Ha-Duong Minh

Nguyen Hoai Son

Subjective satisfaction and objective electricity poverty reduction in Vietnam, 2008-2018

Keywords: Electricity poverty, Vietnam, Sustainable Development Goals, Indicators Q41, Q48, Q56

We estimate the reduction of electricity poverty in Vietnam. The essential argument is that human development is about subjective feeling as much as technology and income. We use a self-reported satisfaction indicator as complementary to objective indicators based on national household surveys from 2008 to 2018. We found that in 2010, the fraction of households with access to electricity was over 96%. However, over 24% declared their electricity use did not meet their needs. Since 2014 the satisfaction rate is around 97%, even if 25% of the households used less than 50 kWh/month. Today there is electricity for all in Vietnam, but electricity bills weigh more and more in the budget of households. Inequalities in electricity use among Vietnamese households decreased during the 2008-2018 period, but are not greater than inequalities in income, contrary to the findings of Son and Yoon (2020). The subjective energy poverty measure allows better international statistics: unlike poverty or needs-based criteria, self-assessed satisfaction of needs compares across income levels and climates. Engineering and econometric objectivist approaches dominate the literature on sustainability monitoring. Out of 232 Sustainable Development Goal Indicators, only two are subjective. Yet our findings show that subjective indicators tell a different part of the story. Grid building is only a mean, the end is a meaningfull provision of power to satisfy the needs.

Introduction

The seventh United Nations Sustainable D evelopment G oal (SDG7) is: Ensure access to affordable, reliable, sustainable and modern energy. In short, Affordable and clean energy is one of our overarching civilization goals this millennium. Statisticians usually measure progress towards SDG7 using objective indicators based on electricity distribution and consumption data. This text argues that objective indicators are not enough. Human development is an issue of subjective feeling as much as a question of technology or economics. Based on national household surveys, self-reported satisfaction indicators offer a complementary perspective to understand society's energy poverty situation more fully.

Vietnam is a Southeast Asia country comprising almost a hundred million people. Its GDP per capita, purchasing power parity, was 8 397 USD in 2019 (World Bank database, accessed 2021-05-22). Vietnam's development has been highly successful in economic terms. In constant local currency, GDP grew by 541% from 1986 to 2019. Table 1 provides more details on the country's trajectory. Vietnam's rural electrification program is oft-cited as an outstanding success in providing energy access [START_REF] Đoàn | Vietnam Rural Electrification Programme[END_REF]Asian Development Bank. 2011). However, in the considerable academic literature on energy poverty, we found few studies about Vietnamese households among the reports on China, India, Brazil and South Africa [START_REF] Li | A Bibliometric Analysis of Energy Poverty Research: Results from SCI-E/SSCI Databases[END_REF][START_REF] Sovacool | Evaluating Energy Security Performance from 1990 to 2010 for Eighteen Countries[END_REF][START_REF] Baltruszewicz | Household Final Energy Footprints in Nepal, Vietnam and Zambia: Composition, Inequality and Links to Well-Being[END_REF]).

Lê Việt Phú (2020) investigated the residential electricity demand in Vietnam using a different microdata source, the 2015 VHRS World Bank survey. He found that demand is elastic to average and marginal prices and confirmed that income elasticity is positive. We will look at the residential demand from a different perspective -energy poverty-using different data: the Vietnam Households Living Standard Surveys (VHLSS) from 2008 to 2018. [START_REF] Son | Reducing Energy Poverty: Characteristics of Household Electricity Use in Vietnam[END_REF] examined the determinants of inequality in Vietnamese households electricity consumption, using VHLSS data from 1993 to 2004. Inequality can be defined, at the population level, by how much the statistical distribution of consumption deviates from the uniform distribution. They found that a) electricity consumption increased more than proportionally with income, and b) the inequality of electricity consumption was larger than income inequality. The grid expanded continuously from 1993 to 2004, increasing electricity access. Son and Yoon warned that increasing access could increase inequality as the wealthier households benefited more from the opportunity. Those who cannot afford to buy electric appliances benefit less from rural electrification. Our analysis of more recent data corroborates their first finding: electricity use increased faster than income between 2008 and 2018. We do not confirm their second finding. In 2018, electricity consumption inequality seemed comparable to or less than income inequality (see Supplementary_Figure 5).

Analyzing the evolution of Vietnamese households energy consumption from 2004 to 2016, T. T. [START_REF] Nguyễn | Energy Transition, Poverty and Inequality in Vietnam[END_REF] found that "Electricity poverty has decreased, but energy-cost poverty has increased." Our analysis vindicates these findings. We clarify and confirm the discrepancy between electricity poverty and electricity-cost poverty using more recent data. This manuscript's outline is as follows. We contrast the objective and subjective perspectives used to observe electricity poverty in section 2. Then we present the data and methods in section 3 before looking at Vietnamese households' electricity use over 2008-2018 from three points of view in section 4-6:

• The engineering perspective looks at grid access and kWh consumed.

• The economic perspective looks at income and expenditures.

• The subjective perspective looks at satisfaction with electricity consumption.

Then we discuss the interactions between the three perspectives ins section 7. Our findings highlight how much the subjective indicator complements objective engineering or economic indicators. Section 8 discusses the results and policy implications, comparing with other ASEAN countries. Finally, section 9 summarizes and concludes.

What is access to clean and affordable energy for all?

The Sustainable Development Solutions Network (SDSN 2015, 137-40) defined four performance indicators to assess progress towards the Sustainable Development Goal 7

« Ensure access to affordable, reliable, sustainable, and modern energy for all » :

• Indicator 50: Share of the population with access to modern cooking solutions (%)

• Indicator 51: Share of the population with access to reliable electricity, by urban and rural (%)

• Indicator 52: Implicit incentives for low-carbon energy in the electricity sector (measured as US$/MWh or US$ per ton avoided CO2)

• Indicator 53: Rate of primary energy intensity improvement While all four dimensions of SDG7 matter, this manuscript focuses specifically on the aspect measured by indicator 51, about access to reliable electricity. We distinguish three perspectives on access to electricity. The engineering perspective sees access as the presence of the distribution network. The economic perspective focuses on affordability.

Finally, the subjective perspective focuses on whether the users feel that their electricity needs are satisfied. This section argues that the subjective perspective answers many problems found in the economic literature on energy poverty. [START_REF] Atkinson | Poverty[END_REF] explains that poverty can be seen as a concern about basic needs, which are multidimensional: food, housing, and clothing. Under this viewpoint, energy poverty can be seen as deprivation of the energy needs for survival. Energy-poor households cannot afford to fight cold in winter or heat in summer. How can we measure the magnitude of energy poverty in a given country? In the subjective perspective, this is straightforward: use a survey asking if the household's energy use met their needs in the last month. The economic perspective is more complex than that. Consider three different approaches to define and measure energy poverty:

The first approach is to estimate "basic needs" directly by calculating the minimum energy services required for a household. [START_REF] Bravo | A First Approach to Defining Basic Energy Needs[END_REF], cited in [START_REF] He | Electricity Demand and Basic Needs: Empirical Evidence from China's Households[END_REF], enumerate energy needs to prepare and preserve food and supply of water; for space conditioning; personal cleanliness; and recreation and social communication. [START_REF] Pachauri | On Measuring Energy Poverty in Indian Households[END_REF] computed the power requirements for energy services of a five-member household such as "scooter 5km/day", "Lighting, one electric bulb (5h/day, 40W)" "Lighting, 1-2 kerosene lamps".

This basic needs direct estimate approach is appropriate on a case-by-case basis, at the scale of communities, but not for international statistics. Different societies have different views on what kinds of energy services constitute basic needs. Needs vary with climate, region, household demography and even ethnocultural habits [START_REF] Pachauri | On Measuring Energy Poverty in Indian Households[END_REF].

Asking experts about the local conditions is open to subjectivity and lack legitimacy.

The second approach sets up absolute thresholds for the total amount of energy consumption regardless of the consumption components. Energy-poor households consume less than X kWh per year, where X depends on the country's economic conditions. [START_REF] Foster | Latin America and Caribbean Regional Studies Program[END_REF] define the threshold as the average energy consumption of households having expenditure per capita within 10% of the official poverty line.

