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We present preprocessing-MPC schemes of arithmetic functions with optimal round complexity, function-independent correlated randomness, and communication and space complexities that grow linearly with...
Algebraic analysis of block ciphers aims at finding the secret key by solving a collection of polynomial equations that describe the internal structure of a cipher for chosen observations of plaintext...
Elliptic Curve Cryptography (ECC) is gaining popularity in recent years. Having short keys and short signatures in particular makes ECC likely to be adopted in numerous internet-of-things (IoT) device...
We give an optimal-size representation for the elements of the trace zero subgroup of the Picard group of an elliptic or hyperelliptic curve of any genus, with respect to a field extension of any pr...
This paper combines cryptographic voting and web page ranking and proves that it is possible to hold elections so as not to limit a voter by a list of candidates, to benefit from voter’s personal ex...
In this paper, we revisit the recent small characteristic discrete logarithm algorithms. We show that a simplified description of the algorithm, together with some additional ideas, permits to obtain ...
Modular exponentiation is core to today’s main stream public key cryptographic systems. In this article, we generalize the classical fractional wNAF method for modular exponentiation – the classical ...
By embedding a Toeplitz matrix-vector product (MVP) of dimension $n$ into a circulant MVP of dimension $N=2n+\delta -1$, where $\delta $ can be any nonnegative integer, we present a $GF(2^n)$ multipli...
This article concerns itself with the triangular permutation group, induced by triangular polynomial maps over $\F_p$, which is a $p$-sylow subgroup of $\perm(\F_p^n)$.
This article concerns itself with the triangular permutation group, induced by triangular polynomial maps over $\F_p$, which is a $p$-sylow subgroup of $\perm(\F_p^n)$. The aim of this article is twof...
We present a complete set of efficient explicit formulas for arithmetic in the degree 0 divisor class group of a genus two real hyperelliptic curve givenin affine coordinates. In addition to formula...
We present a complete set of efficient explicit formulas for arithmetic in the degree 0 divisor class group of a genus two real hyperelliptic curve given in affine coordinates. In addition to formulas...
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 cry...
We discuss arithmetic in the Jacobian of a hyperelliptic curve C of genus g. The traditional approach is to fix a point P1 2 C and rep- resent divisor classes in the form E 􀀀 d(P1) where E ...
From the viewpoint of x-coordinate-only arithmetic on ellip- tic curves, switching between the Edwards model and the Montgomery model is quasi cost-free. We use this observation to speed up Mont- g...

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