Description
There are several algorithms for computing isogenies between elliptic curves, and one of them is Elkies' method using the modular curve. Motivated by that, we will look at an algebraic approach to explicitly compute isogenies of degree p for certain small primes p between elliptic curves, by using the modular curve and 'generic kernel polynomials'.
Next sessions
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Algorithms for post-quantum commutative group actions
Speaker : Marc Houben - Inria Bordeaux
At the historical foundation of isogeny-based cryptography lies a scheme known as CRS; a key exchange protocol based on class group actions on elliptic curves. Along with more efficient variants, such as CSIDH, this framework has emerged as a powerful building block for the construction of advanced post-quantum cryptographic primitives. Unfortunately, all protocols in this line of work are[…] -
Endomorphisms via Splittings
Speaker : Min-Yi Shen - No Affiliation
One of the fundamental hardness assumptions underlying isogeny-based cryptography is the problem of finding a non-trivial endomorphism of a given supersingular elliptic curve. In this talk, we show that the problem is related to the problem of finding a splitting of a principally polarised superspecial abelian surface. In particular, we provide formal security reductions and a proof-of-concept[…]-
Cryptography
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