This approach is convenient. A poverty line is readily available in every country. However, the underlying assumption that income-poor households are also energy-poor households is not always valid [START_REF] Khandker | Are the Energy Poor Also Income Poor? Evidence from India[END_REF].

The third approach sets up relative thresholds. Energy-poor households are those spending more than X % of their income on energy bills. DTI (2007) states that a household is in energy poverty if it spends more than 10% of its income on paying the energy bill, including electricity and fuel for heating and cooking, excluding transportation. This threshold has been set out officially in the U.K. Fuel Poverty Strategy 2001, according to the critical study by [START_REF] Hills | Getting the Measure of Fuel Poverty: Final Report of the Fuel Poverty Review[END_REF]. France also used this approach, according to ONPE (2016).

This approach is convenient. It allows assessing the magnitude of the energy affordability issue from national-scale statistics. Unfortunately, the approach has fatal flaws. The ratio is quite arbitrary; there are no universal norms on the share of electricity in a household budget. Moreover, many consumers with a relatively high energy bill are affluent households living large, while many poor households have a low energy bill because they use non-commercial biomass.

The three approaches to energy poverty reviewed above are based purely on energy quantities, monetary indicators or their combination. They all come from an engineering or econometric approach. In order to fix their theoretical problems, researchers and practitioners have proposed more sophisticated objective approaches. Hill (2012) led the U.K. to replace the 10 % of income criteria by a new definition under which households are considered fuel poor if a/ They have required fuel costs that are above the median level, and b/ Were they to spend that amount they would be left with a residual income below the official poverty line. Econometric approaches based on electricity demand elasticity were explored in [START_REF] Khandker | Are the Energy Poor Also Income Poor? Evidence from India[END_REF] for energy poverty in Bangladesh, [START_REF] He | Electricity Demand and Basic Needs: Empirical Evidence from China's Households[END_REF] for electricity poverty in China, and Nguyen (2019) for electricity poverty in Vietnam.

Finally, Multidimensional Energy Poverty Indices were proposed by [START_REF] Nussbaumer | Measuring Energy Poverty: Focusing on What Matters[END_REF][START_REF] Foster | Latin America and Caribbean Regional Studies Program[END_REF][START_REF] Pachauri | On Measuring Energy Poverty in Indian Households[END_REF], and the Multitier Matrix for Measuring Access to Household Electricity Supply proposed by [START_REF] Bathia | Beyond Connections : Energy Access Redefined[END_REF].

In contrast to these objective approaches, the subjective perspective is more straightforward. It defines the quality of energy services by the satisfaction of their users, not in terms of electricity or money quantities measured from outside. We argue that concerning indicator 51, the definition Share of households replying positively to the question "In the last month, did your consumption of electricity meet the needs of your household?" is as operational as the classical definition "Share of population with access to reliable electricity". The belief that objective engineering / economic indicators are more scientific than indicators based on subjective self-assessment is unfounded.

There is prejudice in the opposition between scientific approaches. The subjective definition prescribes a clear way to measure the phenomenon. Humanities and social sciences have long integrated the need to include the subjects' voice into their research methods, including subjective opinion surveys. Surveys provide objectively repeatable measurements: two independent survey companies applying the same method will find very close results.

The objective approach is not as unambiguous as it may seem. Engineering-based indicators also suffer from imprecision and declaration biases. This is true when collected from declarative surveys and also when collected from electricity bills (fraud exists). The concepts of "reliable" and "access" leave room for interpretation. It is unclear if "access" is only the physical connection to the grid or the economic means to pay for electricity.

Furthermore, "reliable" is vague. Is there a threshold of outage minutes per year? As extreme weather can cause a blackout, at which probability shall access be considered reliable? Do we even have probabilities? Regarding the basic needs approach, to determine the adequacy of someone's habitat objectively, one has to examine its floorplan, building material, insulation, heating, ventilation systems, the local climate, and the age of the inhabitants. It is much simpler just to ask.

Leaving it up to respondents to assess the "needs of your household" resolves the central problem of defining a "basic needs" level. Households themselves know best if their electricity needs were met. Multidimensional Energy Poverty Indexes rely on normative aggregation methods that are hard to justify, whereas households have the legitimacy to integrate the different aspects of their energy consumption experience. Rebound effects in rural electrification projects show that needs are subjective and relative. Human needs expand with economic development.

Contrary to objective and absolute definitions of basic needs, indicators defined by selfassessed satisfaction of needs can be used at different income levels, within and across countries. Ensuring access to modern energy for all -the SDG7 -does not mean bringing the grid close to every house, as Indicator 51 measures. It means everyone actually receives a sufficient provision of energy services.

Data and method

In light of the previous discussion, we will examine progress towards SDG7 in Vietnam using three approaches. From an engineering point of view, we will look at access and quantity of electricity consumption. From an economic point of view, we will look at the share of electricity in the household budget. From a subjective point of view, we will look at the electricity customer satisfaction, in the form of the answer to the question "In the last month, did your consumption of electricity meet the needs of your household?".

The data used to produce all results presented below come from periodic national In 2008 the survey had two waves lasting two months each, starting in May and September.

In 2014 there were four waves of one month, in March, June, September and December.

This reduces the seasonality bias of energy consumption. Assignment of households into waves was random.

The question on needs met was asked in 2010, 2012, 2014 only.

We did not weigh answers, de-bias or otherwise adjusted the data except by clipping outlying values and dropping missing responses. Clipping does not affect the counts and quantiles, but non-responses are known to affect survey results. We were not involved in the data collection.

The results we present below are subject to systematic and random errors unavoidable in all survey data [START_REF] Kasprzyk | Measurement Error in Household Surveys: Sources and Measurement[END_REF]. We did not attempt to quantify these errors formally, but we hereby forewarn that in the numbers presented below, the third digit is not policyrelevant. It is meaningful mathematically only.

We drew the maps in Figure 1 and 4 without tone intensity correction for province size and province population: they reflect energy poverty levels within a province. Thus, a large grey area does not imply that a large number of people are impacted since provinces in remote mountains are less densely populated than provinces in the river deltas.

The engineering view: is electrification complete?

Much has changed since (A. T. [START_REF] Nguyễn | Analysis of Household Energy Demand in Vietnam[END_REF] analysis of household energy demand based on a 1992 survey conducted in four provinces. At that time, 91% of the energy used by households was for cooking and pig feed. Cooking was mostly with coal and residues; electricity was used by less than 2% of rural households, 6% of urban households.

Households commonly used both kerosene and electricity for lighting. This contrasts with the more recent survey by (V. T. To revisit these numbers in 2018, we used answers to the survey question: "What is the main lighting mean in your household?" with possible choices: 1. National-grid electricity, 2. Battery or generator or small-scale hydroelectricity, 3. Gas, oil lamps of various kinds, 4. Other. Figure 1 shows the percentage of households who did not choose option 1. This is a proxy for the state of electrification over 2008-2018. It shows that the situation in the northern mountainous regions of Vietnam has improved over the last ten years, without complete resolution. There are still not many roads in these areas. The cost of these grid connections is high compared to the number of households serviced.

Concerning the overall population, our analysis shows that in 2010, 96.5% of households in Vietnam used grid electricity for lighting. This number increased to 98.9 % in 2018. Our estimate for 2018 is close to the 99.1 % published in (General Statistics Office 2019, 500);

and coherent with (EVN 2019, 14, 19) statement that "EVN provided 100% of communes, more than 99% of rural households, and 11/12 districts of islands with electricity access".

Considering that the population is 94,7 million and that households without access are likely to have more members than the national average, we estimate that the number of people without electricity access in Vietnam was still about one million in 2018. The number of people without access has declined slowly over the period, as Doan Van Binh's statement remains relevant. The positive way to see the evolution is that the number of people with access increased as fast as the population, almost one million per year.

Figure 2 shows the amount of electricity the households declared using in the last month.

In 2018, the median amount of electricity usage was 139 kWh per month, and the first quartile was 81 kWh. In other words, that year, out of four Vietnamese households, one used less than 81 kWh per month, and another used between 81 kWh and 139 kWh. Over the 2010-2018 period, the distribution shifted to the right towards higher quantities. The median electricity consumption per Vietnamese household in the surveyed month went from 74 kWh to 139 kWh in these eight years.

