International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Jean-Claude Bajard

Publications

Year
Venue
Title
2014
EPRINT
2010
EPRINT
A New Security Model for Authenticated Key Agreement
The Canetti--Krawczyk (CK) and extended Canetti--Krawczyk (eCK) security models, are widely used to provide security arguments for key agreement protocols. We discuss security shades in the (e)CK models, and some practical attacks unconsidered in (e)CK--security arguments. We propose a strong security model which encompasses the eCK one. We also propose a new protocol, called Strengthened MQV (SMQV), which in addition to provide the same efficiency as the (H)MQV protocols, is particularly suited for distributed implementations wherein a tamper--proof device is used to store long--lived keys, while session keys are used on an untrusted host machine. The SMQV protocol meets our security definition under the Gap Diffie--Hellman assumption and the Random Oracle model.
2010
EPRINT
Combining leak--resistant arithmetic for elliptic curves defined over $\F_p$ and RNS representation
In this paper we combine the residue number system (RNS) representation and the leak-resistant arithmetic on elliptic curves. These two techniques are relevant for implementation of elliptic curve cryptography on embedded devices.\\ % since they have leak-resistance properties. It is well known that the RNS multiplication is very efficient whereas the reduction step is costly. Hence, we optimize formulae for basic operations arising in leak-resistant arithmetic on elliptic curves (unified addition, Montgomery ladder) in order to minimize the number of modular reductions. We also improve the complexity of the RNS modular reduction step. As a result, we show how to obtain a competitive secured implementation.\\ Finally, %we recall the main advantages of the RNS representation, %especially in hardware and for embedded devices, and we show that, contrary to other approaches, ours takes optimally the advantage of a dedicated parallel architecture.
2004
CHES
2004
EPRINT
Parallel Montgomery Multiplication in $GF(2^k)$ using Trinomial Residue Arithmetic
Jean-Claude Bajard Laurent Imbert Graham A. Jullien
We propose the first general multiplication algorithm in $\mathrm{GF}(2^k)$ with a subquadratic area complexity of $\mathcal{O}(k^{8/5}) = \mathcal{O}(k^{1.6})$. Using the Chinese Remainder Theorem, we represent the elements of $\mathrm{GF}(2^k)$; i.e. the polynomials in $\mathrm{GF}(2)[X]$ of degree at most $k-1$, by their remainder modulo a set of $n$ pairwise prime trinomials, $T_1,\dots,T_{n}$, of degree $d$ and such that $nd \geq k$. Our algorithm is based on Montgomery's multiplication applied to the ring formed by the direct product of the trinomials.