Description
The problem of computing the zeta function of a variety over a finite field has attracted considerable interest in recent years, motivated in part by an application in cryptography. (In less fancy language, the problem is just to compute the number of solutions to a system of polynomial equations over a finite field.) I will discuss a new algorithm for computing zeta functions which is based upon relative p-adic cohomology. The idea is that to compute the zeta function of a single projective hypersurface, say , one puts it in a one-dimensional family of hypersurfaces. As one moves through this family, the zeta function varies in a manner which is controlled by a differential equation. One can arrange matters so that one fibre in the family has an easily computed zeta function. By solving the differential equation locally around this fibre, and using a form of analytic continuation, one can now recover the zeta function of any fibre in the family. In particular, one gets the zeta function of the original hypersurface! The key point is that because the `deformation' from the original hypersurface to the easy one is one-dimensional, the complexity of this approach is largely independent of the dimension of the hypersurface. In fact, one gets a uniform dependence on the input size over all dimensions. This contrasts starkly with existing approaches, whose performance deteriorates as the dimension increases. I believe the talk should be of interest to both cryptographers and p-adic cohomologists.
Next sessions
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SoK: Security of the Ascon Modes
Speaker : Charlotte Lefevre - Radboud University
The Ascon authenticated encryption scheme and hash function of Dobraunig et al (Journal of Cryptology 2021) were recently selected as winner of the NIST lightweight cryptography competition. The mode underlying Ascon authenticated encryption (Ascon-AE) resembles ideas of SpongeWrap, but not quite, and various works have investigated the generic security of Ascon-AE, all covering different attack[…] -
Comprehensive Modelling of Power Noise via Gaussian Processes with Applications to True Random Number Generators
Speaker : Maciej Skorski - Laboratoire Hubert Curien
The talk examines power noise modelling through Gaussian Processes for secure True Random Number Generators. While revisiting one-sided fractional Brownian motion, we obtain novel contributions by quantifying posterior uncertainty in exact analytical form, establishing quasi-stationary properties, and developing rigorous time-frequency analysis. These results are applied to model oscillator[…]-
Cryptography
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TRNG
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CryptoVerif: a computationally-sound security protocol verifier
Speaker : Bruno Blanchet - Inria
CryptoVerif is a security protocol verifier sound in the computational model of cryptography. It produces proofs by sequences of games, like those done manually by cryptographers. It has an automatic proof strategy and can also be guided by the user. It provides a generic method for specifying security assumptions on many cryptographic primitives, and can prove secrecy, authentication, and[…]-
Cryptography
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