Over that period, the use of electricity by Vietnamese households moved towards a more uniform distribution. As apparent in Supplementary_Figure 5, inequality in electricity use reduced faster than inequality in income during that period.

The economic view: is electricity affordable for all?

Figure 3 shows the electricity tariffs in Vietnam from 2004 to 2018. There are many curves because the tariff is an increasing staircase function: the more one consumes electricity, the higher the marginal tariff. In 2010, for example, consumers paid electricity 600 VND/kWh for the first 50 kWh, then 1004 VND/kWh from the 51st kWh to the 100 th kWh, and so on (see Supplementary_Figure 1).

Increasing block tariffs for electricity, water, or gas are popular in many countries since they offer policymakers a tool to address equity and efficiency concerns. First, as far as power demand correlates with wealth, an increasing block tariff improves equity. It gives poor households access to electricity at a relatively low price. The first block can be provided at a tariff lower than production costs, enacting solidarity between users. Second, an increasing block tariff may improve energy efficiency. It presents higher marginal costs of electricity to households with higher electricity consumption. That tends to reduce wasteful uses and moderate the growth of their electricity demand.

The right panel in Figure 3 The average spend of 44 markets surveyed was 3.9%, ranging from a low of 1.5% in Taiwan to a high of 8.2% in Portugal". Supplementary_Figure 4 shows that 95 % of Vietnamese households devoted less than 7 % of their income to electricity.

However, Table 2 shows a trend suggesting that cheap electricity years may not last. The median budget effort was 1.5% in 2010 as a result of the 2008-2010 electricity price control.

After that, the effort increased by fifty per cent between 2010 and 2018. As households become more affluent over time, it is normal that they consume more and that their bills increase in nominal and in real terms. Here we saw not only that, but electricity expenses have increased faster than income.

Economists talk about a luxury or a superior good when the fraction of budget spends purchasing it increases when households income increase. However, this evidence does not imply that electricity is always a luxury/superior good for everybody. First, as exposed above, the relative price of electricity declined over 2010-2020, which can explain a part of the demand increase. Second, the econometric analysis presented in (H.-S. Nguyễn 2019, chap. 6) shows that for households in the lower-income quantiles, the electricity consumption is inelastic to income. Electricity is an essential good for poor households. A systematic survey error may be present. However, according to the survey documentation, the question's wording was the same in 2010, 2012, 2014.

Expanded energy access is not the only explanation. There is a correlation between access and satisfaction; see Figure 1 and4. Satisfaction increased much faster compared to the relatively slow progress of the grid.

Energy-using expectations and behaviours are known to adjust. Would it be that households were more able to meet their needs with what was provided? We believe this effect may rather play in the opposite direction, given that the equipment levels increased.

Regarding the demand for electricity by households, (General Statistics Office of Vietnam 2015, 26) stated that:

The percentage of households with fixed or mobile telephones reached 85%, the rate of households using a computer was 25.1%, the rate of households using a washing machine reached 30.9%, and the rate of households using refrigerators was 59.0%. All of these were at least twice as high as the indicators in the 2009 Census. In addition, the rate of households using air conditioning stood at 13.3%, nearly three times higher than the rate in the 2009 Census.

We cannot rule out a fluke due to needs variations. Energy demand is known to be sensitive to weather, which is random. The weather in 2010 was warmer than in 2012 and 2014. The heatwave could have led to exceptionally high cooling needs and shortages due to low flows to hydropower stations. A small fraction of households had air conditioning at that time, but fans also require electricity. However, we offer a simpler explanation.

We conjecture that satisfaction increased between 2010 and 2012 because the electricity supply reliability improved. In 2010 there were many shortages due to delays in adding new coal power plants. After that year, reserve generation capacity increased and that The subjective indicator provides an integrated measure of the quality of service. People's impressions are not so much based on averages of physical and economic flows than on extreme events: a power outage during a heatwave or coldwave will be remembered.

Interactions between the three viewpoints

Section 4, the engineering viewpoint, looked at access to electricity and quantities consumed. Section 5, the economic viewpoint, looked at tariffs and the weight of the electricity bill in households' budget. Section 6, the subjective viewpoint, looked at the satisfaction of electricity needs. Only that viewpoint allowed us to see the qualitative jump between 2010 and 2012.

This section examines the interactions between the three viewpoints quantitatively. Figure 5 shows the number of respondents of the VHLSS 2014 meeting three different criteria of energy poverty: using less than 30 kWh per month, spending more than 6% of income on electricity, and declaring their electricity usage did not meet their needs. The first two are objective; the third is subjective. The precise limits for the objective criteria are somewhat arbitrary, but the qualitative result does not depend on it: there is little overlap between the three energy poverty indicators.

Consider first the interaction between the 'energy poverty bar' idea based on the quantity of electricity used and the subjective indicator of needs not met. Table 4 shows that in 2014, the electricity consumption of households with unsatisfied needs tends to be lower than in the rest of the population. In 2014, half of the households in Vietnam who declared insufficient electricity used less than 25 kWh per month.

What does 25 kWh per month mean in terms of basic needs? It amounts to about 830 Wh per day. This is more than enough to charge many telephones since a phone battery contains about 5 Wh. It is also enough for lightning, as a modern light bulb is about 10 W, a few hours per day. A TV and fans can also fit within this energy budget. However, it does not go far into modern comfort appliances. This amount of energy is not enough to run an air conditioning unit, refrigerator, electric cooking or heating.

While households who declared that their electricity usage did not meet their needs tend to use little electricity (in 2014), the converse is not true. Using small quantities of electricity can satisfy needs. In our sample, among the households who used less than 30 kWh of electricity, most did not declare their needs unsatisfied (see Figure 5). This shows that the absolute amount of energy used is not a sufficient indicator to determine satisfaction. It is the perceived comparison of the energy used with the needs of the household, determined by the appliances it owns, that determines sufficiency.

Second, consider the interaction between the 'high electricity cost' ideas based on the share of income devoted to electricity and the subjective indicator. In 2014, about 6% of Vietnamese households had 'high electricity cost', defined as an electricity bill larger than 6% of their income. Survey results show a very small overlap between that population and the households declaring that their needs were not met (see Figure 5). Furthermore, respondents declaring their electricity use did not meet their need tended to spend less on electricity than the general population. The share of income devoted to energy is not a sufficient indicator to determine satisfaction. [START_REF] Vignon | Premier Rapport de l'ONPE: Définitions et Indicateurs[END_REF]) also found a low correlation between objective and subjective energy poverty indicators. More specifically, in continental France, only 20% of the households spending more than 10% of their income on energy also declare suffering from cold.

Third, the high electricity cost (budget effort > 6%) subsample also has very little overlap with the 'low electricity use' subsample. This survey confirms that the 'high electricity cost' definition of energy poverty is problematic, as discussed in section 2.

Discussion

This section discusses Vietnam's progress towards SDG7 and the policy implications on energy poverty. It contextualizes by comparing with ASEAN countries, refer to (IEA, IRENA, UNSD, World Bank, WHO 2020, 7; Roseberry 2020) for comprehensive data on electricity poverty and SDG7.

Based on VHLSS survey data, Table 5 summarizes four indicators related to SDG 7 access to clean, reliable and affordable energy for all. The first row is a proxy for SDSN Indicator 51 discussed Section 2, access to reliable electricity. The next three rows correspond to the three viewpoints discussed in sections 4, 5 and 6.

The first row shows that Vietnam has mostly achieved SDG7 access to clean energy for all.

Vietnam has a lower-middle-income economy. That second row shows the share of households using less than 30 kWh per month. The percentage of households below an electricity poverty line is an energy poverty indicator.

We choose 30 kWh here because it is the amount subsidized in official Vietnamese policies.

However, the group covers a diversity of situations, the first three levels in [START_REF] Bathia | Beyond Connections : Energy Access Redefined[END_REF] multi-tier matrix for measuring household electricity consumption. The 'less than 30 kWh'group goes from households without any electricity access to households using about 1 000 Wh per day, which is enough for lighting, charging phones, running fans and television. By 2018 this under-30 kWh/month group comprised less than 7% of households, declining by about one percentage point per year during the period.

