able, in turn, to go and convince other sect members loyal to them to get on board the programme and give it a try. This example reveals the strong influence the leaders and those who occupy the top echelon of Boko Haram have over the sect's foot soldiers.

According to Baba Kura, the efforts of the deradicalisation team began to show some success when the Boko Haram prisoners, who had always previously kept to themselves, gradually involved in different activities with other prisoners. An example, cited by Baba Kura, was the participation of some members in football games. This is noteworthy due to the strict stance held by the sect's ideologues about football (and other sporting activities), which they argue are idolatrous and consequently Islamically forbidden, that is to say, haram.

While I was at Kuje Minimum Security Prison, I also met and interviewed other workers of the deradicalisation programme employed to engage daily with the Boko Haram members. I was told that, at that point, the programme had been placed "on hold" by the Nigerian government, although the rationale behind this was not clear to them. According to the workers interviewed (both men and women), their tasks were compartmentalized, that is to say that specific roles and activities were assigned to them. For instance, there were two Islamic clerics who attended to the religious needs of the participants. The female workers on the team, I was told, mostly engaged in social work with the participants, which I understood to range from engaging with the families of the imprisoned male members (there are also imprisoned female members or female relatives of Boko Haram members) to teaching them technical skills, such as tailoring.

Some observations I made during the course of my prison interviews made me question the efficacy of the deradicalisation programme, wondering if it could bring actual result or if prisoners simply took advantage of it. Indeed, its participants had better living conditions than other inmates, due to the EU direct funding of the programme. I observed that some of the prisoners were also allowed more freedom of movement within the prison than others. For example, I mistook for a prison staff one of the higher-ranking members of Boko Haram participating in the programme because he had been moving around unlike most prisoners, was dressed immaculately, and interacted freely with the other prison staff. I was caught unaware when he was subsequently introduced to me as a prisoner and self-admitted Boko Haram member. This added to the fact that those enrolled on the deradicalisation programme were receiving material incentive. Some of those I interviewed specifically asked me to beg the government for the continuation of the deradicalisation programme, as they benefitted from a better quality of life if compared with "ordinary" prisoners. This differential treatment, I was told, had created divisions within the prison, especially as other prisoners felt that the Boko Haram convicts were worse offenders than they were.

The discovery I made from one of the prison interviews I conducted, I would argue, underscores the importance of giving primacy to the anthropological facet of data production-as there are still several developing layers to the narrative(s) of Boko Haram's insurgency. The particular prisoner was among one of the assumed Boko Haram members and had been convicted of complicity in the sect's acts of violence. During the course of our interview, the prisoner spoke in English and told me his name, which did not sound like a Muslim or typical northern Nigerian name. This piqued my curiosity and so I enquired further. The interviewee then divulged that he was a Christian hailing from Benue State and who had previously been employed as a policeman in Gombe State. He was arrested after it was discovered he had been selling weapons to Boko Haram fighters, and then was tagged as a member of the sect. 24 This unusual case demonstrates the complexity of the narrative around the Boko Haram insurgency and the difficulty in pigeon-holing the different actors involved in it into neatly-defined analytical categories.

Conclusion

Ethical considerations are an integral part of all empirical research. When inserted within a context in which violence is part of data collection, the need for upholding particular standards becomes even more pressing. As Goodhand posits, ethical decision-making is inherently context-specific, due to the fact that, according to him, it addresses "profoundly political questions, about power, information and accountability. " The American Anthropological Association (AAA) also points out, as part of its guidance stipulations, the necessity of giving a considerate amount of thought to the possible ways in which one's research might cause harm, as a prelude to the beginning of any anthropological study (Fluehr-Lobban 1991, 26).

An important factor that I had to consider in depth was the "ethical merit" of my study. As Kilshaw mentioned, in her caution to researchers about proper representation of their work, there is always the tendency for those who choose to participate in a study to "hear what they want to hear" (Kilshaw 2013, 126-27), reflexively wanting their viewpoints to be given preference within the grand narrative of the study. With the knowledge of how they are currently perceived in both the local and international media, I concluded that the Boko Haram members I planned on interviewing could not reasonably expect me to express or promise support for their worldview or opinions in exchange for their permission to be interviewed. As such, I let them know that I was only a student interested in hearing their "side of the story" to counterbalance various views and unfounded theories being propagated about the sect. This incentivised some sect members imprisoned at Prison B to allow me interview them, while most of the other prisoners refused my request.

