Mark Lewko

How to leak on key updates

In the continual memory leakage model, security against attackers who can repeatedly obtain leakage is achieved by periodically updating the secret key. This is an appealing model which captures a wide class of side-channel attacks, but all previous constructions in this model provide only a very minimal amount of leakage tolerance during secret key updates. Since key updates may happen frequently, improving security guarantees against attackers who obtain leakage during these updates is an important problem. In this work, we present the first cryptographic primitives which are secure against a super-logarithmic amount of leakage during secret key updates. We present signature and public key encryption schemes in the standard model which can tolerate a constant fraction of the secret key to be leaked between updates as well as a constant fraction of the secret key and update randomness to be leaked during updates. Our signature scheme also allows us to leak a constant fraction of the entire secret state during signing. Before this work, it was unknown how to tolerate super-logarithmic leakage during updates even in the random oracle model. We rely on subgroup decision assumptions in composite order bilinear groups.

Endpoint restriction estimates for the paraboloid over finite fields

We prove certain endpoint restriction estimates for the paraboloid over finite fields in three and higher dimensions. Working in the bilinear setting, we are able to pass from estimates for characteristic functions to estimates for general functions while avoiding the extra logarithmic power of the field size which is introduced by the dyadic pigeonhole approach. This allows us to remove logarithmic factors from the estimates obtained by Mockenhaupt and Tao in three dimensions and those obtained by Iosevich and Koh in higher dimensions.

Sidonicity and variants of Kaczmarz’s problem@@@Sidonicité et un problème de Kaczmarz

We prove that a uniformly bounded system of orthonormal functions satisfying the

Maximal operators associated to multiplicative characters

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Orthonormal systems in linear spans

condition: (1) must contain a Sidon subsystem of proportional size, (2) must satisfy the Rademacher-Sidon property, and (3) must have its 5-fold tensor satisfy the Sidon property. On the other hand, we construct a uniformly bounded orthonormal system that satisfies the

On the complexity of asynchronous agreement against powerful adversaries

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Finite field restriction estimates based on Kakeya maximal operator estimates

condition but which is not Sidon. These problems are variants of Kaczmarzs Scottish book problem (problem 130) which, in its original formulation, was answered negatively by Rudin. A corollary of our argument is a new, elementary proof of Pisiers theorem that a set of characters satisfying the

New restriction estimates for the 3-d paraboloid over finite fields

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Estimates for the square variation of partial sums of Fourier series and their rearrangements

condition is Sidon.

Refinements of Gál's theorem and applications

We show that the natural analogue of the Carleson-Hunt inequality fails for multiplicative characters.