Considering the electricity consumption per capita, [START_REF] Gu | Practical Experience and Prospects for Energy Accessibility in ASEAN[END_REF] classify ASEAN member states into four groups. The first is Singapore, Thailand and Brunei Darussalam. Vietnam is in the second group, with Malaysia and Indonesia. The third is Lao PDR and the Philippines. The fourth is Cambodia and Myanmar.

Row three shows the share of households spending less than 6 % of income on electricity.

The conclusion that the burden is increasing fast does not depend on the precise 6% value, as Supplementary_Figure 2 shows. Do rows two and three confirm that "Electricity poverty decreased but electricity-cost poverty increased" (T. T. The fourth, bottom row is about satisfaction, the share of households stating that their electricity use did not meet needs last month. We regret that the 2016 and 2018 households surveys did not measure this indicator. As a regulated monopoly provides electricity, it remains useful that national statistical offices provide the government with independent performance indicators. National electricity policies have many objectives. Goals for the energy sector as a whole include independence and sustainability. Objectives facing households include universal access to electricity, affordable tariffs, and a satisfying quality of service. We believe that these three objectives require different indicators. Energy poverty must be measured and discussed with engineering, economic and subjective data.

The subjective energy indicator -designed from surveys asking people they had enough electricity to meet their households needs-provides essential customer satisfaction feedback that cannot be obtained by looking only at kWh and money flows.

For policymaking, the discussions on SDG7 and energy poverty indicators lead to operational criteria defining which households should be eligible for support. Section 7 found that the three different approaches point to different households. We argue that the subjective indicator is the more theoretically satisfying measure of progress towards SDG7.

However, when it comes to identifying which households should receive money, subjective declarative criteria are challenging to trust. Furthermore, the 'high electricity cost' budget effort indicator has problems. Three approaches remain operational to define households eligible for electricity subsidies: a) low income, b) low electricity use, or c) both. The Vietnamese support scheme uses option c). A household with an income poverty certificate could get a subsidy of 30.000 VND/household/month if it consumed less than 50 kWh.

The VHLSS 2014 survey explicitly asked questions about electricity subsidies and poverty certificate. Figure 6 shows how the subsidy mechanism performed. Three-quarters of poor respondents declared they received the electricity subsidy. The Figure shows that only 37% of households using less than 30 kWh did receive the subsidy. The reason is that most of those households do not have a poverty certificate. Finally, only 23% of households who declared their electricity needs not met received a subsidy. The subsidy mechanism worked more to alleviate poverty (SDG 1) than to satisfy electricity needs (SDG 7). The subjective measure of energy poverty could be handy for macro scale international comparisons. The share of households satisfied with electricity service may be a more informative political indicator than the electrification rate. To target households eligible for energy subsidies, income and electricity consumption indicators may be more operational than personal declarations at the micro-scale. That may explain why the Vietnamese electricity subsidy works more to alleviate economic poverty than satisfy energy needs.

The three points of view explored in this paper converge to indicate that Vietnam progressed very close to the SDG7 -Affordable and clean energy for all -over the 2008-2018 period, and that electricity poverty is not an acute social issue in 2018:

• Vietnam achieved close to universal access to electricity. The expansion of the grid matched the demographic expansion. It should exceed it to bring electricity to all (World Bank Group and International Energy Agency 2013). About one million people remain to be electrified, mostly in remote areas in the Northern mountains.

• The quality of service, defined as the satisfaction of customers, has improved to a high level. Between 2010 and 2014, the share of households declaring that their electricity use did not meet their need dropped from 24% to 2.7%.

• Inequalities in electricity use among Vietnamese households decreased during the 2008-2018 period. Inequalities in electricity use are not greater than inequalities in income, contrary to the findings of [START_REF] Son | Reducing Energy Poverty: Characteristics of Household Electricity Use in Vietnam[END_REF] for the 1993-2004 period.

• Electricity is affordable in Vietnam. The electricity tariffs declined in real terms during the last ten years. They are lower than other ASEAN countries, and households spend a smaller share of their budget on electricity.

As the amount of electricity used increase, the cost of electricity weights in the budget of Vietnamese households is rising. Raising further the price of electricity may be necessary at some point to pay for imported fuels, finance investments in capital-intensive solar and wind power plants, reinforce and modernize the grid. As long as the government regulates the retail tariffs, it retains the possibility to share the costs between the different categories of electricity consumers. It could, for example, charge less the households and more the

  population surveys: the Household Living Standards Surveys (General Statistics Office 2019). Conducted under the Ministry of Planning and Investment by the official national statistics office, the surveys aim to systematically collect basic information about population and housing as a basis for research and for assessing and formulating policy mechanisms, programs, targets and plans on national socio-economic development generally, and for the population and housing sectors in particular. It is independent of EVN, the national electricity company.

Figure 1 :

 1 Figure 1: Progress of electrification. The share of households not relying on the national grid for lighting decreased from 2008 to 2018 in most provinces. Rural electrification challenges remain only in the most northern provinces. High resolution figure available as supplementary material.

Figure 2 :

 2 Figure 2: Monthly electricity usage by household in Vietnam, cumulative distributions. The curve moves to the right over time, as households used increasing amounts of electricity.

  shows that the government kept electricity tariffs under control during the high-inflation years after the global economic crisis of 2008 (M. P. Nguyễn 2010). This contributed to protecting the poorer consumers and mitigated inflation. Tariffs eventually caught up when the inflation cooled down, but in real terms, Vietnamese households faced cheaper electricity in 2020 than in 2010. The average electricity tariff in Vietnam is low compared to other countries. In 2014, for example, it was 0.08 US$/kWh. Amongst 29 major countries in Asia and the Pacific, only Buthan, Mongolia, and Myanmar had a lower tariff (World Bank 2020, page 68).

Figure 3 :

 3 Figure 3: Electricity block tariff for households in Vietnam, in nominal terms (left) and adjusted for inflation (right). The real electricity price for households decreased from 2003 to 2018.

  improved reliability. According to IEA (accessed 2021-02-08), the Vietnamese residential sector consumed 31.5 TWh in 2010, 38.4 TWh in 2012 and 45.7 TWh in 2014. The 50% growth in four years shows there was unsatisfied demand in 2010. Numbers for 2010 are not available, but according to EVN 2016 annual report, the System Average Interruption Duration Index went from 8077 minutes per customer in 2012 to 3134 minutes in 2014.

Figure 4 :

 4 Figure 4: Satisfaction levels progress. The share of households declaring their electricity consumption was not sufficient to meet their needs in the previous month decreased rapidly between 2010 and 2012.

Table 4 :Figure 5 :

 45 Figure 5: Interactions between the electricity poverty criteria in VHLSS 2014: 'Used < 30 kWh last month', 'Bill > 6% income', and 'Needs not met'.

Figure 6 :

 6 Figure 6: Overlap between households receiving electricity subsidy and subsamples of households matching different electricity poverty criteria in VHLSS 2014.

Table 1 :

 1 Vietnam's economy and electricity conditions in 2008-2018.

	Economic and political reforms launched in 1986 have transformed Vietnam from one of the world's
	poorest nations to a lower-middle-income country. Source GSO, accessed 2021-02-08, and World Bank
	for GDP PPP.
	Year	2008	2010	2012	2014	2016	2018
	Population (Thous. pers.)	85 119	86 947	88 809	90 729	92 695	94 666
	GDP at constant 2010 prices, trillion Dongs	1 889	2 158	2 413	2 696	3 054	3 493
	GDP per capita, PPP constant 2017 $	4 628	5 089	5 574	6 098	6 767	7 586
	Consumer price index, base 100 in 2007	123	144	186	206	213	228
	Share of population in urban areas	29.0 %	30.5 %	31.8 %	33.1 %	33.9%	34.5%
	Electricity production, annual	71.0 TWh	91.7 TWh 115.1 TWh 141.2 TWh 175.7 TWh 209.2 TWh
	Electricity production, annual per person	834 kWh 1 055 kWh 1 297 kWh 1 557 kWh 1 896 kWh 2 221 kWh

  [START_REF] Lê | A Survey on Electrical Appliance Use and Energy Consumption in Vietnamese Households: Case Study of Tuy Hoa City[END_REF], which showcased air conditioning as the key driver of energy consumption for households living on Vietnam's South-Central coast.

