Formal Verification of Side-channel Countermeasures via Elementary Circuit Transformations

We describe a technique to formally verify the security of masked implementations against side-channel attacks, based on elementary circuit transforms. We describe two complementary approaches: a generic approach for the formal verification of any circuit, but for small attack orders only, and a specialized approach for the verification of specific circuits, but at any order. We also show how to generate security proofs automatically, for simple circuits. We describe the implementation of CheckMasks, a formal verification tool for side-channel countermeasures. Using this tool, we formally verify the security of the Rivain-Prouff countermeasure for AES, and also the recent Boolean to arithmetic conversion algorithm from CHES 2017

On lattice profile of the elliptic curve linear congruential generators

Lattice tests are quality measures for assessing the intrinsic structure of pseudorandom number generators. Recently a new lattice test has been introduced by Niederreiter and Winterhof. In this paper, we present a general inequality that is satisfied by any periodic sequence. Then, we analyze the behavior of the linear congruential generators on elliptic curves (EC-LCG) under this new lattice test and prove that the EC-LCG passes it up to very high dimensions. We also use a result of Brandstätter and Winterhof on the linear complexity profile related to the correlation measure of order k to present lower bounds on the linear complexity profile of some binary sequences derived from the EC-LCG

Actuación en zonas antiguas de pueblos y ciudades

Actuación en zonas antiguas de pueblos y ciudade

Tight Private Circuits: Achieving Probing Security with the Least Refreshing

Masking is a common countermeasure to secure implementations against side-channel attacks. In 2003, Ishai, Sahai, and Wagner introduced a formal security model, named t-probing model, which is now widely used to theoretically reason on the security of masked implementations. While many works have provided security proofs for small masked components, called gadgets, within this model, no formal method allowed to securely compose gadgets with a tight number of shares (namely, t + 1) until recently. In 2016, Barthe et al. filled this gap with maskComp, a tool checking the security of masking schemes composed of several gadgets. This tool can achieve provable security with tight number of shares by inserting mask-refreshing gadgets at carefully selected locations. However the method is not tight in the sense that there exists some compositions of gadgets for which it cannot exhibit a flaw nor prove the security. As a result, it is overconservative and might insert more refresh gadgets than actually needed to ensure t-probing security. In this paper, we exhibit the first tool, referred to as tightPROVE, able to clearly state whether a shared circuit composed of standard gadgets (addition, multiplication, and refresh) is t-probing secure or not. Given such a composition, our tool either produces a probing-security proof (valid at any order) or exhibits a security flaw that directly implies a probing attack at a given order. Compared to maskComp, tightPROVE can drastically reduce the number of required refresh gadgets to get a probing security proof, and thus the randomness requirement for some secure shared circuits. We apply our method to a recent AES implementation secured with higher-order masking in bitslice and we show that we can save all the refresh gadgets involved in the s-box layer, which results in an significant performance gain

Random Probing Security: Verification, Composition, Expansion and New Constructions

International audienceThe masking countermeasure is among the most powerful countermeasures to counteract side-channel attacks. Leakage models have been exhibited to theoretically reason on the security of such masked implementations. So far, the most widely used leakage model is the probing model defined by Ishai, Sahai, and Wagner at (CRYPTO 2003). While it is advantageously convenient for security proofs, it does not capture an adversary exploiting full leakage traces as, e.g., in horizontal attacks. Those attacks target the multiple manipulations of the same share to reduce noise and recover the corresponding value. To capture a wider class of attacks another model was introduced and is referred to as the random probing model. From a leakage parameter p, each wire of the circuit leaks its value with probability p. While this model much better reflects the physical reality of side channels, it requires more complex security proofs and does not yet come with practical constructions. In this paper, we define the first framework dedicated to the random probing model. We provide an automatic tool, called VRAPS, to quantify the random probing security of a circuit from its leakage probability. We also formalize a composition property for secure random probing gadgets and exhibit its relation to the strong non-interference (SNI) notion used in the context of probing security. We then revisit the expansion idea proposed by Ananth, Ishai, and Sahai (CRYPTO 2018) and introduce a compiler that builds a random probing secure circuit from small base gadgets achieving a random probing expandability property. We instantiate this compiler with small gadgets for which we verify the expected properties directly from our automatic tool. Our construction can tolerate a leakage probability up to 2 −8 , against 2 −25 for the previous construction, with a better asymptotic complexity

Incidence of childhood leukaemia in the vicinity of nuclear sites in France, 1990–1998

Overall, 670 cases (O) of childhood leukaemia were diagnosed within 20 km of the 29 French nuclear installations between 1990 and 1998 compared to an expected number (E) of 729.09 cases (O/E=0.92, 95% confidence interval (CI)=[0.85-0.99]). Each of the four areas defined around the sites showed non significant deficits of cases (0-5 km: O=65, O/E=0.87, CI=[0.67-1.10]; 5-10 km: O=165, O/E=0.95, CI=[0.81-1.10]; 10-15 km: O=220, O/E=0.88, CI=[0.77-1.00]; 15-20 km: O=220, O/E=0.96, CI=[0.84-1.10]). There was no evidence of a trend in standardised incidence ratio with distance from the sites for all children or for any of the three age groups studied. Similar results were obtained when the start-up year of the electricity-generating nuclear sites and their electric nuclear power were taken into account. No evidence was found of a generally increased risk of childhood leukaemia around the 29 French nuclear sites under study during 1990-1998