The Mathematics of Post-Quantum Cryptography

Castryck, Wouter and Ducas, Leo and Ehlen, Stephan and Kunzweiler, Sabrina and Randriam, Hugues and Trimoska, Monika and van Woerden, Wessel (2024) The Mathematics of Post-Quantum Cryptography. In: The Mathematics of Post-Quantum Cryptography, 4-5 December 2024, MPIM Bonn. (Unpublished)

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Abstract

Post-Quantum cryptography is a branch of public-key cryptography aiming to design cryptographic schemes building on mathematical problems that are conjectured to be hard to solve on both, classical and quantum computers. Such cryptographic schemes are needed since Shor's quantum algorithms break classical public-key cryptography based on the discrete logarithm problem (in finite fields or elliptic curves) as well as integer factoring in polynomial time (assuming a large enough error-corrected quantum computer will be built).

The main families of post-quantum schemes build on algorithmically hard problems related to lattices (e.g. finding short vectors in euclidean lattices), binary codes (decoding problem), isogenies between elliptic curves over finite fields, and multivariate polynomial systems. More recently, schemes based on finding isometries between lattices and also schemes based on group actions of classical groups have been proposed.

Hence, there are many connections between the research field of post-quantum cryptography and number theory, automorphic forms, algebra, algebraic geometry, representation theory, and so on. In order to evaluate the security of the newly proposed cryptographic schemes, deep connections between the different research communities, in particular between more applied researchers in cryptography and researchers in pure mathematics, have to be established. Otherwise, results from pure mathematics that apply to these schemes and the underlying mathematical problems might be overlooked by the cryptographic research community or discovered many years later.

Item Type:	Conference or Workshop Item (Lecture)
Subjects:	1 Discrete mathematics / algebra > 11-XX Number theory 1 Discrete mathematics / algebra > 14-XX Algebraic geometry 4 Applied mathematics / other > 68-XX Computer science 4 Applied mathematics / other > 81-XX Quantum theory
Divisions:	Research > Talks
Depositing User:	This Admin
Date Deposited:	09 Dec 2024 15:00
Last Modified:	09 Dec 2024 15:24
URI:	https://archive.mpim-bonn.mpg.de/id/eprint/5143

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