	Đoàn Văn Bình (2010) wrote about electricity access in Vietnam as follows :

Vietnam has gone through a rapid increase in electrification since 1990, where electrification levels jumped from a pre-policy reform rate of less than 50% in the late 1980s-early 1990s to 77% by 2001 and 96% by 2009. The Electrification Programme driven by the Vietnamese government has resulted in increased access for 82 million people between 1976 and 2009. One million people, primarily in the northern mountainous regions of Vietnam, are currently without access to electricity.

Table 2

 2 displays the budget effort indicator, defined as the weight of the electricity bill in the households' budget (also Supplementary_Figure 2 and Supplementary_Figure 3 ).

	Electricity is affordable in Vietnam, meaning that the budget effort remains at a modest
	level. In 2018, the median household electricity budget effort was 2.4 % of income. This
	compares favourably with other countries. For example, according to (International Energy
	Consultants 2016), "In the Philippines […] the average size (170kWh/month) household spent an
	estimated 4.5% of monthly disposable income on electricity in January 2016 (down from >6% in 2012).

Table 2 :

 2

Electricity bill as a fraction of income. Source: Authors, from VHLSS data.

6. The subjective view: are electricity needs met?

Table 3 :

 3

	Survey year	2010	2012	2014
		n = 9 251	n = 9 237	n = 9 266
	Not sufficient	24.4 %	4.8 %	2.8 %
	Sufficient	72.6 %	89.6 %	90.9 %
	More than sufficient	3.0 %	5.6 %	6.3 %

Answers to question Q12: 'Has your household's consumption of electricity over the last 30 days been sufficient to meet its needs ?

' in VHLSS 2010' in VHLSS , 2012' in VHLSS and 2014. .

  According to World DevelopmentIndicators(World Bank, accessed 2021-02-18, statistics for 2018), 86,3% of the population had access to electricity in that country group. Vietnam scores above its peers. Its access indicator compares with upper-middle-income countries, where 99.4% of the population had access (World Bank, op. cit.). Historically within ASEAN, Vietnam reached electrification after Brunei Darussalam, Malaysia, Singapore and Thailand, but before the Philipines, Indonesia and the Lao PDR[START_REF] Gu | Practical Experience and Prospects for Energy Accessibility in ASEAN[END_REF]. Cambodia and Myanmar have yet to reach a 95% electrification rate as of 2019.

	The Philippines and Indonesia have a higher income than Vietnam but lots of isolated
	islands, making electrification more difficult. Lao PDR is a continental country well
	endowed in hydroelectric resources and income per capita comparable to Vietnam's.
	Nevertheless, its electricity use per capita is much lower, maybe because it has a higher
	fraction of rural households living in mountain areas. Cambodia and Myanmar are behind
	Vietnam in electricity access because they have lower income per capita. The same logic
	applies when comparing Vietnam with Brunei Darussalam, Malaysia, Singapore and
	Thailand.

  [START_REF] Nguyễn | Energy Transition, Poverty and Inequality in Vietnam[END_REF])? Spending more on electricity is not necessarily a welfare loss. Electricity can substitute other forms of energy, reducing their cost, particularly for rural and less wealthy households, which were still a majority of the population at the start of the period. Biomass use did decrease at the same time as electricity use increased. According to the International Energy Agency (Data and statistics, accessed 2021-02-10), in 2018, the total final energy consumption by the Vietnamese residential sector (households) was 10 059 ktoe, of which 5 352 ktoe (52 %) was as electricity and 2 213 ktoe (22 %) was as biofuel and waste. In 2008 the total was 15 110 ktoe, of which electricity was 2 241 ktoe (15 %) and biomass 11 086 ktoe (73 %). Most of the costs of using biomass energy are non-market. It would be difficult to quantify the welfare gains of using the electric rice cooker over the traditional wood stove, but given a choice, many households choose the first option.Electricity is affordable for most households, but energy poverty remains for many. VND at the third tariff block. To compound the problem, many landlords charge high rates for electricity. If the government gave appliances for free, there would still be energy poverty in the sense of the fourth criteria discussed in section 2.

	According to the General Statistics Office (2019, 435), air conditioner ownership per 100
	households increased from 5.5 to 35.1 between 2008 and 2018. For urban areas, it went from
	17.3 to 70.1. The statistic only increased from 0.1 to 3.3 air conditioner per 100 households
	for the lowest income quintile. Not being able to protect against extreme heat fits with the
	first definition of energy poverty presented in Section 2.
	The barrier to air conditioning is not only capital but also operating costs. During the 2020
	summer heatwave, several mass media raised the issue of cooling affordability for the
	poorer households (B. Lê 2020; Thương and Hà 2020). The monthly income per capita in
	2018 for the first quintile was 923 000 VND, about 41 USD (GSO 2019, p.22). For the
	underprivileged households, each kWh counts. Using 1 kW for 100 hours in a month costs
	about 200 000

Table 5 :

 5 Evolution of performance indicators towards access to clean and affordable energy for all in Vietnam (less is better).

	Source: Authors, VHLSS data.
	Year	2008	2010	2012	2014	2016	2018
	Share of households not using grid	4.3 %	4.7 %	4.4 %	3.3 %	2.0 %	1.6 %
	electricity for lightning, rural/urban	0.3 %	0.3 %	0.3 %	0.1 %	0.1 %	0.0 %
	Share of households declaring less than 30 kWh of electricity use	NA	12.9 %	11.9 %	11.2 %	8.8 %	6.2 %
	within the last 30 days
	Share of households paying more	2.5 %	2.3 %	3.0 %	5.1 %	6.2 %	7.9 %
	than 6 % of their income for electricity
	Share of households declaring their electricity use within the last	NA	24.0 %	4.7 %	2.7 %	NA	NA
	30 days did not meet their needs

industrial, commercial and institutional consumers. The increasing block tariff is not the only tool to protect households from electricity poverty.

Acknowledgements

NHS provided the initial idea and the data, HDM directed the research. The two authors contributed to statistical analysis and writing. This work was started while the first author was visiting professor at the Clean Energy and Sustainable Development Lab (CleanED/USTH). We gratefully acknowledge comments from our colleagues Audrey Berry, Franck Nadaud, Nguyễn The first block is split into two blocks. The first 50 kWh is priced at 35 -40% of the average electricity supply cost. The second 50 kWh is priced at the average supply cost. 2011

The first two blocks are amended. The first block is 0 -50 kWh and priced at the average supply cost. This price is only for low-income households registered with EVN, which consume less than 50 kWh per month. All other households pay the second block price from 0 to 100 kWh. Its price is set to the average approved price of electricity.

A household that has an income poverty certificate and uses less than 50 kWh can get a subsidy of 30.000 VND/household/month. 2014

More households can get the subsidized price. The household must meet the criteria that the Prime Minister define and use less than 50 kWh per month. The subsidized amount equals the consumption of 30 kWh at the price of the first block. 2020

The price of the first three blocks is reduced by 10% from September to December to support households during the second wave of the COVID-19 crisis.

26 Supplementary_Figure 2: Cumulative distribution function of the fraction of income spend on electricity by Vietnamese households. These curves are summarized in Table 2.


Patrick Bas
email: patrick.bas@inpg.fr

Gwenaël Doërr
email: g.doerr@adastral.ucl.ac.uk

Evaluation of an Optimal Watermark Tampering Attack Against Dirty Paper Trellis Schemes

Keywords: H.4.m [Information Systems Applications]: Miscellaneous-Watermarking, H.3.4 [Information Storage and Retrieval]: Systems and Software-Performance Evaluation (efficiency and effectiveness), K.6.m [Management of Computing and Information Systems]: Miscellaneous-Security Security, Algorithms Dirty paper trellis watermarking , security, Attack

Benchmarking watermarking systems now goes beyond only evaluating the ability of the embedded watermark to withstand common signal primitives such as filtering, resampling, lossy compression, D/A-A/D conversions, etc. Evaluation procedures have to consider how much information leaks from a watermarking system since such knowledge could prove most helpful to design very powerful attacks. This paper further refines an attack on dirty paper watermarking schemes which relies on security weaknesses i.e. information leakage. In particular, additional constraints are introduced to be able to handle 'complex' trellises. Moreover, the efficiency of this attack has been evaluated for different trellis configurations. Quite counter-intuitively, increasing the number of states in the trellis seems to enhance both the robustness and the security of the system.

