Description
Lattice-based cryptography is one of the major line of research to build post-quantum public key primitives. In this thesis, we discuss about digital signatures constructions and their implementation. We first describe a Fiat-Shamir transformation from an identification scheme using rejection sampling to a digital signature secure in the random oracle model. Then we describe an identity-based encryption scheme and we prove its security in the standard model. An identity-based encryption scheme is like a classical public key where the public key is the identity of a user such as its email address or its social security number.<br/> A user contacts a third trusted party to get a secret key associated to its identity. In our construction, a secret key consists essentially in a signature of the identity of the user. We also describe this underlying digital signature scheme associated to our identity based encryption scheme.<br/> Finally, we present implementation results of these two schemes and how we choose concrete parameters.<br/> lien: rien
Next sessions
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Verification of Rust Cryptographic Implementations with Aeneas
Speaker : Aymeric Fromherz - Inria
From secure communications to online banking, cryptography is the cornerstone of most modern secure applications. Unfortunately, cryptographic design and implementation is notoriously error-prone, with a long history of design flaws, implementation bugs, and high-profile attacks. To address this issue, several projects proposed the use of formal verification techniques to statically ensure the[…] -
On the average hardness of SIVP for module lattices of fixed rank
Speaker : Radu Toma - Sorbonne Université
In joint work with Koen de Boer, Aurel Page, and Benjamin Wesolowski, we study the hardness of the approximate Shortest Independent Vectors Problem (SIVP) for random module lattices. We use here a natural notion of randomness as defined originally by Siegel through Haar measures. By proving a reduction, we show it is essentially as hard as the problem for arbitrary instances. While this was[…] -
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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