Episode 14: Schnorr, Factoring and Lattices!

Cryptography FM

On March 1st, 2021, a curious paper appeared on the Cryptology ePrint Archive: senior cryptographer Claus Peter Schnorr submitted research that claims to use lattice mathematics to improve the fast factoring of integers so much that he was able to completely “destroy the RSA cryptosystem” -- certainly a serious claim.

Strangely, while the paper’s ePrint abstract did mention RSA, the paper itself didn’t. Two days later, Schnorr pushed an updated version of the paper, clarifying his method.

Does Schnorr’s proposed method for “destroying RSA” hold water, however? Some cryptographers aren’t convinced. Joining us today is Leo Ducas , a tenured researcher at CWI, Amsterdam who specialises in lattice-based cryptography, to help us understand where Schnorr was coming from, whether his results stand on their own, and how the influence of lattice mathematics in applied cryptography has grown over the past decade.

Links and papers discussed in the show:

• Schnorr's ePrint submission
• Leo Ducas's implementation of Schnorr's proposed algorithm in Sage

Music composed by Toby Fox and performed by Sean Schafianski.

Special Guest: Léo Ducas.

Sponsored By:

• Symbolic Software: This episode is sponsored by Symbolic Software. Symbolic Software helps you bring in the experience and knowledge necessary to design, or prove secure, state-of-the-art cryptographic systems for new solutions. We've helped design and formally verify some of the world's most widely used cryptographic protocols.

Links:

• Fast Factoring Integers by SVP Algorithms by Claus Peter Schnorr — "[...] This destroys the RSA cryptosystem."
• Testing Schnorr's factoring Claim in SageMath