Program

Opening Remarks by Daniele Micciancio, Ted Chinburg and Frauke Bleher

Abstract 

Abstract:  On July 28th, Anthropic researchers Straznickas and Weis and its Claude AI published a successful attack on NIST-candidate post-quantum digital signature scheme HAWK. They proceed by computing a new automorphism of the HAWK lattice on the public basis, which by previous work of G–Pulles suffices to halve the security parameter of the scheme. In this talk I will explain the attack assuming little prior knowledge on module-LIP-based schemes, and if time permits propose a potential direction towards a new scheme.

Abstract: Several recent results in arithmetic statistics have stimulated the investigation of the structure of the pro-nilpotent tower of a number field and how this structure is informed by the underlying randomness. A precise instance of this was established in 2023 in joint work with Koymans where we proved that the 2-step nilpotent closure (of certain number fields) can be encoded in a decorated graph on the set of primes, we have shown that this graph is pseudo-random, and with that we deduced that the isomorphism class of the group admits an explicit combinatorial description. This shows that distinct number fields can have isomorphic 2-nilpotent Galois groups, upon matching the primes in a graph-preserving manner. Building on this description, in joint work in progress with Zuccon, we establish that these are (in a precise sense) the only possible identifications between these Galois groups. In other words, the 2-step nilpotent group "knows" about the totality of the primes in the abelianization: they form a rigid set that can be at most permuted. The key idea of the proof of this rigidity result was discovered by Aletheia, an internal agent at Google DeepMind.

Abstract: In 1981, van Emde Boas conjectured that computing a shortest non-zero vector of a lattice in a Euclidean space is NP-hard. In this talk, we outline a proof of this conjecture. We follow the derandomization program as formulated by Micciancio (1998–2014) who conjectured the existence of an efficient deterministic construction of locally dense lattices . The main part of our work is to resolve this conjecture. Our proof builds on the construction of locally dense lattices via Reed-Solomon codes by Bennett and Peikert (2023), and depends crucially on Deligne's work on the Weil conjectures for higher-dimensional varieties over finite fields.

Abstract:  In this talk, we measure a number field not by its degree or discriminant, but by its covering radius. We show that this is bounded by n^{0.661} for infinitely many fields of increasing degree n for the L_2 norms. By contrast, for ϵ > 0, there are only finitely many cyclotomic fields with L_2 covering radius less than n^{1−ϵ}. 

Abstract: 

Abstract: I will do a high-level view of the key ideas behind two recent papers on new, complementary ways of SIMD packing (TCC) and handling large plaintext moduli (Crypto).

Discussion of AI and the future of lattice cryptography