INTRODUCTION

Watermarking security is defined today as the possibility to estimate all or a part of the secret parameters of a watermarking system [START_REF] Comesaña | Fundamentals of data hiding security and their application to spread-spectrum analysis[END_REF]. In contrast with robustness attacks, security attacks inherently involve two steps: (i) the adversary devise some strategy to estimate part or all the secret of the attacked watermarking system and (ii) the adversary exploit this acquired knowledge to perform some action. The first step of any security attack is commonly categorized depending on the kind of material available to the adversary e.g. Known Message Attack (KMA), Constant Message Attack (CMA), Known Original Attack (KOA) and Watermarked content Only Attack (WOA) setups [START_REF] Comesaña | Fundamentals of data hiding security and their application to spread-spectrum analysis[END_REF][START_REF] Cayre | Watermarking security: theory and practice[END_REF]. Additionally the classification of security attacks can be further refined by incorporating the objective of the adversary during the second step. Depending on the acquired knowledge in the first step, attacks which goes beyond the usual erase-only might be possible.

A first effort in that direction has been reported in [START_REF] Kalker | Considerations on watermarking security[END_REF] where the authors proposed three different attack objectives: watermark removal, unauthorized watermark estimation and/or detection, and unauthorized watermark writing which encompasses the copy attack [START_REF] Kutter | Watermark copy attack[END_REF]. However, this early classification fails to address a couple of issues. First, the denomination "watermark removal" is well fit for zerobit watermarking schemes [START_REF] Furon | A constructive and unifying framework for zero-bit watermarking[END_REF] but possibly inappropriate for multi-bit schemes. Indeed, in that case, it is not always necessary to erase the watermark to defeat the system. Forcing the detector to output a message which is different from the embedded one might prove critical in some application. Second, the classification in [START_REF] Kalker | Considerations on watermarking security[END_REF] does not reflect the fact that the knowledge acquired in the first step of the attack will be used if necessary to tailor modifications which achieve the desired objectives while preserving at most the fidelity of the attacked content.

Based on these observations, a new terminology is adopted to describe more accurately the potential objectives of an adversary: -Unauthorized watermark copying. From one or more contents watermarked with the same message, the goal is to design a procedure which copies with high probability the watermark into a 'blank' content. Depending on the number of available watermarked contents, preserving fidelity may be an issue.

-Unauthorized watermark detection/reading. The objective is to detect whether a given content contains a watermark or not, and, in the case of a multi-bit scheme, what is the embedded message.

-Unauthorized watermark tampering. The objective is to modify the watermarked content while preserving fidelity so that the detector no longer outputs the embedded message with high probability. This includes for instance the Oracle attack [START_REF] Kalker | A security risk for publicly available watermark detectors[END_REF][START_REF] Comesaña | Blind newton sensitivity attack[END_REF] when the detector is available.

Figure 1: Geometrical comparison of a blind and an optimal watermark tampering attack. In the blind case, the adversary goes in any random direction since she has no knowledge about the secret, here the decoding region D(c). On the other hand, relying on some knowledge acquired during a security analysis, the optimal attack finds the shortest way outside the decoding region where is the watermarked content y.

-Unauthorized watermark writing. The objective it to modify a content so that the detector outputs a given message with high probability. In contrast with a copy attack, it does not require that watermarked contents with this specific message embedded are available during the first phase. Ideally, the distortion induced by a this attack should be of the same order than if the message was embedded with the official embedder.

Each objective involves a different knowledge of the secret parameters of the watermarking system to be performed e.g. the feature space being watermarked, the detection regions of the used set of codewords, the message encoded by each codeword, etc.

This paper focuses on devising an optimal watermark tampering attack against Dirty Paper Trellis (DPT) watermarking schemes in the WOA scenario. As illustrated in Figure 1, in contrast with a blind attack, such optimal tampering attacks aims at identifying the most damaging direction for modification i.e. the direction which indicates the shortest way outside the decoding region where the watermarked content lies. Such knowledge can be acquired because DPT watermarking schemes have been proven to leak information.

PREVIOUS WORKS

Dirty Paper Trellis Watermarking

Dirty Paper Trellis codes [START_REF] Miller | Applying informed coding and embedding to design a robust, high capacity watermark[END_REF] have been introduced as an alternative implementation of digital watermarking when it is modeled as communications with side information [START_REF] Costa | Writing on dirty paper[END_REF]. In comparison with the popular lattice codes, DPT codes are significantly more robust against requantization (e.g. lossy compression) and by construction immune to valuemetric scaling (e.g. contrast enhancement for an image, volume change for a song). DPT watermarking schemes mostly rely on two fundamental components: a high-dimensional trellisstructured dirty paper code and a computationally intensive iterative embedding procedure.

DPTs rely on a small modification to conventional binary trellises design in order to provide a one-to-many mapping between messages and codewords. A trellis is basically a In this example N b = 3, Ns = 3, Na = 2. Three alternative codewords are available in the expurgated trellis to represent the message m. The codeword g with the highest correlation with x is identified using the Viterbi algorithm. Afterward, the watermarked vector y is computed taking into account g. On the receiver side, the detector uses the whole DPT to retrieve the embedded payload.

graph which can be fully described with its number of states N b , its number of arcs per state Na, and its number of steps Ns. For each step, the arcs defines how the incoming states are connected to outgoing states. In a conventional binary trellis, there are only two arcs entering/reaching each state, one encoding 1 and the other 0. Therefore, there is a one-to one mapping between messages and codewords. In order to obtain the desired dirty paper property, a DPT allows several arcs entering/reaching each state, half of them encoding 1 and the other half encoding 0. As a result, multiple paths through a DPT encode the same message. In addition to a binary label, a symbol sa, taken from an alphabet A consisting of Na pseudo-randomly generated Nv-dimensional unit norm symbols (also referred to as patterns), is attached to each arc of the trellis. Thus, each path through the trellis can be seen as a message or, alternatively, as a succession of symbols emitted by the DPT communications system. Concatenating these symbols altogether defines one of the DPT codewords, and the set of all possible codewords defined by a DPT trellis results in a spherical dirty paper code.

As depicted in Figure 2, the first step of a DPT watermarking scheme is referred to as informed coding. It consists in finding the codeword g which (i) encodes the desired message m and (ii) is the closest to the original cover content x. To do so, the DPT is first simplified by eliminating all the arcs which do not encode the desired message. Therefore, any path through this simplified DPT encodes the desired message and informed coding is only a matter of finding which of them is the closest to the cover. In other words, it is necessary to compute some distance between the cover and each one of the codewords, and to retain the one with the smallest distance. Hopefully, thanks to the trellis structure of the code, this search can be performed efficiently using the Viterbi decoding algorithm [START_REF] Viterbi | CDMA: Principles of Spread Spectrum Communication[END_REF].

The next step of DPT watermarking is informed embedding which is tightly related to the detection procedure applied on the receiver side. Indeed the goal of this step is to bring the cover content inside the decoding region D(g) of the identified codeword g, possibly with some level of robustness to be able to withstand distortions onto the watermarked content during transmission. This decoding region is fully defined by the detection procedure which is a basic nearest codeword search performed once again using the Viterbi decoding algorithm. However, since the receiver does not know the hidden message m, it uses the full nonsimplified trellis. Once the best path through the trellis is identified, the hidden message can easily be retrieved by looking at the bits encoded by the arcs along that path. Unfortunately, 'bringing the content inside the desired decoding region' is a complex problem which cannot be easily solved. Today, informed embedding relies on an iterative embedding algorithm [START_REF] Miller | Applying informed coding and embedding to design a robust, high capacity watermark[END_REF], which basically simulates the communication channel for some specified noise level and terminates when there is no longer any decoding error.

Security Analysis and Tampering Attack

Although DPT watermarking schemes have resisted for quite a long time to attacks from hostile adversaries, a recent study [START_REF] Bas | Practical security analysis of dirty paper trellis watermarking[END_REF] has reported that it is feasible to acquire valuable secret information from such systems through security analysis, which then allows to perform powerful watermark tampering attacks. The secret parameters of a DPT consist of:

1. the pseudo-randomly generated alphabet A = {sa} containing the symbols {sa} attached to the arcs, 2. the connectivity of the trellis i.e. the incoming and outgoing states for each arc (which can be assimilated to a symbol),

3. the binary labels attached to the arcs.

