Description
Pairings on elliptic curves are involved in signatures, NIZK, and recently in blockchains (ZK-SNARKS).<br/> These pairings take as input two points on an elliptic curve E over a finite field, and output a value in an extension of that finite field. Usually for efficiency reasons, this extension degree is a power of 2 and 3 (such as 12,18,24), and moreover the characteristic of the finite field has a special form. The security relies on the hardness of computing discrete logarithms in the group of points of the curve and in the finite field extension.<br/> In 2013-2016, new variants of the function field sieve and the number field sieve algorithms turned out to be faster in certain finite fields related to pairing-based cryptography. Now small characteristic settings (with GF(2^(4*n)), GF(3^(6*m))) are discarded, and the situation of GF(p^k) where p is prime and k is small (in practice from 2 to 54) is unclear.<br/> The asymptotic complexity of the Number Field Sieve algorithm in finite fields GF(p^k) (where p is prime) and its Special and Tower variants is given by an asymptotic formula of the form A^(c+o(1)) where A depends on the finite field size (log p^k), o(1) is unknown, and c is a constant between 1.526 and 2.201 that depends on p, k, and the choice of parameters in the algorithm.<br/> In this work we improve the approaches of Menezes-Sarkar-Singh and Barbulescu-Duquesne to estimate the cost of a hypothetical implementation of the Special-Tower-NFS in GF(p^k) for small k (k <= 24), and update some parameter sizes for pairing-based cryptography. This is a joint work with Shashank Singh, IISER Bhopal, India. lien: http://desktop.visio.renater.fr/scopia?ID=721273***5165&autojoin
Prochains exposés
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Verification of Rust Cryptographic Implementations with Aeneas
Orateur : Aymeric Fromherz - Inria
From secure communications to online banking, cryptography is the cornerstone of most modern secure applications. Unfortunately, cryptographic design and implementation is notoriously error-prone, with a long history of design flaws, implementation bugs, and high-profile attacks. To address this issue, several projects proposed the use of formal verification techniques to statically ensure the[…] -
On the average hardness of SIVP for module lattices of fixed rank
Orateur : Radu Toma - Sorbonne Université
In joint work with Koen de Boer, Aurel Page, and Benjamin Wesolowski, we study the hardness of the approximate Shortest Independent Vectors Problem (SIVP) for random module lattices. We use here a natural notion of randomness as defined originally by Siegel through Haar measures. By proving a reduction, we show it is essentially as hard as the problem for arbitrary instances. While this was[…] -
Endomorphisms via Splittings
Orateur : Min-Yi Shen - No Affiliation
One of the fundamental hardness assumptions underlying isogeny-based cryptography is the problem of finding a non-trivial endomorphism of a given supersingular elliptic curve. In this talk, we show that the problem is related to the problem of finding a splitting of a principally polarised superspecial abelian surface. In particular, we provide formal security reductions and a proof-of-concept[…]-
Cryptography
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