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
Next sessions
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Dual attacks in code-based (and lattice-based) cryptography
Speaker : Charles Meyer-Hilfiger - Inria Rennes
The hardness of the decoding problem and its generalization, the learning with errors problem, are respectively at the heart of the security of the Post-Quantum code-based scheme HQC and the lattice-based scheme Kyber. Both schemes are to be/now NIST standards. These problems have been actively studied for decades, and the complexity of the state-of-the-art algorithms to solve them is crucially[…]-
Cryptography
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Présentations des nouveaux doctorants Capsule
Speaker : Alisée Lafontaine et Mathias Boucher - INRIA Rennes
2 nouveaux doctorants arrivent dans l'équipe Capsule et présenteront leurs thématiques de recherche. Alisée Lafontaine, encadrée par André Schrottenloher, présentera son stage de M2: "Quantum rebound attacks on double-block length hash functions" Mathias Boucher, encadré par Yixin Shen, parlera des algorithmes quantiques et des réseaux euclidiens. -
Design of fast AES-based Universal Hash Functions and MACs
Speaker : Augustin Bariant - ANSSI
Ultra-fast AES round-based software cryptographic authentication/encryption primitives have recently seen important developments, fuelled by the authenticated encryption competition CAESAR and the prospect of future high-profile applications such as post-5G telecommunication technology security standards. In particular, Universal Hash Functions (UHF) are crucial primitives used as core components[…]-
Cryptography
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Lie algebras and the security of cryptosystems based on classical varieties in disguise
Speaker : Mingjie Chen - KU Leuven
In 2006, de Graaf et al. proposed a strategy based on Lie algebras for finding a linear transformation in the projective linear group that connects two linearly equivalent projective varieties defined over the rational numbers. Their method succeeds for several families of “classical” varieties, such as Veronese varieties, which are known to have large automorphism groups. In this talk, we[…]-
Cryptography
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Some applications of linear programming to Dilithium
Speaker : Paco AZEVEDO OLIVEIRA - Thales & UVSQ
Dilithium is a signature algorithm, considered post-quantum, and recently standardized under the name ML-DSA by NIST. Due to its security and performance, it is recommended in most use cases. During this presentation, I will outline the main ideas behind two studies, conducted in collaboration with Andersson Calle-Vierra, Benoît Cogliati, and Louis Goubin, which provide a better understanding of[…]