2025-10-09
14:00
Salle 1
Towards Post-Quantum Bitcoin Blockchain using Dilithium Signature
Bitcoin is one of the famous cryptocurrencies in the world. It is a permissionless blockchain, and all transactions are stored in a public decentralized ledger. In its security design, Bitcoin utilizes various cryptographic primitives, such as hash functions and signature schemes. In the current version of Bitcoin, the Elliptic Curve Digital Signature Algorithm (ECDSA) is employed, which is not considered post-quantum secure due to Shor’s algorithm. In this talk, we will analyze the potential replacement of ECDSA with Dilithium, which is a postquantum digital signature based on lattices and recently standardized by NIST as ML-DSA. Bitcoin operates on a pseudonymous system rather than providing complete anonymity. To enhance privacy protection, the Bitcoin community has adopted a special type of deterministic wallet as outlined in Bitcoin Improvement Proposal 32 (BIP32). We will show how to construct deterministic wallets from Dilithium by first designingDilithiumRK, a signature scheme with rerandomizable keys build on top of Dilithium. We will then discuss the unlinkability, unforgeability and efficiency of DilithiumRK and the resulting wallets. This is joint work with Adeline Roux-Langlois.
2025-10-07
11:00
Salle 2
Reduction of plane quartics and Cayley octads
For a long time, number theorists have been interested in studying the reduction modulo $p$ of algebraic varieties defined over number fields. For example, in the case of an elliptic curve $E$, where we distinguish between good, multiplicative, and additive reduction, the Birch and Swinnerton-Dyer conjecture predicts that the reduction plays a crucial role in understanding the rank of $E(Q)$. For hyperelliptic curves $y^2 = f(x)$, the reduction has been studied extensively through the Weierstrass points, i.e. the roots of $f(x)$. In this talk, I will tell about recent work joint with Jordan Docking, Vladimir Dokchitser, Reynald Lercier, Elisa Lorenzo Garcia, and Andreas Pieper, in which we study the situation for the first case of non-hyperelliptic curves: plane quartics. As a result of numerous computations, we made a prediction how the reduction type of a plane quartic can be determined from the Cayley octad, a set of eight points in $P^3$ associated to the curve.
2025-09-30
11:00
Salle 2
The lattice packing problem in dimension 9 by Voronoi’s algorithm
In 1908 Voronoi introduced an algorithm that solves the lattice packing problem in any dimension in finite time. Voronoi showed that any lattice with optimal packing density must be a so-called perfect lattice, and his algorithm enumerates the finitely many perfect lattices up to similarity in a fixed dimension. However, due to the high complexity of the algorithm this enumeration had, until now, only been completed up to dimension 8. In this talk we will present our work on a full enumeration of all 2,237,251,040 perfect lattices in dimension 9 via Voronoi's algorithm. As a corollary, this shows that the laminated lattice gives the densest lattice packing in dimension 9. Furthermore, as a byproduct of the computation, we classify the set of possible kissing numbers in dimension 9. We will discuss Voronoi's algorithm and the many algorithmic, implementation, and parallelization efforts that were required for this computation to succeed. This is joint work with Mathieu Dutour Sikirić.
2025-09-23
11:00
Salle 2
Exponential sums and Linear cryptanalysis: Analysis of Butterfly-like constructions
This presentation focuses on the recently identified links between algebraic geometry and symmetric cryptography. Specifically, we demonstrate how bounds on exponential sums, based on results from Deligne, Denef–Loeser and Rojas–León, can be used to evaluate the correlations of linear approximations in cryptographic constructions with a low algebraic degree. This yields concrete bounds for Butterfly-like designs, such as the Flystel. These results reinforce security arguments against linear cryptanalysis, notably by resolving a conjecture on the Flystel construction.
2025-09-16
11:00
Salle 2
The Poincaré Biextension
I will describe the elliptic net structure of the Poincaré biextension for elliptic curves. I will explain how this can be generalized to $R$-biextensions, where $R$ is an order in an imaginary quadratic field, and how it respects the CM structure of an elliptic curve and relates to sesquilinear Weil and Tate pairings.