24. Interview with a prisoner detained (charged with membership of Boko Haram) at Kuje Minimum Security Prison, Abuja. 18 December 2015. Also, in the process of re-reading through my fieldnotes for the purpose of my academic writing, I have exercised my prerogative to decide to redact certain interviews or parts of them which I felt had the potential to offend humane sensibilities. Philippe Bourgois's writings on the agency of writing is instructive in this regard. As an anthropologist researching the Salvadorian civil war, the metric on which Bourgois based the self-censoring of interviews he conducted was his fear of his work being used to further the repression of Salvadorians (Bourgois 1990, 48). For me, I did not want to be a contributor towards the fostering of negative ideas, and so, for instance, I decided not to make use of the views expressed by an interviewee, a confidante of the late Mohammed Yusuf and acquaintance of Abubakar Shekau who I met in November of 2013. This was because in the course of our session, he expressed sympathetic views about the massacre of more than forty school pupils at a government secondary school in the Mamudo district of Yobe in July 2013, 25 which I considered to have been based on prevalent conspiracy theories and to also have been insensitive to the deceased and their close relatives.

The escalation of violence in northern Nigeria perpetrated by Boko Haram since 2009 has rendered the region an unsafe location for researchers to conduct ethnographic fieldwork as it is impossible for them to decipher the patterns which dictate the frequency or location choices for the launching of attacks. As a response to this situation, a significant amount of research has been undertaken without physical immersion in the field itself, resulting in the production of theoretically and statistically-rich scholarship on Boko Haram. Much of this literature has helped to lay the foundation for nuanced analyses of the nebulous dimensions of Boko Haram within and beyond Nigeria's borders. As such, conducting fieldwork within a zone where researchers could be affected by violence or put themselves at risk of being arrested, or even worse, should not be considered to be a rigid rule or barometer for measuring the value of academic contributions to the literature on Boko Haram.

However, as this article has attempted to explain, the burgeoning field of study on Boko Haram, regardless of the different disciplinary approaches adopted, requires the injection of new and unrecycled data into the literature in order to advance a more updated, nuanced and complex understanding on the sect. A large part of the scholarship already produced in relation to the Boko Haram insurgency has been predicated on the same limited studies. However, new studies that are historically informed and anthropologically grounded are needed to produce fresh and truly empirical data, renew the perspective as well as explore recent changes. 26 With the lack of access to Boko Haram camps within the hinterlands of north-eastern Nigeria for non-members of the sect, a step towards filling the many knowledge gaps about the sect would be the decriminalisation by the Nigerian security forces of the 25. Hall, John. 2013. "Nigeria Massacre: Boko Haram Islamists Kill 42 at Boarding School in Yobe State." The Independent, 8 July. URL: https://www.independent.co.uk/news/world/africa/ nigeria-massacre-boko-haram-islamists-kill-42-boarding-school-yobe-state-8695355.html [archive].

26. See, for example, Mohammed (2014); Walker (2012); and Higazi (2015). possession of literature-from tracts to letters to written statements and booksand of recordings and videos produced by Boko Haram. Also, making revelatory reports, such as the Galtimari report 27 (Galtimari 2011), accessible to researchers and the general public might prove effective in helping sources-reliant research on Boko Haram in the intervening period, until the sect's violence in northern Nigeria subsides significantly. Only first-hand data collection, I argue, can help move away from oft too rigid categories and instead access the variety and sometimes blurred nature of real-life situations, specifically in Nigeria's north-eastern region.

  16. For example, see: "Nigerian Army Clashes with Boko Haram in Kano, Seven Killed." 2013. Reuters, 9 November. URL: http://uk.reuters.com/article/uk-nigeria-bokoharam-idUKBRE9A80B020131109 [archive].

  12. Interviews conducted between July 2014 and December 2015 with residents of Railway Quarters, Maiduguri. 13. Olusegun Obasanjo in conversation with Richard Dowden, the Head of the Royal African Society, during the UK launch of his autobiography titled My Watch on Wednesday, 11 February, 2015, at the Royal Society of Medicine in London. 14. Audu, Ola'. 2016. "Jonathan only Called Me 19 days after Chibok Girls' Abduction -Borno Governor." Premium Times, 28 March. https://www.premiumtimesng.com/news/ headlines/200942-jonathan-only-called-me-19-days-after-chibok-girls-abduction-bornogovernor.html [archive].

Interview with an individual who was previously engaged by the Nigerian government, under the Goodluck Jonathan administration, to conduct negotiations between the state and Boko Haram.Maiduguri, Borno. 8 December, 2015.