William Richard

David Evrard
email: evrard@chimie.ups-tlse.fr

Pierre Gros

New insight into 4-nitrobenzene diazonium reduction process: Evidence for a grafting step distinct from NO 2 electrochemical reactivity

Keywords:

Electrochemical and spectroscopic investigations were performed in order to clarify the mechanism of 4nitrobenzene diazonium reduction on glassy carbon in protic medium. The number and nature of the electron transfer processes were found to be strongly correlated to the electrode surface state. On polished electrode two different reduction peaks were observed. Selective electrolyses realized at the corresponding potential definitely proved that the grafting process actually occurs at a potential distinct from NO 2 electroreduction, this latter inducing the presence of the quasi-reversible NO/NHOH redox couple at the electrode surface. These results were confirmed by XPS analyses. Furthermore, voltammetric experiments using FeðCNÞ 3À 6 showed that the electrochemical properties of the modified electrode strongly depend on the potential applied for grafting, which modulates the nitro group oxidation state. All the results suggested that the electrode functionalization was more efficient when grafting and NO 2 reduction were performed separately.

Introduction

Among all the numerous strategies reported in the literature for carbon-based surface modification, diazonium grafting is probably the most promising one since it provides an easy covalent way to immobilize additional functional group of interest. Since the first report by Pinson and coworkers in the early 1990s [1], functionalization via diazonium reduction has received an increasing interest and the numerous studies devoted to explore the wide range of its potentialities have been recently reviewed [2][3][4]. The immobilized group affords specific chemical and physicochemical properties to the surface which are exploited in many application fields such as molecular electronics [5,6], energy conversion [7][8][9] and chemical [10][11][12] or biological [13,14] sensing. Depending on the aim of the work, it can also be used for further modification using chemical reaction such as click chemistry [15][16][17] and amine/carboxyl condensation [18,19] or to directly interrogate the functionalized surface.

Because it is commercially available and bears an electroactive NO 2 moiety, 4-nitrobenzene diazonium (NBD) is concerned with many applications, both as an electrochemical probe to characterize a surface or to modify its intrinsic properties. On the one hand, it has been used to evidence the difference of reactivity between graphene single and multilayers [20], to identify diamond surface terminations and measure the density of hydrogen atoms bonded to the surface [21] or to illustrate nanoscale patterning of carbon surface [22]. On the other hand, NBD was reported to modify the electrical properties of graphene field-effect transistors [23] or to help at covalent immobilization of organometallic model of enzyme onto carbon surface [24]. All these applications need the electrochemical reactivity of NBD to be clearly defined and this is the reason why it has been extensively investigated in both organic and aqueous media [25][26][27][28][29][30]. It is nowadays well established that the reduction of the nitro moiety in protic medium leads to the formation of hydroxylamine (NHOH) group [31] which belongs to the reversible nitroso/hydroxylamine (NO/NHOH) redox couple. Moreover, further reduction results in amination of the hydroxylamine groups (Scheme 1). In aprotic solution, NO 2 can be reversibly converted into radical anion ðNO ÅÀ 2 Þ [32]. Despite numerous comparative works on the influence of the electrolyte salt or the effect of substrate material [31,33,34], the whole reduction mechanism of NBD still remains unclear and gave rise to contradictory interpretations in the literature. Particularly our attention was drawn on diazonium grafting and NO 2 first reduction step. Depending on the authors, one or two irreversible peaks are reported for NBD reduction (Table 1). Brooksby and Downard noticed that the first, smaller peak was not always present and that its corresponding current varied from one experiment to another [31]. On the contrary Baranton and Belanger systematically noticed a first reduction peak distinct from that assigned to diazonium reduction [33,35]. Since the origin of this first peak remains unknown, many ⇑ Corresponding author at: Université de Toulouse, INPT, UPS, Laboratoire de authors assumed both NBD grafting and NO 2 reduction reactions to occur simultaneously [3,30,31,[36][37][38]. Only very recently Cline et al. [27] suggested a grafting process to occur at less cathodic potential although without providing further details on the grafted species. These discrepancies are certainly the reason why a high cathodic overpotential is systematically applied to ensure the interface modification (Table 1). Nevertheless a full comprehension of NBD reduction mechanism is of critical interest since the chemical and electrochemical properties of the resulting modified surface strongly depend on the nature of the functional group borne on the organic layer.

In this work, we present simple considerations based on cyclic voltammetry and potentiostatic grafting experiments to definitely clarify (i) the conditions inducing a double cathodic signal and (ii) the reactions occurring at both reducing steps in order to provide a fully understood tool to chemists aiming at surface functionalization. Electrochemical results are confirmed and completed by XPS analyses highlighting the relationship between the potential used for grafting and the major chemical group present onto the electrode surface. Finally the evolution of the functional group redox state, which depends on the potential applied to the electrode, has been evidenced by means of cyclic voltammograms using FeCN 3À=4À 6 as a redox probe.

Experimental

Chemicals

All products were used as received. 4-nitrobenzene diazonium (NBD) tetrafluoroborate (C 6 H 4 N 3 O 2 BF 4 , 97%) was purchased from Aldrich. Potassium ferricyanide(III) (K 3 Fe(CN) 6 , 99% powder) was Scheme 1. The three possible reduction steps for NBD in aqueous media. Sodium hydrogen carbonate (NaHCO 3 ) was purchased from Fischer Chemical. Acid solutions were prepared by dilution of hydrochloric acid (HCl 37%) from VWR using Milli-Q water (18 MX cm), and were deaerated by bubbling Nitrogen during 10 min. A gas stream was maintained over the solutions during experiments.

Apparatus

All the electrochemical experiments were performed at room temperature using a Metrohm l-Autolab II potentiostat interfaced to a personal computer and controlled with NOVA 1.7 software package. A classical three-electrode glass cell was used with a Metrohm platinum rod and a Radiometer saturated calomel electrode (SCE) connected to the cell by a capillary as counter and reference electrode, respectively. All the potentials are given with respect to SCE. Working electrode was a 3 mm diameter glassy carbon (GC) rotating disk electrode from Radiometer.

XPS measurements were performed with a K alpha spectrometer from Thermo Scientific, using the monochromatized Al Ka line at 1486.6 eV. A fixed analyser pass energy of 50 eV was used for N(1s) core level scans. The binding energy scale was calibrated to 284.5 ± 0.1 eV for the main C(1s) feature. Experiments used GC plate (5.5 mm diameter) from Mersen as substrate material.

Electrode modification

Prior to modification, GC electrodes and GC plates were manually polished to a mirror-like finish successively with 9 lm, 3 lm and 1 lm diamond powder from Presi on a cloth polishing pad.

After each step, the electrode was thoroughly rinsed with Milli-Q water and sonicated in ethanol for 5 min in order to remove any impurity.

In order the influence of GC surface state to be evaluated, some electrodes were only coarsely polished with 9 lm diamond powder. For the sake of clarity, this kind of electrode is referred to as ''unpolished electrode''.

Freshly polished electrode was modified from acetonitrile + 0.1 M Bu 4 NBF 4 or 0.1 M HCl (pH 1) solutions both containing 2.5 mM NBD, either by constant potential electrolysis at 0.3 V during 300 s or by simply dipping the electrodes into the solution for the same duration. After modification, the electrode was carefully rinsed with Milli-Q water before and after sonication in ethanol during 5 min to remove weakly adsorbed moieties. The same procedure was used for GC plate modification.

Solution preparation

Most cyclic voltammograms were recorded in 0.1 M HCl (pH 1). pH modification between 0 and 2 was also performed using HCl solution at the corresponding concentration. For higher pH value, 0.1 M solutions of KPF 6 (pH 3.6), carbonate buffer (pH 5 and 6) and phosphate buffer (pH 7) were used.

Results and discussion

Influence of GC surface state

Fig. 1 presents the cyclic voltammograms (CVs) recorded on bare GC electrode in 0.1 M HCl (Fig. 1A) and in acetonitrile (Fig. 1B) both containing 2.5 mM NBD. On a properly polished electrode (as described in the Experimental Section) a cathodic signal was systematically observed around 0.4 V in both solutions (solid lines). Furthermore a second signal was recorded around 0.05 V in HCl (Fig. 1A, solid line), thus proving that two distinct processes actually occurred in aqueous solvent. Although a standard potential E°= 0.05 V has been found by Andrieux and Pinson, a contribution from phenyl radical reduction could hardly be invoked, the same authors reporting a corresponding small peak at À0.64 V [39], far beyond the potential range used here. Moreover, the rather slow scan rate used here is not favorable to the observance of radical species. In comparison no more reduction reaction was observed in acetonitrile (Fig 1B, solid line) in the same potential range. This last result is in accordance with literature data indicating that NO 2 reduction in aprotic solution did not afford NHOH groups formation but rather led to the corresponding radical anion at very negative potential [32]. Consequently, in aprotic medium the cathodic peak observed around 0.4 V corresponds to NBD grafting. On unpolished electrode only one cathodic peak was noticed whatever the electrolytic solution (dashed lines). Clearly the presence of the peak at 0.4 V is strongly correlated to the surface state, in accordance with the work by Cline et al. [27]. However, the hypothesis proposed by these authors that the multiple peaks could be the result of different carbon sites seems to be caught out: assuming that the solvent has no influence on these sites, the latter hypothesis fails at accounting for the differences reported here. It is noteworthy that all these peaks disappeared on the second scan (not shown) whatever the medium and the electrode preparation, as a consequence of a blocking process of the GC surface. All these results were also observed when experiments were conducted with a diazonium concentration ten times lower. Once the conditions leading to the observation of two reduction peaks are clarified, an important question arises: since in aqueous media a peak is observed at 0.05 V whatever the surface state of the electrode, does a unique reaction occur on first and second peaks in the case of properly polished electrode, or is there two distinct reduction reactions? In other words, do electrolyses performed at both potentials lead to a same or different grafted layer? To answer these questions, several grafting experiments were performed at different potentials.

