Description
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 susceptible to subexponential quantum attacks, due to Kuperberg's algorithm. These attacks force us to work over large base fields, heavily impacting practical performance. We present a new method for evaluating the CSIDH group action, which admits several desirable cryptographic features (in particular, it is branchless, deterministic, dummy free, and constant time). We furthermore show that a natural extension of the algorithm allows to mitigate Kuperberg's attack, without increasing the size of the base field.
Practical infos
Next sessions
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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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