The mentioned study has revealed that, in a WOA setup, it is possible to estimate the secret alphabet and, subsequently, the connectivity of the trellis. This gained knowledge about the secret parameters of the trellis can then be used as a keystone to design an optimized distortion-preserving watermark tampering attack. It could be noted that the estimation of the third secret parameter would require to be in a KMA setup and would open avenues to perform unauthorized read/write attacks. The estimation of the secret alphabet A is made possible by the fact that DPT watermarking schemes tend to cluster watermarked contents around the different codewords in order to guarantee some level of robustness. Due to the trellis structure of the code, the same observation is also valid to some extent at the step level. In other word, the segments of watermarked content, a segment of content corresponding to one step in the trellis, tends to be clustered in the direction of the different symbols of the alphabet. Moreover, the stronger the specified robustness constraint is, the more valid this observation is. As a result, it is possible to estimate the collection of Ns.Na symbols A = {sa} by applying clustering techniques, such as the K-means algorithm [START_REF] Macqueen | Some methods for classification and analysis of multivariate observations[END_REF], to a large set Y of segments of watermarked contents 1 .

The estimation of the alphabet permits to infer the connectivity of the trellis by looking at the sequences of emitted signals, and more particularly at couple of successive symbols. A state in the trellis always outputs the same subset of symbols. Consequently, when two symbols are followed by the same subset of symbols, it clearly indicates that the emission of these two symbols lead to the same state in the trellis. The identification of such similarities allows to estimate the outgoing state of each symbol. Moreover, since the outgoing state of the first symbol is also the incoming state of the second symbol, it is then possible to also assign Figure 3: Trellis connectivity estimation. Similar rows in the co-occurrence matrix indicate that the same state has been reached after the emission of the symbols associated to these rows. Such similarities can be automatically identified with clustering techniques, e.g. the K-means algorithm. Once the outgoing state has been identified for each symbols, it is then possible to build an outgoing state matrix. A majority vote along the columns of this matrix then indicate the incoming state for the symbols associated to the columns.

Figure 4: DPT watermark tampering attack. To be optimal with respect to distortion, the adversary needs to find the closest point to y outside the decoding region D(g) of the embedded codeword g. To do so, she needs to identify the second nearest codeword from y (b1 in the Figure). To do so, the adversary simply needs to run N b Viterbi decoders in parallel, a single arc of the best path g being forbidden each time. This gives N b eligible candidates and the one which is the closest to y is retained.

an incoming state for all the symbols in the alphabet. As depicted in Figure 3, [START_REF] Bas | Practical security analysis of dirty paper trellis watermarking[END_REF] relies on clustering techniques applied to the rows of a co-occurrence matrix to estimate the outgoing states, and subsequently performs a majority vote to identify the incoming state of each arc.

Once the adversary has access to this secret information, she can easily find the codeword g embedded in a watermarked content by running the Viterbi decoder with the estimated trellis and the content itself. In the context of a tampering attack, the goal is then to find the shortest path outside this detection region. This requires finding the boundary of the decoding cell which is the closest to the watermarked content. Figure 4 clearly shows that this can be approximated by finding the second nearest codeword from y. This can be done by running N b Viterbi decoders in parallel, each one using a slightly different trellis. The idea is to remove a single arc of g in the original DPT trellis to identify a codeword which is close enough to y to be a potential candidate. Out of the N b eligible codewords, the one which is the closest to y is retained as the second nearest codeword b1. Subsequently, running the embedding procedure for this codeword with minimal robustness constraint permits to leave the original decoding region while main-taining fidelity. Note that by selecting the closest codeword to the one used during the embedding, the adversary is able to devise an attack which is close to optimal. Nevertheless since the watermarked content in not located exactly on a codeword, the direction toward the closest codeword may not be the direction toward the closest boundary hence the optimality is not guarantied in this case. However in practice the trellis produces distances between closest codewords that are of the same order of magnitude and the attack is very close to optimal.

EXTENSION TO REAL-LIFE DPT CON-FIGURATIONS

Although the experimental results reported in [START_REF] Bas | Practical security analysis of dirty paper trellis watermarking[END_REF] clearly demonstrated the proof of concept of this attack, they were mostly considering toy example trellis configurations which would probably never be used in practice. In particular, the alphabet A was designed using only orthogonal or opposite symbols, thus limiting the cardinality of the alphabet to 2.Nv. Moreover, the study was limited to a single trellis configuration, namely a trellis using Nv = 12-dimensional symbols, Ns = 6 states and Na = 4 arcs per state.

In practice, the alphabet is usually significantly larger and the symbols, which are independently pseudo-randomly generated [START_REF] Miller | Applying informed coding and embedding to design a robust, high capacity watermark[END_REF], exhibit some cross-correlation. Additionally, several alternative trellis configurations would be investigated since it has been shown that robustness performances can be significantly be affected depending on which trellis configuration is used [START_REF] Wang | Toward a better understanding of dirty paper trellis codes[END_REF]. To deal with such real-life DPT configurations it is necessary both to define a new metric to assess the quality of the alphabet estimation and to improve the trellis connectivity estimation procedure to be able to handle discrepancies appearing when the complexity of the trellis is increased.

Alphabet Estimation Assessment

Although an adversary will never have access to the secret parameters of the watermarking system in practical cases, it is commonly admitted that, during the design phase of the attack, these parameters are available in order to be able to assess the quality of the estimation performed by the adversary. For instance, in the proposed attack, it is important to evaluate how close the estimated alphabet  = {ŝa} output by the K-means procedure is from the actual secret one A. This is of utmost importance since the follow-up estimation of the trellis connectivity will rely on the estimation of the secret alphabet. Therefore, the quality of this alphabet will have a tremendous impact on the efficiency of the attack.

In [START_REF] Bas | Practical security analysis of dirty paper trellis watermarking[END_REF], the following metric has been proposed:

∆ = 1 NsNa X ŝa∈ Â » max1 sa∈A nc(ŝa, sa) -max2 sa∈A nc(ŝa, sa) - (1)
where the max1 and max2 respectively output the highest and second highest values of some set, and nc(., .) denotes the normalized correlation operator. The score ∆ basically indicates how close, in average, each estimated symbol ŝa is from any of the original one sa. If a symbol given by the K-means algorithm is not a good estimate, the max1 and max2 values will be similar and their difference close to 0. On the other hand, in case of a good estimate, the max1 value will be close to 1 and the max2 value close to 0 since the symbols in A are opposite or orthogonal in [START_REF] Bas | Practical security analysis of dirty paper trellis watermarking[END_REF], thus leading to a difference close to 1. In summary, this metric returns a value close to 0 when the estimation of the secret alphabet is very poor and a value close to 1 in case of a nearly perfect match. Now, in the case of a generic randomly generated alphabet, the situation is slightly different. In the case of a good estimation, the second term in the difference would no longer be close to 0 since symbols are not orthogonal, and subsequently, the resulting difference would not be close to 1. To address this issue, the metric is modified as follows: ∆ = 1 NsNa X ŝa∈ Â maxs a ∈A nc(ŝa, sa)maxr a ∈R nc(ŝa, ra)

1maxr a ∈R nc(ŝa, ra)

(2) where R is a randomly generated alphabet. In other words, the modified metric measures the difference between (i) the distance between the estimated alphabet and the secret one and (ii) the distance between the estimated alphabet and a random one. The denominator is simply used as a normalization factor to guarantee that the metric varies between 0 and 1. It is immediate to check that, in the case of a bad estimation, this metric will have a value close to 0. Conversely, for a good estimation, the metric value will be close to 1.

Improved Trellis Connectivity Estimation

As described in Subsection 2.2, the estimation of the trellis connectivity basically relies on processing the co-occurrence matrix C(i, j) defined as follows:

C(i, j) = occ(os ∈ C i , os+1 ∈ C j ), 1 ≤ i, j ≤ Ns.Na (3)
where os is a segment of watermarked content observed at step s, C i is the set of segments of watermarked content associated with the i th symbol in the estimated alphabet Â, and occ(A, B) is an occurrence function that counts the number of times both A and B are true. The test (os ∈ C i ) is performed using the classification results of the K-means algorithm used for the alphabet estimation. The estimation of the outgoing state of each symbol can then be determined by applying the K-means algorithm onto the rows of the cooccurrence matrix.