Influence of grafting potential

In order to identify the reduction process occurring around 0.4 V, a constant potential electrolysis was performed at 0.3 V during 300 s in the 2.5 mM NBD-containing HCl solution with a freshly polished GC electrode. This potential was chosen in order the corresponding reaction to be diffusion-controlled. The resulting modified electrode was rinsed as described in the Experimental Section. Then two successive CVs were recorded in a diazonium-free HCl solution (Fig. 2). On the first cycle (solid line), a reduction peak was observed at À0.1 V on the forward scan. Comparatively no significant cathodic current was shown in the same potential range without NBD in the electrolysis solution (dotted line). This last result proves that the electrolysis performed at 0.3 V with NBD leads to a grafting process inducing the presence of redox species at the electrode surface. Then a quasi-reversible signal was recorded at 0.20 V on the following cycle (dashed line), corresponding to the redox nitroso/hydroxylamine couple as already mentioned [32]. It is noteworthy that this signal was visible only from the first reverse scan, contrary to the observation by Ortiz et al. who performed NBD reduction at À0.72 V and thus noticed this signal from the first cathodic sweep [29]. Practically no cathodic current was observed on the first forward scan before the electrode potential decayed to À0.1 V. Consequently no hydroxylamine moiety was produced during the constant potential electrolysis at 0.3 V. Reduction of NO 2 into NHOH actually occurred at À0.1 V during the first CV. The corresponding peak dramatically decreased on the second CV indicating that most of the accessible NO 2 functions were reduced during the first scan. All these results clearly indicate that (i) NBD grafting occurred during the electrolysis at 0.3 V, which is a much higher potential than those usually reported for NBD potentiostatic grafting (see Table 1 for an overview of grafting potential values) and, (ii) at this potential the NO 2 moiety does not experience any reduction into NHOH. Thus, on carefully polished GC substrate, it is possible to distinguish NBD grafting from NO 2 reduction, contrary to what was suggested by Brooksby and Downard or by the group of Saveant who performed NBD reduction at À0.3 V [31] and À0.2 V [36] respectively. Fig. 3 shows CV recorded in a diazonium-free HCl solution with a polished GC electrode modified by constant potential electrolysis at 0.3 V during 300 s in the 2.5 mM NBD-containing HCl solution (curve b). The voltammogram exhibited a more capacitive response than that observed on a clean polished GC electrode (curve a), thus confirming that a grafting process actually occurred during the electrolysis at 0.3 V. Contrary to that observed in Fig. 2 (dashed line), no reversible signal corresponding to the redox nitroso/ hydroxylamine couple was recorded in this case. The main reason is that the lowest potential applied during the CV was 0 V, thus avoiding the reduction of NO 2 into NHOH group as demonstrated before. Only a little, bad-defined reversible system was observed around 0.27 V on both grafted and unmodified electrodes and was assumed to belong to the quinone redox system often observed on GC after polarization [40][41][42]. The same behavior was obtained when the electrolysis at 0.3 V was performed in acetonitrile containing 2.5 mM NBD. This last result proves once again that the reaction occurring at 0.3 V corresponds to a grafting process which leaves NO 2 groups unchanged, this latter being reduced at a more cathodic potential as shown in Fig. 1.

To get further information on the grafted layer, the modified electrode was held at À0.1 V during 300 s in diazonium-free HCl solution. A CV was then recorded (Fig. 3,curve c) highlighting another redox activity centered at 0.20 V. The influence of the potential scan rate on both cathodic and anodic peak currents is shown in Fig. 4A. The linear variation observed for potential scan rates from 5 to 200 mV s À1 suggests that the electroactive species involved in the reaction did not diffuse from the bulk solution but rather were grafted onto the electrode surface [START_REF] Bard | Electrochemical methods[END_REF]. On the other hand the peak potential difference (ca. 80 mV) suggested a quasireversible redox system. The 80 mV value observed was probably due to the electron transfer resistant properties of the grafted layer. The evolution of both peak potentials as a function of pH (Fig. 4B) confirmed the presence of a pH-dependent redox process. The experimental slopes (À50 and À63 mV per decade for anodic and cathodic peaks, respectively) were very close to the theoretical one which corresponds to a one proton/one electron exchange [START_REF] Compton | Understanding Voltammetry[END_REF]. It was verified that CV was identical to that obtained with a clean GC electrode (Fig. 3, curve a) when the first electrolysis at 0.3 V was performed without NBD. All these data are in agreement with the presence of the NHOH/NO reversible couple whose apparent standard potential is consistent with literature data [31]. Keeping in mind that the second electrolysis at À0.1 V was performed in a NBD-free HCl solution, all these results demonstrate undoubtedly that NO 2 group was already present onto GC surface at the end of the first electrolysis. Actually, the diazonium function was reduced at 0.3 V and the grafted nitro moiety was further reduced into hydroxylamine group at À0.1 V. For the sake of clarity, the corresponding modified electrodes were indicated as GC-NO 2 and GC-NHOH, respectively.

The integration of the cathodic peak of the quasi-reversible system exhibited by GC-NHOH electrode (Fig. 3 curve c) gave an average surface coverage C = 1.5 Â 10 À10 mol cm À2 (considering a two electron-exchange process), which is close to the value reported by many authors for a monolayer [31,32]. However, it has to be noticed that in the experimental self-inhibiting conditions used, the formation of a multilayer organic film was expected, so that the C value obtained may be correlated only to the accessible NHOH moieties. When GC electrode was simply dipped into NBD solution during 300 s without applying any potential and then experienced electrolysis at À0.1 V in diazonium-free HCl, a similar redox system at 0.20 V was observed (Fig. 3,curve d). The corresponding very little surface coverage deduced from the integration of the cathodic peak (ca. 3.5 Â 10 À11 mol cm À2 ) is consistent with some NBD spontaneous grafting on GC leading to a submonolayer film [START_REF] Adenier | [END_REF][46][47]. The comparison between both C values clearly evidences that the reduction process at 0.3 V is associated to diazonium grafting, thus inducing a higher surface coverage. It is noteworthy that the NO/NHOH quasi-reversible system was also observed when both electrolyses at 0.3 and À0.1 V were performed in 0.1 M HCl containing 2.5 mM NBD; however in this case, another ill-defined, quasi-reversible system (DE = 75 mV) around 0.36 V was noticed (Fig. 3, curve e). This latter may be explained by the presence of NO/NHOH redox systems that experienced different electronic environments due to the successive grafting. This last result is indicative of the formation of a thicker and non-homogeneous organic layer, which is in accordance with the work of Haccoun et al. [37] who reported the structural characteristics of the grafted layer to be potential and grafting time dependent. Consequently it seems better to separate the grafting and the NO 2 reduction steps in order the functionalized electrode to be the most efficient. This is only possible on carefully polished GC electrodes, the surface state of which undergoes NBD first reduction peak to occur around 0.4 V.

XPS characterization

In order to confirm our proposal, XPS experiments were performed on bare GC, GC-NO 2 and GC-NHOH electrodes (Fig. 5). The spectrum recorded for GC-NO 2 exhibited two peaks at 405.9 and 399.9 eV (Fig. 5B), the former being slightly lower. Comparatively the first peak was not visible on bare GC spectrum (Fig. 5C). According to literature data, this first peak can be attributed to nitro groups [48,[START_REF] Briggs | Practical Surface Analysis: by Auger and x-Ray Photoelectron Spectroscopy[END_REF]. This result undoubtedly proves our hypothesis that diazonium grafting occurred when electrolysis was performed at 0.3 V. The second peak at lower energy is more difficult to assign, since it can be assigned to several nitrogen-bearing groups. Ortiz et al. [29] suggested a complex contribution of various nitrogen reduced forms, namely NH 2 , NHOH and azo groups. In our case, the presence of NHOH moieties is excluded by electrochemical measurements which did not exhibit the reversible NHOH/NO system on GC-NO 2 electrode (Fig. 3, curve b). Because of the long electrolysis time (ca. 300 s), we propose the peak at 399.9 eV to be assigned both to azo groups, in accordance with the study by Doppelt et al. [START_REF] Doppelt | [END_REF] and to amine groups generated by nitro reduction under the XPS beam [51,52]. It is noteworthy that a peak was recorded on bare GC at the same energy. This observation has been previously reported [32] but remains unexplained. The spectrum of GC-NHOH electrode exhibited the same two peaks at 405.9 and 399.9 eV (Fig. 5A). The first peak attributed to nitro group was significantly lower than that on GC-NO 2 , thus confirming the reduction of NO 2 groups when operating at À0.1 V. On the contrary, the intensity of the second peak at 399.9 eV remained nearly constant. However, the global amount of nitrogen decreased, indicating a loss of material. This fact has already been observed by Ortiz et al. [29] who proposed a fraction of the grafted phenyl groups to be cleaved from GC surface. Here, the fact that the peak at 399.9 eV remained constant whereas the peak corresponding to NO 2 group decreased indicates a conversion of this latter into another nitrogen-bearing function, namely NHOH. This is consistent with electrochemical data which indicate the presence of the NO/NHOH redox couple (Fig. 3, curve c). A little amination process could also be envisaged, although the reducing potential used was significantly too high. The presence of the peak at 405.9 eV, although lower than for GC-NO 2 , is in agreement with the hypothesis of a partial reduction of the nitro groups, the most accessible ones only being reduced at À0.1 V.

