Talks
Spring 2020

Drinfeld Modules are not for Isogeny Based Cryptography

Monday, February 24th, 2020 4:15 pm4:45 pm

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Speaker: 

Antoine Joux, Institut de Mathématiques de Jussieu

Elliptic curves play a prominent role in cryptography. For instance, the hardness of the elliptic curve discrete logarithm problem is a foundational assumption in public key cryptography. Drinfeld modules are positive characteristic function field analogues of elliptic curves. It is natural to ponder the existence/security of Drinfeld module analogues of elliptic curve cryptosystems. But the Drinfeld module discrete logarithm problem is easy even on a classical computer. Beyond discrete logarithms, elliptic curve isogeny based cryptosystems have have emerged as candidates for post-quantum cryptography, including supersingular isogeny Diffie-Hellman (SIDH) and commutative supersingular isogeny Diffie-Hellman (CSIDH) protocols. We formulate Drinfeld module analogues of these elliptic curve isogeny based cryptosystems and devise classical polynomial time algorithms to break these Drinfeld analogues catastrophically.

 

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