Hugues Randriam

Efficient indifferentiable hashing into ordinary elliptic curves

We provide the first construction of a hash function into ordinary elliptic curves that is indifferentiable from a random oracle, based on Icarts deterministic encoding from Crypto 2009. While almost as efficient as Icarts encoding, this hash function can be plugged into any cryptosystem that requires hashing into elliptic curves, while not compromising proofs of security in the random oracle model. We also describe a more general (but less efficient) construction that works for a large class of encodings into elliptic curves, for example the Shallue-Woestijne-Ulas (SWU) algorithm. Finally we describe the first deterministic encoding algorithm into elliptic curves in characteristic 3.

On a conjecture about binary strings distribution

It is a difficult challenge to find Boolean functions used in stream ciphers achieving all of the necessary criteria and the research of such functions has taken a significant delay with respect to crypt-analyses. Very recently, an infinite class of Boolean functions has been proposed by Tu and Deng having many good cryptographic properties under the assumption that the following combinatorial conjecture about binary strings is true: Conjecture 0.1. Let St, k be the following set: St,k = {(a, b) ∈ (Z/(2k - 1)Z)2 |a + b = t and w(a) + w(b) < k}. Then: |St,k| ≤ 2k-1. The main contribution of the present paper is the reformulation of the problem in terms of carries which gives more insight on it than simple counting arguments. Successful applications of our tools include explicit formulas of |St,k| for numbers whose binary expansion is made of one block, a proof that the conjecture is asymptotically true and a proof that a family of numbers (whose binary expansion has a high number of 1s and isolated 0s) reaches the bound of the conjecture. We also conjecture that the numbers in that family are the only ones reaching the bound.

New uniform and asymptotic upper bounds on the tensor rank of multiplication in extensions of finite fields

We obtain new uniform upper bounds for the tensor rank of the multiplication in the extensions of the finite fields

On the Number of Carries Occurring in an Addition Mod

\mathbb{F}_q

Hecke operators with odd determinant and binary frameproof codes beyond the probabilistic bound

for any prime power

Yet another variation on minimal linear codes

q

Lower bounds on the minimum distance of long codes in the Lee metric

; moreover these uniform bounds lead to new asymptotic bounds as well. In addition, we also give purely asymptotic bounds which are substantially better by using a family of Shimura curves defined over

Divisibility of exponential sums via elementary methods

\mathbb{F}_q

On a conjecture about binary strings distribution.

, with an optimal ratio of

Trace codes over \({\mathbb {Z}}_4,\) and Boolean functions

\mathbb{F}_{q^t}