Electrochemical response towards redox probes

Finally, the response of the modified electrodes towards an electrochemical probe, namely FeðCNÞ 3À 6 , was examined in 0.1 M HCl (Fig. 6). The electrochemical response of FeCN 3À=4À 6 was almost totally suppressed on GC-NO 2 electrode (Fig. 6, curve b). Comparatively, the typical redox activity appeared on GC-NHOH (Fig. 6, curve c) although both anodic and cathodic peak currents were lower than those recorded on bare GC electrode (Fig. 6, curve a). These results strongly support the hypotheses proposed above and the blocking behavior of the functionalized electrode can thus be clearly explained. During the first electrolysis at 0.3 V, NBD was effectively grafted onto the electrode surface but the NO 2 moiety remained unchanged, providing a high electronic density interface which enhanced the electrostatic repulsion with ferricyanide anions. By applying À0.1 V, most of NO 2 groups were reduced into NHOH moieties. At pH 1, these latter are expected to be under their corresponding protonated form (assuming the pKa of hydroxylamine functions to be close to that of phenylhydroxylamine [53] ca. 1.96), thus making a more positively charged organic layer which favors mass transfer of ferricyanide anions to the electrode. Moreover, the material loss occurring during the electrolysis at À0.1 V should result in a thinner layer, thus contributing to some extend to a less pronounced barrier effect. Finally, when both electrolyses at 0.3 and À0.1 V were performed in NBD-containing solution, the resulting voltammogram of FeðCNÞ 3À 6 exhibited a capacitive behavior, typical of a strong barrier effect resulting from a thick layer (Fig. 6, curve d). Indeed, in this case both diazonium grafting and NO 2 reduction into NHOH occur during the second electrolysis at À0.1 V in the presence of NBD. This is also true when a single electrolysis was performed at À0.1 V in NBD-containing solution; in this case the CV of FeðCNÞ 3À 6 exhibited a rather more capacitive behavior, suggesting a highly disordered layer (not shown). The comparison between curves (c and d) demonstrates once again the interest of grafting NBD at higher potential than that commonly used in the literature.

Conclusion

This work demonstrates that NBD grafting actually occurs at 0.3 V on carefully polished GC and that this reaction is strongly correlated to the electrode surface state. This potential value is much less reducing than that usually reported for NBD potentiostatic grafting. XPS data proved that electrolysis at 0.3 V affords a NO 2 layer onto the electrode surface. Consequently on properly polished substrate it is possible to distinguish between diazonium grafting process and NO 2 electrochemical reduction reactions. Supplementary reduction of NO 2 into NHOH in protic solvent was clearly identified at À0.1 V. Moreover the electrochemical properties of the modified electrode were found to be strongly dependent on the grafting potential which modulates the nitro group oxidation state. This result is of dramatic importance for chemists aiming at surface modification since it allows a better control of the barrier effect induced by the organic layer.

Fig. 1 .

 1 Fig. 1. Cyclic voltammograms recorded in 0.1 M HCl (A) and in acetonitrile (B) solutions both containing 2.5 mM NBD. Solid lines: polished GC electrode (see Section 2.3); dashed lines: unpolished GC electrode. Scan rate: 100 mV s À1 .

Fig. 2 .

 2 Fig. 2. Cyclic voltammograms recorded in 0.1 M HCl on polished GC electrode modified by electrolysis at 0.3 V during 300 s in 0.1 M HCl (dotted line) and in 2.5 mM NBD-containing 0.1 M HCl solution (solid line: first scan; dashed line: second scan). Scan rate: 50 mV s À1 .

Fig. 3 .

 3 Fig. 3. Cyclic voltammograms recorded in 0.1 M HCl on: (a) bare GC electrode; (b) GC electrode modified by electrolysis at 0.3 V during 300 s in 2.5 mM NBDcontaining 0.1 M HCl solution (GC-NO 2 electrode); (c) electrode (b) polarized at À0.1 V during 300 s in diazonium-free 0.1 M HCl solution (GC-NHOH electrode); (d) GC electrode dipped in 2.5 mM NBD-containing 0.1 M HCl solution during 300 s and polarized at À0.1 V during 300 s in diazonium-free 0.1 M HCl solution; (e) GC electrode modified by two successive electrolyses during 300 s at 0.3 V and À0.1 V in 2.5 mM NBD HCl solution. Scan rate: 50 mV s À1 .

Fig. 4A .

 4A Fig. 4A. Influence of the potential scan rate on both cathodic (white circles) and anodic (black squares) peak currents observed at 0.20 V on the CV recorded in 0.1 M HCl solution with GC-NHOH electrode.

Fig. 4B .

 4B Fig. 4B. Influence of pH on both cathodic (white circles) and anodic (black squares) peak potentials on the CV plotted with GC-NHOH electrode. Scan rate: 50 mV s À1 .

Fig. 5 .

 5 Fig. 5. X-ray photoelectron spectra of N(1s) core levels of: (A) GC-NHOH electrode; (B) GC-NO 2 electrode; (C) bare GC.

Table 1

 1 Literature survey on NBD grafting and reduction steps. Bu 4 NBF 4 , 98%), potassium dihydrogenophosphate (KH 2 PO 4 ), di-potassium hydrogenophosphate (K 2 PHO 4 ) and acetonitrile (extra dry) were supplied by Acros Organics.

	Medium/conditions	Substrate	E p (V) a	Attribution	E g (V) b	Ref.
	ACN, 0.1 M Bu 4 NBF 4	GC	À0.08 irrev c	Diazonium reduction	À0.88	[54]
	2 mM		À1.28 rev	NO 2 reduction into radical anion
	ACN, 0.1 M Bu 4 NBF 4	GC	0.08 irrev	Diazonium reduction	ocp d	[55]
	1 mM		À1.17 rev	NO 2 reduction
	ACN, 0.1 M Bu 4 NBF 4	GC	0.02 irrev	Diazonium reduction	From À0.2 to À1.2 e	[46]
	5 mM		No further investigation
	ACN, 0.1 M Bu 4 NBF 4	GC	0.03 irrev	Diazonium reduction	ocp	[45]
	2 mM		No further investigation
	ACN, 0.1 M Et 4 NClO 4	GC	0.2 irrev	Diazonium reduction	À0.6	[32]
	1.8 mM		À1.19 rev
	ACN, 0.1 M Et 4 NClO 4	HOPG	0.27 irrev	Diazonium reduction		[32]
	1.8 mM		À1.2 rev	No discussion
	ACN, 0.1 M Bu 4 NBF 4	GC	À0.07 irrev	Diazonium reduction	À0.72	[30]
	1 mM		À1.22 rev	NO 2 reduction into radical anion
	ACN, 0.1 M Et 4 NBF 4	GC	0.41 irrev	Unattributed	0.06, À0.24	[33]
	1 mM		0.06 irrev	Diazonium reduction
	ACN, 0.1 M Bu 4 NBF 4	GC	À0.02 irrev	Diazonium reduction	À f	[3]
	2 mM		À1.17 rev	NO 2 reduction into radical anion
	ACN, 0.1 M Bu 4 NBF 4	GC	0.08 irrev	Diazonium reduction	À0.17, À0.42, À0.67	[38]
	1 mM		À0.89 irrev	No discussion
	ACN, 0.1 M Bu 4 NBF 4 , after NO 2 grafting		À1.16 rev	No discussion
	ACN, 0.1 M Bu 4 NBF 4	Carbon nanofiber	À0.04 irrev	Diazonium reduction	À0.04, À0.6	[36]
	1 mM		À1.18	NO 2 reduction into radical anion
	ACN, 0.1 M Et 4 NBF 4	GC	0.46 irrev	Unattributed	0.1, À0.2	[35]
	1 mM		0.1 irrev	Diazonium reduction
	ACN, 0.1 M Bu 4 NBF 4	PPF	0.19 irrev	Unattributed	À0.3	[31]
	0.59 mM		À0.15 irrev	Diazonium reduction
	ACN, 0.1 M Bu 4 NBF 4	GC	0.49 irrev	Unattributed	0.53	[27]
	2 mM		0.05 irrev	Diazonium reduction
	0.1 M H 2 SO 4 after NO 2 grafting		À0.6 irrev
	0.5 M HCl	GC	0.48 irrev	Unattributed	0.1, À0.2	[35]
	1 mM		0.1 irrev	Diazonium reduction
	1 M HCl, 1 M KCl	GC	0.4	Diazonium reduction	À0.72	[29]
	5 mM		À0.34 irrev	NO 2 reduction into amine
	0.1 M H 2 SO 4	PPF	À0.03 irrev	Diazonium reduction	À0.3	[31]
	0.89 mM
	0.1 M H 2 SO 4	GC	À0.14 irrev	Diazonium reduction	À0.2	[36]
	1.5 mM		À0.49 irrev	NO 2 reduction into amine

a Cathodic peak potential obtained from CV experiment. All the potential values are referred to SCE. b Potential used for electrochemical grafting. c irrev: Irreversible; rev: reversible. d ocp: Open-circuit potential.e In this work, different potential values were applied for grafting, together with different electrolysis times. f No grafting potential is provided in this work since it is a review.

Acknowledgements

The authors thank Jerome Esvan from the Centre Inter-universitaire de Recherche et d'Ingénierie des Matériaux (CIRIMAT) for XPS measurements and fruitful discussion.


Vincent Savaux

Yves Louët

Moïse Djoko-Kouam

Alexandre Skrzypczack

Alexandre Skrzypczak

Near LMMSE channel estimation performance with artificial channel at receiver for OFDM systems

This paper proposes a LMMSE-based channel estimator which, unlike the classical LMMSE estimator, does not require the covariance matrix of the channel nor its estimation. Actually, we add at the receiver side a fully adjustable filter, which acts like an artificial channel and hides the physical channel. We then perform an LMMSE estimation of the sum of the physical and artificial channel using the filter covariance matrix and the channel estimation is obtained by subtracting the filter. Theoretical developments, shown in this paper, prove that the performance of the proposed solution can be driven by the parameters of this additional filter and can reach the one of the theoretical LMMSE estimator closely. Simulations, proposed in a DRM context, also display the validity of this technique for both preamble-based and scattered pilot distributions. It is shown that the proposed solution is only about 1 dB from the LMMSE technique in term of Minimum Mean Square Error (MMSE) and Bit Error Rate (BER).

INTRODUCTION

The Orthogonal Frequency Division Multiplexing (OFDM) modulation is nowadays known as a robust and powerful solution for wireless or wired transmissions and is now normalized in many standards of telecommunication like DVB-T, LTE, xDSL technologies, etc. This attractiveness mainly comes from the modulation robustness against the frequency selectivity due to the multipath channel. Indeed, by a simple addition of a guard interval (GI), we limit intersymbol interference in an efficient way. Similarly, the decomposition of the OFDM signal over several narrow frequency bands is an appropriate technique to fight against frequency selectivity and also allows an only one-tap per carrier equalization.

