arXiv subjects

Emmanuel Fouotsa

Publications and source records attributed to Emmanuel Fouotsa.

4 recordsLinked to original sources

arXiv2026

Factorization of Isomorphisms of $(H,\theta)$-twisted Lie algebroids

We study the isomorphism groupoid $\mathcal{T}(M)$ of $\theta$-almost twisted Poisson ($\theta$-atP) structures on a smooth manifold $M$, focusing on the internal structure of its morphisms. A morphism in $\mathcal{T}(M)$ is a $C^\infty(M)$-linear isomorphism $\Phi:\gO^1(M)\to\gO^1(M)$ that simultaneously intertwines the anchor maps and the $(H,\theta)$-twisted Koszul brackets associated with two $\theta$-atP structures. Every such morphism induces a canonical isomorphism in $\theta$-atP cohomology. We define a classifying functor $$ \Delta : \mathrm{Mor}(\mathcal{T}(M)) \longrightarrow (Z^1_{\mathrm{dR}}(M) ,+), \qquad \Delta(\Phi)=\theta' - \theta, $$ which is additive under composition and partitions the morphisms into two complementary families: the sub-groupoid $\mathcal{T}_{\mathrm{fix}}=\ker\Delta$ of isomorphisms preserving $\theta$, and the family $\mathcal{T}_{\mathrm{mod}}$ of isomorphisms shifting $\theta$. We describe each element in this partition.

math.DS↗

arXiv2021

Low-Rank Parity-Check Codes Over Finite Commutative Rings

Low-Rank Parity-Check (LRPC) codes are a class of rank metric codes that have many applications specifically in network coding and cryptography. Recently, LRPC codes have been extended to Galois rings which are a specific case of finite rings. In this paper, we first define LRPC codes over finite commutative local rings, which are bricks of finite rings, with an efficient decoder. We improve the theoretical bound of the failure probability of the decoder. Then, we extend the work to arbitrary finite commutative rings. Certain conditions are generally used to ensure the success of the decoder. Over finite fields, one of these conditions is to choose a prime number as the extension degree of the Galois field. We have shown that one can construct LRPC codes without this condition on the degree of Galois extension.

cs.IT↗

arXiv2020

Parallel Computation of Optimal Ate Cryptographic Pairings at the $128$, $192$ and $256$-bit security levels using elliptic net algorithm

Efficient computations of pairings with Miller Algorithm have recently received a great attention due to the many applications in cryptography. In this work, we give formulae for the optimal Ate pairing in terms of elliptic nets associated to twisted Barreto-Naehrig (BN) curve, Barreto-Lynn-Scott(BLS) curves and Kachisa-Schaefer-Scott(KSS) curves considered at the $128$, $192$ and $256$-bit security levels, and Scott-Guillevic curve with embedding degree $54$. We show how to parallelize the computation of these pairings when the elliptic net algorithm instead is used and we obtain except in the case of Kachisa-Schaefer-Scott(KSS) curves considered at the $256$-bit security level, more efficient theoretical results with $8$ processors compared to the case where the Miller algorithm is used. This work still confirms that $BLS48$ curves are the best for pairing-based cryptography at $256$-bit security level \cite{NARDIEFO19}.

math.AG↗

arXiv2020

Optimal Ate Pairing on Elliptic Curves with Embedding Degree $9,15$ and $27$

Much attention has been given to the efficient computation of pairings on elliptic curves with even embedding degree since the advent of pairing-based cryptography. The few existing works in the case of odd embedding degrees require some improvements. This paper considers the computation of optimal ate pairings on elliptic curves of embedding degrees $k=9$, $15$, $27$ which have twists of order three. Our main goal is to provide a detailed arithmetic and cost estimation of operations in the tower extensions field of the corresponding extension fields. A good selection of parameters enables us to improve the theoretical cost for the Miller step and the final exponentiation using the lattice-based method as compared to the previous few works that exist in these cases. In particular, for $k=15$, $k=27$, we obtain an improvement, in terms of operations in the base field, of up to 25% and 29% respectively in the computation of the final exponentiation. We also find that elliptic curves with embedding degree $k=15$ present faster results than BN12 curves at the 128-bit security level. We provide a MAGMA implementation in each case to ensure the correctness of the formulas used in this work.

math.AG↗