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octobre 2020

CRYPTO : Édouard Rousseau (LMV UVSQ) : Trisymmetric multiplication formulas in finite fields

22 octobre / 10:30 - 12:30
Bâtiment Descartes, salle 301,

Finite fields have a central role in cryptography, since many protocols use them as their foundation. Therefore, it is crucial to have efficient arithmetic operations, e.g. multiplication and addition, over finite fields. Multiplication is usually quite expensive, hence there has been extensive research to find Karatsuba-like formulas reducing the number of multiplications involved when computing a bilinear map over a finite field. The minimal number of multiplications in such formulas is called the bilinear complexity, and it is also of…

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novembre 2020

CRYPTO : Dmitrii Koshelev (LMV UVSQ) : Hashing to elliptic curves y^2 = x^3 + b provided that b is a quadratic residue.

5 novembre / 11:00 - 12:00
Bâtiment Descartes, salle 301

Let Fq be a finite field and E_b : y^2 = x^3 + b be an ordinary elliptic Fq-curve of j-invariant 0 such that sqrt(b) is in Fq. In particular, this condition is fulfilled for the curve BLS12-381 and for one of sextic twists of the curve BW6-761 (in both cases b=4). These curves are very popular in pairing-based cryptography. The article provides an efficient constant-time hashing h: Fq -> E_b(Fq) of an absolutely new type for which at worst…

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