However, before equalization, an estimation of the channel coefficients is necessary. In many standards, some positions in the time-frequency lattice are reserved for this estimation and contain no information data. These positions are termed as pilot tones. The repartition and the number of these tones in the time-frequency lattice depends on the nature of the channel and its severity.

Among the wide range of possible estimation techniques (see references [START_REF] Morelli | A Comparisaon of Pilot-Aided Channel Estimation Methods for OFDM Systems[END_REF][START_REF] Biguesh | Training-Based MIMO Channel Estimation : A Study of Estimator Tradeoffs and Optimal Training Signals[END_REF][START_REF] Dong | Linear Interpolation in Pilot Symbol Assisted Channel Estimation for OFDM[END_REF] for a short description), the LS (Least Square) solution offers an acceptable level of performance with a low complexity as one estimates the channel coefficient on a pilot tone by computing the ratio between the received data and the pilot data value. After that, an interpolation is performed to provide the entire channel at each instant and frequency. However, this technique is very sensitive to transmission noise and the interpolation that is considered.

Another well known estimation technique is the 2D Wiener filtering, described in [START_REF] Hoeher | Two-dimensional pilot-symbol-aided channel estimation by Wiener filtering[END_REF], obtained thanks to the minimization of the MSE (Mean Square Error) criterion. In the case of separated pilots in an OFDM frame, reference [START_REF] Edfords | OFDM Channel Estimation by Singular Value Decomposition[END_REF] proves that we obtain the same level of performance as the 2D Wiener filtering by interpolating the channel coefficients, estimated with the LS criterion, with the LMMSE algorithm (Linear Minimum Mean Square Error). This performance is also very close to the perfect estimation bound. As the LMMSE estimation needs a channel covariance matrix to be performed [START_REF] Van De Beek | On Channel Estimation in OFDM Systems[END_REF], its main drawback lies in the necessity to know some channel parameters like path delays or gains. Unfortunately, these parameters (or their statistics) are a priori unknown and need to be estimated, as proposed in [START_REF] Zhou | A fast LMMSE channel estimation method for OFDM systems[END_REF]. However, this covariance matrix estimation must be regularly updated to ensure an acceptable level of performance.

We here propose a LMMSE-based channel estimation technique which does not necessitate the channel covariance matrix nor its estimation. The basic idea of our technique is to inject pilots through a filter at the receiver side whose parameters can be fully set up by the user. Actually, this filter plays the role of an artificial channel. From the estimator block point of view, the resulting signal is the sum of pilots signal through this artificial channel and the OFDM signal through the physical channel. This hybrid channel (composed by the sum of the physical and artificial channels) can be estimated by a LMMSE estimator. Its performances can be driven by an appropriate choice of filter parameters. We get an estimation of the physical channel by subtracting the filter from the estimated hybrid channel. Using a suitable filter, our method is independent from the variations of the statistics of the channel. The covariance matrix is consequently computed only once.

In order to describe this solution in a better way, we first detail in Section 2 our system model. Then, in Section 3, the basic LS and LMMSE solutions are presented, leading to the description of our solution in Section 4. From the expression of the hybrid channel covariance matrix given in Section 5, we propose a set of parameters for the artificial channel allowing this estimation. Section 6 then proves the validity and shows the performance of our proposed solution in a DRM context, in preamble-based and scattered pilot distribution contexts.

BASEBAND SYSTEM MODEL

In this paper, we consider the transmission of an OFDM signal over a time-varying multipath fading channel according to the model describe in [START_REF] Patzold | Mobile fading channels[END_REF]. This channel, denoted ℎ( ), is composed of a sum of different and independent paths:

ℎ( ) = -1 ∑ =0 ℎ ( -), (1)
where the variable ℎ follows a zero-mean complex Gaussian process with a power-delay profile Θ( ) and the delay is distributed with a probability density function Π( ) [START_REF] Edfords | OFDM Channel Estimation by Singular Value Decomposition[END_REF]. The OFDM system also includes a cyclic prefix (CP) which guarantees a transmission with a good robustness against the multipath effects of the channel.

For discrete time OFDM systems we are considering in the rest of the paper, we note the number of carriers and the length of the CP.

In the following, matrices are depicted in underlined and bold font (M), vectors in bold font (V) and scalars in normal font. We also note ℂ × the set of complex-valued matrices composed of rows and columns. Superscripts and respectively assign the matrix transpose and the Hermitian transpose. In the discrete time domain, the channel impulse response is represented by an element of ℂ ×1 , i.e. a complex vector of length . Considering the th transmitted OFDM symbol, this impulse response h (resp. this frequential response H ) is formed by the coefficients ℎ , , ∈ {0, . . . , -1} in the time domain (resp. , in the frequency domain). The coefficient ℎ , is obtained by sampling ℎ( ) at the frequency sampling = 0, with 0 the intercarrier frequency of the OFDM system. At the receiver side, after the removal of the CP, the th received symbol in the frequency domain U = ( 0, , . . . , -1, ) is such that:

U = H C + W , (2)
where H and W = ( 0, , . . . , -1, ) are respectively the channel matrix and the noise in the frequency domain. In addition, the vector C = ( 0, , . . . , -1, ) is composed of pilot tones and elements of a given constellation like BPSK or M-QAM. Reference [START_REF] Gray | Toeplitz and circulant matrices : A review[END_REF] also ensures that H is a ℂ × diagonal matrix, formed with the channel coefficients , . As H is diagonal matrix, we can rewrite (2) as:

U = C H + W , (3)
where H = ( 0, , . . . , -1, ) and C is a × diagonal matrix whose diagonal elements are 0, , . . .

-1, .

CHANNEL ESTIMATION

In this section, we first recall the algorithm description and the performance of the LMMSE estimation techniques, which we consider as reference solutions. We also suppose that a frame of OFDM symbols is transmitted. A preamble repartition is considered, denoting 0 ∈ {0, . . . , -1} its position in the frame. The LMMSE estimation [START_REF] Edfords | OFDM Channel Estimation by Singular Value Decomposition[END_REF][START_REF] Van De Beek | On Channel Estimation in OFDM Systems[END_REF] is a very efficient way to estimate a response channel all over the time-frequency lattice. After an estimation of the channel coefficients on the pilot tones with an LS estimation, we exploit the statistical properties of the channel to build this LMMSE estimator. Considering a preamble-based scheme, we may derive the expression of the LMMSE estimation [START_REF] Edfords | OFDM Channel Estimation by Singular Value Decomposition[END_REF][START_REF] Van De Beek | On Channel Estimation in OFDM Systems[END_REF]:

Ĥ 0 = R (R + 2 (C 0 C 0 ) -1 ) -1 Ĥ 0 , (4)
where 2 is the supposed known noise power and R ∈ ℂ × is the frequency covariance matrix of the channel, defined by R = {H 0 H 0 }. Ĥ 0 is the Least Square estimation of the channel, i.e. Ĥ 0 = ( 0, 0 0, 0

, 1, 0 1, 0 , ..., -1, 0 -1, 0
)

. From references [START_REF] Biguesh | Downlink Channel Estimation in Cellular Systems with Antenna Arrays at Base Stations Using Channel Probing with Feedback[END_REF][START_REF] Lütkepohl | Digital Radio Mondiale (DRM);System Specification[END_REF], we get the following expression of the minimum of MMSE:

= 1 / 2 + (R -1 ) . ( 5
)
As R is an Hermitian, definite and positive matrix [START_REF] Biguesh | Training-Based MIMO Channel Estimation : A Study of Estimator Tradeoffs and Optimal Training Signals[END_REF], its eigenvalues are all strictly positive and it ensures that (R -1 ) > 0.

As for LS (see reference [START_REF] Biguesh | Downlink Channel Estimation in Cellular Systems with Antenna Arrays at Base Stations Using Channel Probing with Feedback[END_REF]) : = 1 / 2 , we easily retrieve that, for all / 2 ratios, is greater than .

LMMSE ESTIMATION WITHOUT CHANNEL COVARIANCE MATRIX R

How to estimate H without computing R ?

The LMMSE estimator is known as an excellent estimator of the propagation channel but necessitates the calculation (or in practice the estimation) of the covariance matrix R . Our approach is different as here, we propose an estimation technique having an efficiency close to the LMMSE one, without computation of R . To do so, we add an artificial signal composed by pilots (placed at the same positions as at the emitter side) distorted by a filter to the received signal. The illustration of this principle is given in Fig. 1. We assume that the pilot-signal is perfectly synchronized with the received signal. We also suppose that the time-varying coefficients of this filter are randomly chosen according to a statistic that is perfectly known by the receiver. Due to the random nature of the filter coefficients, the filter somehow acts like an artificial channel, but its statistical evolution is perfectly controlled through its statistics. Consequently, we use a channel terminology to describe .

The basic idea of our proposed solution lies on the estimation of = + with LMMSE. In the following, is called "hybrid channel" as it is the result of the addition of the physical channel and the artificial channel . As we do not also have any knowledge of the evolution of the propagation channel , we propose a way to design so that the covariance matrix of can be fully computed thanks to the statistics of only (or, so that R ≈ R ). We can easily retrieve an estimation of by subtracting from the estimation of , without any a priori information on .

As our proposed solution is obtained with the help of an artificial channel , this channel estimation technique is referred in the rest of the paper as the artificial channel-aided LMMSE (ACA-LMMSE) estimation.

ACA-LMMSE estimation

In this section, we consider the same assumptions and notations as in Section 3. If we note S 0 the set of data that are obtained after

S 0 = (H 0 + G 0 ) C 0 + W 0 = K 0 C 0 + W 0 . (6)
At this step in the transmission chain, a LMMSE estimation of the hybrid channel is performed. From (4), we obtain :

K 0 = R (R + 2 (C 0 C 0 ) -1 ) -1 K 0 , ( 7
)
where R is the ℂ × covariance matrix of . K 0 contains the LS estimation of the hybrid channel coefficients on the preamble. This LS estimation can be made as it is performed on the preamble position 0.

