Description
Recent algorithmic improvements of discrete logarithm computation in special extension fields threaten the security of pairing-friendly curves used in practice. A possible answer to this delicate situation is to propose alternative curves that are immune to these attacks, without compromising the efficiency of the pairing computation too much. We follow this direction, and focus on embedding degrees 5 to 8; we extend the Cocks-Pinch algorithm to obtain pairing-friendly curves with an efficient ate pairing. We carefully select our curve parameters so as to thwart possible attacks by “special” or “tower” Number Field Sieve algorithms. We target a 128-bit security level, and back this security claim by time estimates for the DLP computation. We also compare the efficiency of the optimal ate pairing computation on these curves to k = 12 curves (Barreto–Naehrig,Barreto–Lynn–Scott), k = 16 curves (Kachisa–Schaefer–Scott) and k = 1 curves (Chatterjee–Menezes–Rodríguez-Henríquez).<br/> lien: http://desktop.visio.renater.fr/scopia?ID=724108***7354&autojoin
Prochains exposés
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Lightweight (AND, XOR) Implementations of Large-Degree S-boxes
Orateur : Marie Bolzer - LORIA
The problem of finding a minimal circuit to implement a given function is one of the oldest in electronics. In cryptography, the focus is on small functions, especially on S-boxes which are classically the only non-linear functions in iterated block ciphers. In this work, we propose new ad-hoc automatic tools to look for lightweight implementations of non-linear functions on up to 5 variables for[…]-
Cryptography
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Symmetrical primitive
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Implementation of cryptographic algorithm
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Algorithms for post-quantum commutative group actions
Orateur : Marc Houben - Inria Bordeaux
At the historical foundation of isogeny-based cryptography lies a scheme known as CRS; a key exchange protocol based on class group actions on elliptic curves. Along with more efficient variants, such as CSIDH, this framework has emerged as a powerful building block for the construction of advanced post-quantum cryptographic primitives. Unfortunately, all protocols in this line of work are[…] -
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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