Description
The LLL lattice reduction algorithm of 1982 has proven to be useful in a wide variety of fields. It can be used to approximately solve computationally difficult lattice-based problems, such as the shortest vector problem, in polynomial time. We present a new algorithm for lattice reduction which is the first algorithm to have a complexity bound which is both polynomial and quasi-linear bound in the bit-length of the input.<br/> To achieve this we present an independently interesting toolkit for analyzing incremental lattice reductions.
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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