In order to get the LMMSE estimation of in [START_REF] Zhou | A fast LMMSE channel estimation method for OFDM systems[END_REF], the covariance matrix R = R + has to be computed. As the statistics of (and consequently, those of ) are unknown, our solution aims at setting the statistics of (recalling that these statistics are fixed by the user) so that R ≈ R whatever the variations of . Furthermore, justifying R ≈ R implies that the matrix R needs to be compute only once. By satisfying this condition, we ensure that the LMMSE of can be performed. Section 5 explains how to correctly choose the statistics of for a feasible LMMSE estimation of . Finally, we retrieve an estimation of by:

Ĥ 0 = K 0 -G 0 . (8)
The coefficients of can also be stored in a memory after their generation so that G 0 can be fully accessible for the estimation step in Eq. (8).

MMSE of the ACA-LMMSE estimator

To compare the performance of the ACA-LMMSE estimator to the one of the LMMSE estimator, we derive an expression of its MMSE as follows:

= {||H 0 -Ĥ 0 || 2 } = ( {[ H 0 -( K 0 -G 0 ) ] × [ H 0 -( K 0 -G 0 ) ] }) = ( {[ (H 0 + G 0 ) -K 0 ] × [ (H 0 + G 0 ) -K 0 ] }) (9)
As, from ( 6), K 0 = H 0 + G 0 , we get:

= ( {[ K 0 -K 0 ] × [ K 0 -K 0 ] }) = { K 0 -K 0 2 } . (10)
(10) then proves that the MSE of the proposed estimation technique is exactly the same as the MSE of the LMMSE estimator of the hybrid channel = + . Consequently, from (5), we can derive the expression of the minimal MSE of this estimator:

= 1 / 2 + (R -1 ) . (11)
Recalling that we determine so that R ≈ R , (11) then proves that the performance of the ACA-LMMSE estimator can be controllable by an appropriate choice of .

As LMMSE can be also used in a scattered pilot repartition [START_REF] Edfords | OFDM Channel Estimation by Singular Value Decomposition[END_REF], our technique is then also valid for that case. It then acts like an interpolation of the channel coefficients over the time and frequency dimensions but it is not possible to derive an analytical expression of the MMSE.

CHOICE OF THE ARTIFICIAL CHANNEL PARAMETERS

The goal of this section is, in a first time, to express the coefficients of R . From this, we put the light on the parameters that may impact the MSE value and that allows the condition: R ≈ R .

Expression of the channel covariance matrix

In our mathematical developments, we suppose that the artificial channel also follows the model in [START_REF] Morelli | A Comparisaon of Pilot-Aided Channel Estimation Methods for OFDM Systems[END_REF]. Then, by noting the length of the impulse response of , we get:

( ) = (ℎ + )( ) = -1 ∑ =0 ℎ ( -) + -1 ∑ =0 ( -) = -1 ∑ =0 ( -), (12)
where ≤ + is the number of paths of ( ) and , ∈ {0, 1, ..., -1} the gain of each path in ( ). Thus, for a given path delay , may be equal to ℎ (respectively ) if ( ) = 0 (respectively ℎ( ) = 0) or equal to ℎ + if ( ) and ℎ( ) have a common path at = . Recalling that is a random variable, we suppose that = 0 with 0 being the sampling time and a random real value which is distributed according to the multipath intensity profile Γ( ) on the interval [0, ]. We then apply a -points DFT (Discrete Fourier Transform) on (12), so for all ∈ {0, . . . , -1}, we obtain the following expression of the frequency response of the hybrid channel at the frequencies = /( 0):

= ( ) = -1 ∑ =0 exp(-2 ). ( 13
)
By denoting (R ) , = { * } the general term of the matrix R , we get from [START_REF] Edfords | OFDM Channel Estimation by Singular Value Decomposition[END_REF]:

(R ) , = -1 ∑ =0 ∫ 0 Γ( ) -2 ( -) , (14)
The delay = 0 represents the maximal delay of the hybrid channel . Thus, we respectively define and as the maximal delay of the artificial channel and the physical channel . Consequently, we necessarily get = max( , ).

Filter features

The analysis of the filter leading to the approximation of the hybrid channel covariance matrix by the one of the artificial channel (i.e. R ≈ R ) being too long to be developed in this paper, we only give here the results. From Eq. ( 14), terms in the channel covariance matrix R may vary according to three parameters:

• the number of paths in the hybrid channel ,

• the artificial channel maximal delay ,

• the multipath intensity profile Γ( ).

Recalling that we want to obtain R ≈ R , we notice that the first two parameters in the aforementioned list are easily driven by . Indeed, as ≤ + , choosing as large as possible is sufficient to guarantee that ≈ . As = max( , ), we ensure that = by choosing = , with the guard interval time duration. As a matter of fact, is chosen in standards using an OFDM modulation so that > to avoid intersymbol interferences. Finally, in (14), the multipath intensity profile is the one of . From the previous analysis, as has a very large number of paths and has a longer impulse response, here, we assume that the multipath intensity profile of is somehow prevailing on the multipath intensity profile of . Consequently, we make the assumption that, under theses conditions, the intensity profile of is close to the one of . Finally, by fixing an intensity profile for , >> and = , we get: R ≈ R .

SIMULATIONS

The DRM standard

Our simulations are based on the DRM standard [12], that proposes a set of digital audio broadcasting technologies designed to work over the bands currently used for AM broadcasting. The transmitted signal is modulated by an OFDM modulation, with different numbers of carriers and different constellation sizes according to the severity of the propagation channel. In the following, we consider the transmission mode C, i.e. the OFDM system counts 148 independent carriers, each carrier modulating a data issued from a 64-QAM constellation. A guard interval (GI) of time duration = 5.33 ms is added to each OFDM symbol. The sampling frequency of the considered system is 10 kHz. Finally, we generate DRM frames which is composed of 20 OFDM symbols (including the GI) whose time duration is then 400 ms. The DRM channel profiles are generated according to the description given in [12, Annex B]. Each channel is characterized by its number of paths and paths gains. For each path, the Doppler shift and Doppler spread is also provided. In all our simulations, we use the US Consortium channel with = 4 and = 2.2 ms. The delay profile follows the one given by the standard.

Analysis of the ACA-LMMSE performance

This paragraph aims at validating our proposed solution and the requirements given in subsection 5.2. We consider two different configurations for . The first one (labelled as config. 1 in the following) does not satisfy our requirements: we set = 3, = 1.18 ms and the delay profile follows a decreasing and exponential profile. The second one (labelled as config. 2) has the following characteristics:

= 15, = and the delay profile also follows a decreasing and exponential profile. Config. 2 is then coherent regarding the requirements. Note that, unlike and the delay profile, we here set knowing the number of paths of given by the DRM standard. In other contexts where is totally unknown, choosing excessively large is then sufficient. Fig. 2 compares the performance of the proposed method (ACA-LMMSE) with LS and theoretical LMMSE in term of MMSE, computed by

{ 1 ∑ -1 =0 | -ˆ | 2 }
, according to two pilots repartitions : a preamble-based (PB), as our developments were obtained assuming this repartition scheme, and a scattered (SP) pilot repartition, according to the DRM standard . Concerning the SP case for LS, a polynomial interpolation over the time and frequency dimensions is made as it efficiently limits the degradation of the MSE. Considering in the first time the PB case, we observe that an appropriate choice of the characteristics of has a great impact on the MMSE performance. Besides, if we follow the requirements given in subsection 5.2 (config. 2), the performance of the estimation technique is clearly improved. This remark then validates the analysis about the parameters choice in subsection 5.2. Now considering ACA-LMMSE, it clearly outperforms LS as it offers an almost 10 dB MMSE gain. The ACA-LMMSE performance is slightly degraded compared to LMMSE, as our estimation uses the covariance matrix R which is naturally different from R . However, this loss is very limited (only 1 dB from LMMSE bound). Our work is now based on the parameters characterization of to obtain MMSE values that may reach the optimal performance.

For the SP repartition, we then notice that we exactly have the same MMSE evolutions, then proving that our technique is also efficient in this case. Indeed, as in this context, the MMSE depends on the nature of the interpolation technique, no theoretical expression of the MMSE can be found in the literature. Note then that the differences between the SP and PB cases are issued from the interpolation technique that inevitably degrades the estimation quality.

Following the DRM standard, the BER of ACA-LMMSE, LMMSE and LS estimations are computed in the SP case (Fig. 3), with the same parameters of parameters. Concerning the LS estimation, a polynomial interpolation in the frequency dimension is made (pointed out "poly." in the legend). Whereas the LS estimation reaches an error floor at = 6.10 -3 , our method has performance close to the theoretical LMMSE estimation. We then observe only 1 dB loss when compared to the LMMSE estimation and just 2 dB loss when compared to the perfect estimation. These results confirm the ACA-LMMSE efficiency in channel estimation. In addition, it requires no direct computation of R (as for LMMSE solution) and no estimation of this matrix.

CONCLUSION

This paper proposes a channel estimation technique, called ACA-LMMSE, which allows an efficient estimation of a physical channel without any knowledge of its covariance matrix nor the need to compute its estimation. This solution is based on the addition at the receiver side of a fully tunable filter that plays the role of an artificial channel and that permits an efficient estimation of the physical channel by an appropriate choice of parameters. We have also shown that it can be used in a preamble-based or a scattered pilot repartition scheme. As the performance of this estimator can be headed by the artificial channel parameters, further works are led concerning the optimization of the parameters set. It aims at justifying at best the approximation of the hybrid channel covariance matrix by the one of the only articial channel.

Fig. 1 .

 1 Fig. 1. Schema of the proposed solution

Fig. 3 .

