2026-11-03
11:00
Salle 2
Spherical Codes from Craig’s Lattices
Spherical codes are collections of points on a high-dimensional sphere with the property that any two points are far apart. They are a classical model for transmitting data reliably over noisy channels. A central goal is to construct codes that are both large and efficiently decodable. A 2015 result by Bacher implies that Craig's lattices give rise to spherical codes of at least super-polynomial size. In this talk, we show that these codes can also be efficiently (list) decoded. Furthermore, we provide computational evidence that the code size asymptotically outperforms all previously known constructions.
2026-10-13
11:00
Salle 2
Reduction of Polarizations on Products of Elliptic Curves
Let $A=E_1 \times E_2$ be a product of elliptic curves. Polarizations on $A$ can be represented by positive definite Hermitian matrices $H=\begin{pmatrix}a & h \\ \hat h & b \end{pmatrix}$, with $a, b \in \mathbb{Z}$ and $h \in \mathrm{Hom}(E_1,E_2)$. Equivalence of polarizations corresponds to the natural congruence action of $\mathrm{Aut}(A)$ on these matrices. We develop algorithms for reducing such matrix representatives within their equivalence classes. The algorithms transform a given polarization into an equivalent representative with controlled coefficients. By analyzing the reduction process, we derive explicit bounds on $a$, $b$, and $\deg(h)$ for the resulting representatives. This talk is based on ongoing joint work with Harun Kir, Eli Orvis, and Benjamin Wesolowski.
2026-10-04
11:00
Salle 2
MIKE (Module Isogeny Key Exchange): a fast and compact post-quantum NIKE
In this talk, we will present MIKE, a new post-quantum NIKE (Non-Interactive Key Exchange), based on a construction originally due to Serre. Its security reduces to the hardness of the supersingular endomorphism-ring problem (in the algebraic isogeny model). It is the most compact PQC NIKE in the world, beating the previous record holder by a factor of 3–6 while being 100–200 times faster. It can also bring back loved ones, reconcile Alice and Bob without any interaction, remove quantum curses, restore lost secrets, ensure success in grant applications, and protect against AI agents. Results guaranteed. Payment after results. This is joint work with the MIKE team.
2026-09-29
11:00
Salle 2
Geometric characterization of p-exceptional monomial GAPN functions
On finite fields of characteristic $p$, PN (perfect nonlinear) functions for odd $p$ and APN (almost perfect nonlinear) functions for even $p$ are well-known classes of highly nonlinear functions. GAPN (generalized almost perfect nonlinear) functions were introduced as a generalization of APN functions for even $p$ to all $p$. One of the main targets of studies on such highly nonlinear functions is their classification. While $p$-exceptional monomial PN and 2-exceptional monomial APN functions have been classified, the corresponding problem for GAPN functions remains open. Here, a polynomial over $\mathbb{F}_p$ is called a $p$-exceptional PN (resp. APN, resp. GAPN) function if it is a PN (resp. APN, resp. GAPN) function on $\mathbb{F}_{p^n}$ for infinitely many positive integers $n$. In this talk, we give a geometric characterization of $p$-exceptional monomial GAPN functions. To this end, for a prime power $q$, we establish a geometric characterization of non-zero polynomials in $\mathbb{F}_q[x, y]$ having no absolutely irreducible factor defined over $\mathbb{F}_q$.
2026-09-22
11:00
Salle 2
A unified reduction from RLWE to MP-LWE
Ring Learning With Errors (RLWE) is a central assumption in lattice-based cryptography, but its hardness depends on the underlying number field. Middle-Product Learning With Errors (MP-LWE) offers a structured alternative whose definition is independent of any particular number field. Previous reductions from RLWE to MP-LWE cover different families of fields, and neither of the two main approaches subsumes the other. In this talk, I will present a unified reduction framework for both primal and dual RLWE, parameterized by a pair of field elements, which recovers both previous approaches. Using geometry of numbers, we prove the existence of parameters giving polynomial noise growth for every monic irreducible defining polynomial whose coefficients are polynomially bounded in its degree. The result holds for sufficiently large prime moduli coprime to the polynomial discriminant, extending the families covered by previous reductions. I will explain the algebraic mechanism and the geometry behind the noise bound. The reduction is non-uniform: suitable parameters are proved to exist, while finding them in polynomial time cost in general remains open.
