International Association for Cryptologic Research

International Association
for Cryptologic Research


Nicolas Thériault


SPA Resistant Left-to-Right Integer Recodings
Nicolas Th\'eriault
We introduce two new left-to-right integer recodings which can be used to perform scalar multiplication with a fixed sequence of operations. These recodings make it possible to have a simple power analysis resistant implementation of a group-based cryptosystem without using unified formulas or introducing dummy operations. This approach is very useful for groups in which the doubling step are less expensive than the addition step, for example with hyperelliptic curves over binary fields or elliptic curves with mixed coordinates.
Unified Point Addition Formul{\ae} and Side-Channel Attacks
Douglas Stebila Nicolas Th\'eriault
The successful application to elliptic curve cryptography of side-channel attacks, in which information about the secret key can be recovered from the observation of side channels like power consumption or timing, has motivated the recent development of unified formul{\ae} for elliptic curve point operations. In this paper, we give a version of a previously-developed family of unified point addition formul{\ae} that uses projective coordinates for improved efficiency. We discuss the applicability of a recent attack by Walter on this family of projective formul{\ae} and describe how the field arithmetic can be implemented to obtain fully unified formul{\ae} and avoid this type of attack.
A double large prime variation for small genus hyperelliptic index calculus
In this article, we examine how the index calculus approach for computing discrete logarithms in small genus hyperelliptic curves can be improved by introducing a double large prime variation. Two algorithms are presented. The first algorithm is a rather natural adaptation of the double large prime variation to the intended context. On heuristic and experimental grounds, it seems to perform quite well but lacks a complete and precise analysis. Our second algorithm is a considerably simplified variant, which can be analyzed easily. The resulting complexity improves on the fastest known algorithms. Computer experiments show that for hyperelliptic curves of genus three, our first algorithm surpasses Pollard's Rho method even for rather small field sizes.