 3 Fig. 3. BER of the proposed method comparing with LMMSE and LS.


Jean Da Rolt
email: darolt@lirmm.fr

Amitabh Das
email: amitabh.das@esat.kuleuven.be

Giorgio Di Natale
email: dinatale@lirmm.fr

Marie-Lise Flottes
email: flottes@lirmm.fr

Bruno Rouzeyre
email: rouzeyre@lirmm.fr

Ingrid Verbauwhede
email: ingrid.verbauwhede@esat.kuleuven.be

A Scan-based Attack on Elliptic Curve Cryptosystems in presence of Industrial Design-for-Testability Structures

Keywords: Scan-based attacks, Elliptic Curve Cryptography, Design-for-Testability, Montgomery Ladder, Test compression I

This paper presents a scan-based attack on hardware implementations of Elliptic Curve Cryptosystems (ECC). Several up-to-date Design-for-Testability (DfT) features are considered, including response compaction, X-Masking and partial scan. Practical aspects of the proposed scan-based attack are described, namely timing and leakage analysis that allows finding out data related to the secret key among the bits observed through the DfT structures. We use an experimental setup which allows full automation of the proposed scan attack on designs including DfT configurations. We require around 8 chosen points to implement the attack for retrieving a 192-bit scalar.

INTRODUCTION

Scan chain side-channel attacks exploit the scan chain DfT infrastructure inserted for testing a security circuit. Even if cryptographic algorithms are proven to be secure, accessing intermediate states via the test facilities compromises their strength. Testing ensures the product quality and is essential in secure ICs since design bugs may compromise the security. However, scan chains open a backdoor or side-channel through which secret information inside the chip leaks.

One of the scan-based attacks proposed in the literature, targets the ECC algorithm [START_REF] Nara | Scan-based attack against elliptic curve cryptosystems[END_REF]. This attack relies on the assumption that the circuit contains a single scan chain. In actual designs this assumption is not realistic, since more complex DfT methods are required for meeting the design requirements and reducing the test cost. Techniques such as multiple scan chains, pattern decompression, response compaction and filters to increase tolerance to unknowns are nowadays current practices in the test infrastructure. These structures are often supposed to behave as countermeasures against scan attacks, due to the apparent reduction on the observability of internal states, as proposed in the Mentor Graphics Whitepaper [START_REF]High Quality Test Solutions for Secure Applications[END_REF] and by Liu et al. [START_REF] Liu | Effects of Embedded Decompression and Compaction Architectures on Side-Channel Attack Resistance[END_REF].

Breaking the continuity of the scan chains after manufacturing test, known as unbounding, is also not suitable. This is so since the in-field debug and test capability of the device, required for code or firmware upgrades during the lifetime of a product, is lost. Unbounding requires the use of fuses in the scan path which can be both expensive in terms of cost and area. Moreover, even if the scan chains are unbounded, probing attacks can be mounted on parts of the scan chains [START_REF] Kömmerling | Design Principles for Tamper-Resistant Smartcard Processors[END_REF]. Additionally, for satisfying the higher levels of Common Criteria for Information Technology Security Evaluation [START_REF]Common Criteria for Smart Cards[END_REF], the device must be testable, which can be guaranteed through scan testing.

As presented in [START_REF] Da Rolt | A New Scan Attack on RSA in Presence of Industrial Countermeasures[END_REF], scan-based attacks are effective against RSA implementations. In this paper, we target ECC implementations reusing the same attack algorithm adapted for the purpose. We describe all the issues in carrying out the attack in the presence of test compression, X-Masking and other advanced DfT methods and how to overcome them. Additionally, we prove its feasibility by empirically performing the attack on an ECC design in presence of such DfT structures. Moreover, the attack may be applied without knowledge of the DfT structures, which makes the attack more realistic.

The rest of the paper is structured as follows. Section II gives an overview of scan attacks and countermeasures previously described in the literature. General aspects of ECC are presented in Section III, with a description of the ECC hardware components targeted by the scan attack. It also contains our attacker model. Section IV describes the assumptions taken by the proposed attack as well as the scan attack principles and the differential attack mode. The new scan attack on DfT implementations and details of the practical aspects of the attack are presented in Section V. The tool developed for practical implementation of the proposed attack is described in Section VI. The experimental results of the scan attack on different DfT configurations are reported in Section VII. Finally, we conclude the paper with future work in Section VIII.

II. RELATED WORK

A. Scan Attacks

Scan attacks first appeared for symmetric-key implementations. The first work [START_REF] Yang | Scan based side channel attack on dedicated hardware implementations of Data Encryption Standard[END_REF] in this domain was directed against a Data Encryption Standard (DES) block cipher. Yang et al. presented a two-step process starting with finding the position of the intermediate registers in the scan chain, and then extracting the DES first round key using only three chosen plaintexts. This was followed by a scan attack on the Advanced Encryption Standard (AES) [START_REF] Yang | Secure Scan: A Design-for-Test Architecture for Crypto Chips[END_REF] employing differential analysis. The attack proposed in [START_REF] Yang | Secure Scan: A Design-for-Test Architecture for Crypto Chips[END_REF] has the advantage that it does not need finding out the position of the intermediate registers. In [START_REF] Da Rolt | Are advanced DfT structures sufficient for preventing scan-attacks?[END_REF] authors propose a scan attack based on differential analysis to cope with multiple scan chains, linear compaction and mask decoders. Some scan attacks have been proposed against stream ciphers [START_REF] Liu | Scan-based Attacks on Linear Feedback Shift Register Based Stream Ciphers[END_REF]. The authors demonstrate that the scan chain structure of Linear Feedback Shift Registers used as stream ciphers may be determined and then it may compromise the device security.

Public-key ciphers have also been proven to be vulnerable to scan attacks. The scan attack on RSA in [START_REF] Satoh | Scan-based side-channel attack against RSA cryptosystems using scan signatures[END_REF] targets the Binary exponentiation algorithm. Similarly, the scan attack on ECC in [START_REF] Nara | Scan-based attack against elliptic curve cryptosystems[END_REF] is directed at the Montgomery multiplication method. Additionally to these works, in [START_REF] Da Rolt | A New Scan Attack on RSA in Presence of Industrial Countermeasures[END_REF] authors proposed a scan attack on RSA that deals with DfT structures such as response compaction.

B. Comparision with previous works

As far as we know the only scan attack that targets ECC is described in [START_REF] Nara | Scan-based attack against elliptic curve cryptosystems[END_REF]. It considers a single scan path and it does not take into account the effect of other secret dependent FFs on the scan chain that may complicate the attack. In our proposed attack, we perform a detailed leakage analysis and work in differential mode. Our scan attack is successful even if there are other FFs that change their values along with the intermediate register of interest. Additionally, we require less number of messages to find the ECC secret key compared to [START_REF] Nara | Scan-based attack against elliptic curve cryptosystems[END_REF]. The attack in [START_REF] Nara | Scan-based attack against elliptic curve cryptosystems[END_REF] requires 29 points on an average and 35 points in the worst case to find a 163-bit ECC secret scalar. Our attack, on the other hand, requires 8 points on an average to retrieve a 192-bit secret scalar.

In comparison to [START_REF] Da Rolt | Are advanced DfT structures sufficient for preventing scan-attacks?[END_REF], which also considers advanced DfT structures on symmetric-key ciphers, our work focus on public-key primitives. Since the structure of public-key algorithms is different than symmetric key ones, we need to apply a different approach. For instance, public-key algorithms usually perform an initial operation that involves the register that stores secret data, but this initial operation is not related to the key. This can be used to identify the position of the secret data in the scan chains. The same approach cannot be applied for symmetric key ciphers.

The principle of the attack presented here is similar to the one presented in [START_REF] Da Rolt | A New Scan Attack on RSA in Presence of Industrial Countermeasures[END_REF]. It has been adapted for ECC instead of RSA implementations. The target algorithm is a Simple Power Analysis (SPA) resistant Montgomery Ladder, instead of the Montgomery exponentiation (not SPA-resistant) targeted in [START_REF] Da Rolt | A New Scan Attack on RSA in Presence of Industrial Countermeasures[END_REF]. Additionally, in this paper we provide more results depending on different compaction ratios.

C. Scan-based attack Countermeasures

Scan-based attack countermeasures may be classified into three different categories: (1) methods to control the access to the test facilities through the use of secure test wrappers [START_REF] Das | Challengeresponse based secure test wrapper for testing cryptographic circuits Test Symposium[END_REF]; (2) methods to detect unauthorized scan operations [START_REF] Hely | Secure scan techniques: a comparison[END_REF] such as probing and other invasive attacks;

(3) methods that provide confusion of the stream shifted out from the scan outputs [START_REF] Hely | Secure scan techniques: a comparison[END_REF]. Additionally, it was suggested in [START_REF]High Quality Test Solutions for Secure Applications[END_REF] and [START_REF] Liu | Effects of Embedded Decompression and Compaction Architectures on Side-Channel Attack Resistance[END_REF] that advanced industrial DfT methods such as response compaction are enough to impede any attack. However authors [START_REF] Liu | Effects of Embedded Decompression and Compaction Architectures on Side-Channel Attack Resistance[END_REF] do not consider differential scan-based attacks, and therefore they suppose that identifying registers that store secret data is not feasible. Advanced attacks [START_REF] Da Rolt | Are advanced DfT structures sufficient for preventing scan-attacks?[END_REF] have been conceived to hack AES ciphers even in presence of linear compactors.

III. ELLIPTIC CURVE CRYPTOSYSTEMS

For public-key cryptographic implementations, ECC provides equivalent security to RSA with much smaller key sizes (160-bit ECC equivalent to 1024-bit RSA). An elliptic curve E over prime fields may be defined as the set of points P(x, y) satisfying an elliptic curve equation of the form: y 2 mod p = x 3 + ax + b mod p, where x, y, a and b belong to a finite field F p and p is a prime number.

In this paper, we are using the 192-bit NIST ECC curve and work in prime fields (F p ), where the curve parameters used in our ECC implementation are obtained from [START_REF] Hankerson | Guide to Elliptic Curve Cryptography[END_REF].