At this point, the original design of the attack relied on a majority vote along the columns of the outgoing state matrix to assign an incoming state to each symbol. Unfortunately, when the number of arcs Ns.Na is increased, empirical observations have revealed that this strategy could get confused e.g. some states could end up not being assigned as an incoming state for any symbol. The direct consequence is that the estimated trellis becomes erroneous thus leading to a less efficient tampering attack. To fix this problem, the estimation of the incoming states has been revisited along the following two axis: -keep the voting weights when building the outgoing state matrix; -inject some a priori information during the incoming state assignment e.g. each state should be assigned exactly Na symbols.

The first point is simply a matter of combining the information of the co-occurrence matrix C(i, j) together with the estimation of the outgoing state. More practically, looking at Figure 3 and reading the first column from top to bottom, the matrix is now changed to: 233 votes for state 1, 12 votes for state 2, 211 votes for state 1 and 3 votes for state 2. Pooling the votes for this column, state 1 gets 444 votes and state 2 gets 15. States are then considered one after the other and the Na symbols with the highest voting score for this state are assigned this state as incoming state. The cumulated voting score for this state assignment is also recorded e.g., when state 1 is assigned to symbols 1 and 4 in Figure 3, the score 444 + 418 = 862 is recorded. That state can then no longer be considered as a potential incoming state for any other symbol. The order in which states are scanned has a strong influence on the outcome of this process. This is why it is repeated times with different scanning order. the incoming state assignment which gives the highest average cumulated voting score is retained.

EXPERIMENTAL RESULTS

As mentioned earlier, the main objective of this paper is to verify if the proof of concept reported in [START_REF] Bas | Practical security analysis of dirty paper trellis watermarking[END_REF] for a toy example trellis configuration can be extended to more realistic ones. To this end, we have considered an alphabet A composed of 128 Nv-dimensional symbols. This alphabet can be arranged into seven alternative trellises i.e. 1 (resp. 2, 4, 8, 16, 32, 64) state and 128 (resp. 64, 32, 16, 8, 4, 2) arcs per state. We also have generated a collection of 256.000 synthetic cover contents. Each cover is 120 samples long, each sample following a normal distribution. This implies that the trellises used for watermarking will have 120/12 = 10 steps. Moreover, the robustness parameter used during the embedding procedure has been adjusted for each trellis configuration so that the resulting average Watermark to Content Ratio (WCR) is equal to -5 dB.

Figure 5 depicts how well the secret alphabet A is estimated using the metric defined in Equation 2 for different trellises configurations and for a varying number of observations. Keeping in mind that the K-means algorithm is performed using 12-samples long segments of watermarked content, it should be noted that each watermarked content provide 10 observations. The estimation of the alphabet is repeated 10 times and the resulting ∆ scores averaged. First of all, it is easy to verify that, as expected, the quality of the estimation improves when more observations are considered. However, one can also notice that the configuration of the Figure 6: Relationship between the memory of a trellis and its configuration. A 6 × 2 trellis has a 3step long memory i.e. it takes a t least 3 steps to come back to the same state as a given path after deviating from it. In contrast, a 1 × 12 trellis has a one step long memory. Even if we deviate from the path at some point, the same state is reached after the step. trellis seems to have a strong impact on the quality of the estimation. With 10.000 observations, the estimation for the 64×2 trellis is quite poor whereas it is almost perfect for the 1 × 128 trellis. This could be quite surprising at first since, after all, the size of the secret is the same in all cases i.e. an alphabet of 128 symbols. Nevertheless, it should be kept in mind that the configuration of a trellis is directly related with its memory as illustrated in Figure 6. In a 1 × 128 trellis, all the arcs are parallel. As a result, for the embedding process to be successful, it needs to individually modify each segment of content so as to avoid any confusion with competing arcs. This results in well-clustered observations, thus resulting in a good estimation. On the other side of the spectrum, a 64 × 2 trellis has a 7-steps long memory. In other words, the embedding algorithm can distribute its distortion budget along 7 steps so as to avoid the confusion between two competing paths. This results in significantly less well separated observations, thus making the task of the K-means algorithm more difficult and leading to a poorer estimation of the alphabet.

Using the estimated alphabet, the trellis connectivity estimation process is run and the optimal DPT watermark tampering attack applied. The success of the attack is evaluated with respect to the Codeword Error Rate (CER) i.e. the probability of moving the watermarked content outside its decoding region 2 . Figure 7 depicts the performance gain achieved with the new incoming state assignment technique (cf. section 3.2) compared to the original one for two different trellis configurations. Two observations can be made: -there is no noticeable gain when the alphabet estimation is either very poor or very good; -the potential gain seems to decreases when the number of states increases, possibly because the increased sparsity of the co-occurrence matrix in that case helps the assignment process.

The interplay between these two aspects is not yet well understood and will require further investigations. Finally, the performances of the attack with the proposed incoming state assignment process are reported in Figure 8 for the different trellis configurations under investigation. It clearly highlights a strong correlation between the quality of the alphabet estimation and the efficiency of the attack. For two different trellis configuration, if the quality of the estimated alphabet as measured by the ∆ metric is similar, then subsequent CERs are comparable. This tends to suggest that the number of states involved in the trellis connectivity estimation process only has a marginal impact on performances.

CONCLUSION AND PERSPECTIVES

The main contribution of this paper is to extend the security attack against DPT watermarking schemes presented in [START_REF] Bas | Practical security analysis of dirty paper trellis watermarking[END_REF] to more realistic configurations e.g. using a larger alphabet of symbols which are not necessarily orthogonal or opposite. Moreover, the estimation of the trellis connectivity has been tested for various trellis configurations. The experimental results reported in Section 4 clearly indicate that DPT watermarking schemes leaks enough information about the secret parameters to allow adversaries to devise an effective watermark tampering attacks. In comparison with blind attacks, these attacks make the best use of the gained information to design a procedure which brings the watermarked content outside the decoding region where it lies while preserving fidelity as much as possible. 2 It should be noted that the attack does not guarantee that the decoded message will be different from the embedded one. Still, empirically we observed that it is the case with high probability.

Next, this study provided further insight regarding the different parameters having an impact on the security level of DPT watermarking schemes, the security level being defined as the minimum number of observations required to perform a successful attack. It was already reported in [START_REF] Bas | Practical security analysis of dirty paper trellis watermarking[END_REF] that the security level decreases when the embedding distortion increases. Indeed, increasing the distortion simply reduces to rejecting more host interference, hence producing more well separated observations. The clustering operation is subsequently more accurate and leads to a better attack. In this study, we have highlighted that the memory of the trellis has a strong impact on the performances of the proposed watermark tampering attack. For a fixed alphabet size, the memory of the trellis increases with the number of states. The reported experimental results clearly showed that trellis with larger memory were more difficult to estimate. This could be explained by the fact that the embedding algorithm has then more flexibility to distribute its distortion budget, hence producing less clearly isolated clusters.

Figure 2 :

 2 Figure 2: Main principles of DPT watermarking.In this example N b = 3, Ns = 3, Na = 2. Three alternative codewords are available in the expurgated trellis to represent the message m. The codeword g with the highest correlation with x is identified using the Viterbi algorithm. Afterward, the watermarked vector y is computed taking into account g. On the receiver side, the detector uses the whole DPT to retrieve the embedded payload.

Figure 5 :

 5 Figure 5: Assessment of the quality of the alphabet estimation for different trellis configurations (represented by Ns × Na).

Figure 7 :

 7 Figure 7: Performances of the DPT watermark tampering attack for the two different trellis connectivity estimation procedures.

Figure 8 :

 8 Figure 8: Efficiency of the optimal watermark tampering attack for different trellis configurations (represented by Ns × Na).

Due to the curse of dimensionality, the clustering process is more efficient when working on segments of contents than directly on the contents themselves[START_REF] Bas | Practical security analysis of dirty paper trellis watermarking[END_REF].

ACKNOWLEDGEMENTS

Patrick Bas thanks the National French projects ACI-SI Fabriano, RIAM Estivale and ARA TSAR for their financial support. Gwenaël Doërr's research is supported in part by the Nuffield Fundation through the grant NAL/32707.