ALGORITHM I. MONTGOMERY LADDER FOR ELLIPTIC CURVE CRYPTOGRAPHY

Inputs:

k = (1, k m-2 , . . . , k 1 , k 0 ) 2 , P ∈ E(F p ) Output: Q 0 = k.P 1: Q 0 ⇐ P 2: Q 1 ⇐ 2P 3: for i = m -2 to 0 do if ki =0 Q 1 = Q 0 + Q 1 , Q 0 = 2 Q 0 else Q 0 = Q 0 + Q 1 , Q 1 = 2 Q 1 end if 4:
end for 5:

return Q 0

The scalar or point multiplication of P with k is generally performed using the Montgomery Powering Ladder [START_REF] Montgomery | Speeding the pollard and elliptic curve methods for factorizations[END_REF] (shown in Algorithm I). This is one of the most efficient methods of performing scalar multiplication. This is so since it does not require any extra storage and has fast calculation times compared to other methods, thus allowing its efficient implementation. Also in this algorithm, a point addition and doubling operation are performed in each iteration of the main loop, making it resistant to simple power analysis attacks.

A. Attacker Scenario

The attack proposed in this paper can be classified as chosen-point attack, where the attacker knows the point P. We consider the case that the attacker can observe the result of each ECC point multiplication with help of the DfT structure. The base point is assumed to be stored in nonvolatile memory (ROM) while the scalar for the point multiplication is stored in RAM, as it keeps on changing. This is the usual case with smart-card implementations.

We consider various scenarios where the ECC point multiplication result can be observed or controlled. In these cases, we perform our scan attack on the ECC point multiplication at a certain point in the execution of one of the cryptographic protocols employing ECC. For instance, in the signature generation phase of the Elliptic Curve Digital Signature Algorithm (ECDSA) algorithm, knowing scalar 'k' in the generation of (x1, y1) = k.G (G is the base point) which is used to derive the signature, r = x1 mod n, we can deduce part of the secret. Another possible case is Elliptic curve based static Diffie-Hellman (ECDH) Key Exchange which is normally used to setup the session key for communication employing symmetric-key encryption. Here, the target of our attack will be generation of the public-key for the two communicating parties (x A .G or x B .G), which is actually an ECC point multiplication of the scalar secret keys with the generator base-point.

B. ECC Implementation

As seen in Algorithm I, a point multiplication is performed through a series of point addition (Q 0 + Q 1 ) and point doubling (2 Q 0 or 2 Q 1 ) steps. We perform both point addition and point doubling in projective coordinates for avoiding the costly modular inversion operation. In projective coordinates, Q 0 and Q 1 cost each three 192-bit register (Q 0 [X], Q 0 [Y] and Q 0 [Z] and so on). There are various methods of performing point addition and doubling. We have used the 1998 Cohen-Miyaji-Ono mixed coordinates [START_REF] Cohen | Efficient Elliptic Curve Exponentiation Using Mixed Coordinates[END_REF] for point addition, and 2007 Bernstein-Lange formulae [START_REF] Bernstein | Analysis and optimization of elliptic-curve single-scalar multiplication[END_REF] for point doubling from the Explicit Formulae database [START_REF]Explicit Formula Database for Jacobian coordinates with a4=-3 for short Weierstrass curves[END_REF].

Irrespective of the implementation method, intermediate values Q 0 and Q 1 are temporarily stored in flip-flops (FFs) to be available at the next iteration step. These FFs are referred to as Secret Flip-Flops (SFFs) in the rest of this paper and will be the target of our scan attack.

IV. PRINCIPLES OF SCAN ATTACKS

A. Assumptions of Scan Attacks

The scan attack proposed in this paper relies on some assumptions:

 the cryptographic algorithm is known;  the scan chain structure is not known to the attacker. However, the input/output test pins are controllable;  it is possible to control the scan enable pin and also to switch from functional mode to test mode, which allows the cipher operation to be interrupted at any moment;  it is possible to control the cipher inputs and to observe the values related to the intermediate states by means of scan out;

B. Differential Scan Attack

Contrary to the previous ECC scan attack, our approach works in the presence of test compression and X-masking. We use the differential mode [START_REF] Yang | Secure Scan: A Design-for-Test Architecture for Crypto Chips[END_REF] [START_REF] Da Rolt | Are advanced DfT structures sufficient for preventing scan-attacks?[END_REF] to overcome the obscurity caused by response compactors inserted by most of the industrial DfT tools. Fig. 1 shows a crypto core, its cipher plaintext, and the intermediate register that is inserted in a multiple scan chain circuit with response compaction. The rest of the circuit is not shown to give a more clear description. Real scenarios where other circuit registers are present are discussed in Section V.

Boxes S0 to S11 represent the 12 SFFs in intermediate register. Due to the response compaction, the test response R1 stores the parity of S0 to S3 (slice 1), R2 stores the parity of S4 to S7 (slice 2) and R3 stores the parity of S8 to S11 (slice 3). It means that the actual value stored in any of these SFFs is not directly observable at the test responses. However, a difference in one of these SFFs implies a difference on the slice parity and hence at the response. This can be exploited by the attacker.

In the differential mode, a pair of plaintexts (points in the case of ECC) is applied, for example (P 0 , P 1 ). The circuit is first reset and the message P 0 is loaded. Then after N clock cycles of mission mode (N depending on the cryptographic implementation), the circuit is halted and the intermediate register state I 0 is shifted out. The same procedure is repeated for the message P 1 for which I 1 is obtained.

Let the Hamming distance between I 0 and I 1 be equal to 6, as shown in Fig. 1. In this example highlighted boxes represent a bit flip between I 0 and I 1 . We also suppose that the bits S0, S5, S6, S7, S8 and S10 are flipping. The parity of the differences at the intermediate register is equal to 0, since the Hamming distance is even. The flip at S0 is sensed at the test response R1. R2 flips due to odd number of flips at slice 2, while R3 does not flip since slice 3 has an even number of flips.

The parity of flips in the intermediate register matches with the parity of flips at the output of the response compactor. This comes from a basic property of this kind of response compactors: the parity of the Hamming Distance at the test output is equal to the parity of the Hamming Distance at the intermediate register. This property is valid for any possible configuration of scan chains (number of scan chains versus slices). Additionally it is also valid for compactors with multiple outputs. In this case, the measured parity should consider all compactor outputs. Thus using the differential mode the attacker may observe differences in the intermediate register, leading to a security breach.

V. DISTINGUISHING ATTACK

In this section, we show how the parity may be used as a distinguisher in order to retrieve the secret key using a chosen point attack. We first consider that the SFFs are inserted in the scan chain. Then, in Section V.A the practical aspects of leakage analysis are shown, for instance, when there are other FFs changing with the SFFs in the scan chains, or when not all of the SFFs are on the scan chains.

As presented in Section III, the Montgomery Powering Ladder method consists of repeating point addition and point doubling several times. For each iteration, the value stored in Q 0 is the result of the point doubling if the key bit is 0; otherwise Q 0 stores the result of the point addition. Thus observing Q 0 allows the detection of the current value of the key bit. This procedure must be repeated for the entire key length (192 bits in our example).

In order to detect if Q 0 stores the value of the point addition or the value of the point doubling, Q 0 must be scanned out. Additionally, as explained in the Section V.B, differential attacks use pairs of plaintexts to overcome the obscurity due to response compaction. In the case of ECC, plaintexts are actually the input points. This pair must be properly chosen so that a difference on the parity of Q 0 would lead to the key bit. The process to derive 'good' pairs of points is shown in Fig. 2: These useful pairs are software generated. First, a random pair of 192-bit points is generated using a software pseudo-random number generator. We denote them here as (P 0 , P 1 ). Then, the corresponding output responses (after one iteration of the multiplication algorithm) are computed for each of these points assuming the current key bit to be '0' (Hypothesis Hyp 0 ) or '1' (Hypothesis Hyp 1 ). Let R ij be the response to point P i with a current key bit j. For instance, (R 00 , R 01 , R 10 , R 11 ) are the responses to points P 0 and P 1 for key bit '0' and '1' respectively. Let Parity(R 00 ), Parity(R 01 ), Parity(R 10 ) and Parity(R 11 ) be the parities of these responses.

Let D 0 be the Hamming distance between Parity(R 00 ) and Parity(R 10 ) and D 1 be the Hamming distance between Parity(R 01 ) and Parity(R 11 ). If D 0 ≠ D 1 , then the points (P 0 , P 1 ) are taken to be useful, otherwise they are rejected because the value of the current key bit cannot be deduced from the responses to (P 0 , P 1 ). This process is thus repeated till a pair of 'good' points is obtained.

After a good pair of points is calculated, it may be applied to the actual circuit. For both elements of the pair, the application is executed in mission mode for the number of clock cycles corresponding to the targeted step (key bit). Then, switching to test mode, the scan contents are shifted out and the difference of parities at the test output bitstream is measured. If it is equal to D 0 , then the hypothesis 0 is correct and the secret key bit is 0. If it is equal to D 1 , then the secret key bit is 1. This procedure is repeated for all the bits of the secret scalar. Fig. 3 depicts an example of good pair choice. The points P 0 to P 7 represent a set of points which contains at least one pair that verifies the good pair property for each bit of the secret key. I 0 to I 6 represents the intermediate register Q 0 (or Q 1 depending on the attack target). As it can be seen, for retrieving the first bit of the key, the attacker needs a single pair of points (P 1 , P 6 ). Then for retrieving the second bit of the private key, if the pair (P 1 , P 6 ) does not satisfy the good property, then a third point must be added to the set of points, that satisfies the good property when combined with at least one of the previous pairs (P 1 or P 6 ). In this case P 4 verifies the good property with P 6 . Verifying the good property of a new point against all the previous points reduces the number of required points drastically. Theoretically, the probability of verifying the good property for each bit of the secret key given a set with n points is:

( ) ( )
Suppose n equal to 9, the probability of finding the good property is 94.44%.

A. Practical Aspects: Leakage Analysis

In the procedure above we assumed that the entire state of Q 0 is inserted at the scan chain (Q 1 can be targeted as well without any additional issue) and that there are no other flipflops in the scan chain. However, in presence of partial scan or X-Masking logic, which is used to prevent unpredictable internal states that can corrupt the test output [START_REF] Mitra | X-compact: an efficient response compaction technique for test cost reduction[END_REF], part of the Q 0 register may be filtered and thus not totally observable. In addition, scan chains may include scan FFs not related to the crypto core. We detail here the proposed attack in such cases. Fig. 4 shows a design containing three types of FFs, depending on the value they store. UFFs correspond to the other cores in the design that store data unrelated to the secret. SFFs belong to the registers directly related to the intermediate register, which store information related to the secret key. DFFs store data related to the cipher but not the intermediate registers themselves (such as input/output buffers or other cipher registers). The leakage, if it exists, concerns the SFFs. Fig. 4 shows examples of different scenarios of test responses that are classified in three main cases:

1) Useless responses Useless responses are the ones that are not related to the secret. In other words, the response depends only on UFFs (it is the case of R6).

2) Exploitable responses Exploitable responses are the ones that depend only on SFFs or on SFFs plus UFFs (like R3 and R5). The attacker can observe SFF flips at these response bits. It must be noticed that UFFs present no difference since the "other inputs" are kept constant during all the differential procedure.

3) Non-exploitable responses Non-exploitable responses are the ones that depend at least on one DFF (like R2, R4 and R1). The attacker cannot observe SFF flips due to the presence of DFFs that are affected by the plaintext input whose logic is not supposed to be known. Section 5.B describes the reasons for not considering this as an inherent countermeasure. The goal of the leakage analysis is to find out if a particular bit of the intermediate register (SFF) can be observed at one of the test response bits. Thus the analysis is focused on a single SFF at a time, looking for an eventual bit flip. In our example, we start with S0. We denote S0 i N as the value stored in S0 after N clock cycles while the design is running in mission mode from the point P i (the first event in mission mode is a reset). Similar definitions hold for the other scan FFs. In order to find out which test response bit is related to S0, we use the differential procedure described in Section IV.B with a special set of pairs (P i , P j ) 0 with the following property:

(P i , P j ) 0 : S0 i N ≠ S0 j N
, and SX i N = SX j N for X = 1 to 3.

In other words the pairs (P i , P j ) 0 cause a single bit flip on the SFFs (in this case: S0), as highlighted in Fig. 4. Unfortunately, S0 is compressed with D4 that may eventually flip for the pair (P i , P j ) 0 and thus mask the S0 flip. This is a case where R3 is not exploitable and thus differences on S0 are not observable.

If we repeat the same procedure for S1, S2 and S3, with respective set of pairs (P i , P j ) 1 (P i , P j ) 2 (P i , P j ) 3 , we will notice that the only test response bits that always change are R3 and R5 (they are not masked by any DFF).

In the case of ECC this method must be repeated for all the intermediate register bits (192 times), until one leakage is found. It must be noticed that all the 192 bits of the intermediate register depend on the secret scalar. Thus observing at least one of them through the test response allows the attacker to retrieve the secret (using the good pairs described in Section V).

Finding set of pairs (P i , P j ) X is rather easy since the first two operations to be executed in Algorithm I are independent of the key, but the results are stored in the intermediate register.

It must be noted that in SoC designs, each IP is probably compliant with the IEEE 1500 wrapper. It allows access to single IPs, and thus it may help the attacker to focus only on the cryptographic IP.

B. Inherent Countermeasure

It must be noticed that the case "Non-exploitable responses" described in Section V.A may be eventually considered as an inherent countermeasure against scan attacks: if each SFF is in the same slice as a DFF. However, this solution contains two drawbacks. The first one is that it is not easily implementable because the position of the scan flip-flops is set by place and route (P&R) tools, and choosing the position at will requires internal modification of that design step. The second and most important issue concerns the security of this solution. In Section V.A we supposed that the attacker does not known the relationship between DFFs and the plaintext, in order to propose an attack that does not depend on deep knowledge of design details. There may be attackers that have this kind of information, which would compromise this countermeasure; however this is a case of security by obscurity.

C. Timing Estimative

The scan-based attack on ECC is targeted at finding the secret scalar (192-bits in our case). It is crucial to find the exact time to scan out the contents of the intermediate registers using the scan chains.

Since the same hardware is commonly used for both encryption and decryption, we can run a second hardware with a known scalar in order to get the timing estimations.

For instance, the attacker must find out the number of clock cycles that a pair of point operations takes. For our target Montgomery Powering Ladder, it is the sequence of point addition and doubling operations. With a known scalar, we know the number of point operations required for the addition and doubling operations of the ECC point multiplication (Algorithm I). Dividing the total time of execution for this multiplication by the number of pairs of operations gives the approximate time required for one combined point addition and doubling operation. Then using repeated trial-and-error steps of comparing the actual output with the expected result after one pair of point operations, it may be possible to find out the exact number of clock cycles required.

VI. SCAN ATTACK EXPERIMENTAL SET-UP

In order to perform the attack in actual designs, we developed a scan attack tool. It has two main features: to find the possible leakage points (as explained in Section V), and to automatically apply the attack method to a given gatelevel netlist of a design. With the help of this tool, the security of several DfT configurations may be analyzed. Besides the attack on ECC explained in this paper, this tool can also comprise of methods to attack RSA [START_REF] Da Rolt | A New Scan Attack on RSA in Presence of Industrial Countermeasures[END_REF], as well as AES. More details on the attack tool can be found in [START_REF] Da Rolt | A New Scan Attack on RSA in Presence of Industrial Countermeasures[END_REF].

VII. EXPERIMENTAL RESULTS AND DISCUSSION

In order to test the effectiveness of the attack, we implemented a 192-bit ECC algorithm in hardware using the Gezel environment [START_REF]Gezel Hardware/Software Codesign Environment[END_REF], and then synthesized the gate-level design using Synopsys DfT Compiler (v2010.12) with a TSMC 130nm library. The total number of FFs in the design is 3355. Out of these, 855 belong to the UFF type. Q 0 consists of 576 FFs, from which each projective coordinate (Q 0 [X], Q 0 [Y] and Q 0 [Z]) has 192 FFs (SFF type). Q 1 contains 576 FFs as well (also SFF type). And finally 1348 belong to the DFF type (see Section V A). For all the test cases, Synopsys DfT Compiler was used to insert the DfT structures, including decompression/compaction and X-Masking logic. All the runs were performed on a 4 GB Intel Xeon CPU X5460 with four processors.

1) Scan attack timing & number of points

Concerning the attack timing, it consists in two phases: identification of leakage points, as described in Section V A; and the use of these observable points to perform the attack. The first phase takes approximately 49.37 seconds per bit (in average) and the second one takes 49 seconds. 89% of both the timings are due to the design simulation in ModelSIM SE, the remaining time comes from the C++ code execution.

For our test case, we required around 8 points over the elliptic curve to find out the secret multiplier k. In other words, all the necessary good pairs (P 0 , P 1 ) are created from these 8 points.

2) In Presence of DfT Methods

A set of representative DfT configurations for which the scan attack was proven to be effective are shown in Table I. Config. 1 and Config. 2 have no compression structures. Config. 3 and Config. 4 have 120 scan chains and they have compression rate equal to 12 and 24 respectively. Config. 5 shows a test case where X-Masking is activated. In Table I, 'attack successful' means that all the bits of the secret scalar were retrieved.

3) In presence of proposed countermeasures a) In presence of inverters

One of the countermeasures proposed in the literature is the insertion of dummy inverters after some SFFs of the scan chain [START_REF] Sengar | An Efficient Approach to Develop Secure Scan Tree for Crypto-Hardware[END_REF]. This technique aims at confusing the attacker, since the sensitive data observed at the scan chain may be inverted. However, these inverters are placed always at the same location in the scan chain and thus they are completely transparent to differential scan attacks.

The effectiveness of the attack against this countermeasure was validated on the ECC design with Config. 3 of Table I. Two implementations were considered with 1677 and 2516 inverters (50% and 75 % of the overall FFs in the design respectively) randomly inserted in the scan chains. For both cases, the tool was able to find leakage points and then to retrieve the secret scalar.

b) In presence of partial scan Depending on the design, not all the FFs need to be inserted in the scan chain in order to achieve high testability. As proposed in [START_REF] Inoue | Partial Scan Approach for Secret Information Protection[END_REF], partial scan may be used for increasing the security against scan attacks. However, the authors suppose that the attacker needs the whole sensitive register to retrieve the secret key. As was described in Section V, the leakage analysis feature can be used to find out which bits of the sensitive register are inserted in the scan chain. Once these bits are identified, the attack can proceed with only partial information, since each bit of the sensitive register is related to the key.

For evaluating the effectiveness of the scan attack tool in the presence of partial scan, we configured the DfT tool in such a way so as not to insert some of the sensitive register FFs in the scan chain. In the first case, half of the SFFs were inserted in the chain. The tool was able to correctly identify all the leaking bits and then to retrieve the secret scalar. Also in the worst case situation, i.e., where only one secret bit was inserted in a scan chain of a design with multiple scan chains and test compression, the tool was still able to find out the correct secret scalar.

VIII. CONCLUSION

In this paper, we show that the scan-based attack that is useful against RSA implementation can be adapted to work against ECC. Actual gate-level designs with advanced DfT configurations were evaluated against the proposed attack. With the help of our new scan attack setup we retrieved the secret in ECC circuits containing multiple scan chains with linear response compaction and X-Masking. We also experimentally proved the effectiveness of our new attack against some countermeasures proposed in the literature.

Fig. 2 . 1 Fig. 1 .

 211 Fig. 2. Hypothesis Decision

Fig. 3 :

 3 Fig. 3: Finding good set of points

ACKNOWLEDGEMENT This work was supported in part by the Research Council K.U.Leuven: GOA TENSE (GOA/11/007) and by the European Commission through the ICT programme under contract ICT-2007-216676 ECRYPT II. In addition, this work is supported in part by the Flemish Government, FWO G.0550.12N, by the Hercules Foundation AKUL/11/19.