Description
Hash Proof Systems were first introduced by Cramer and Shoup (Eurocrypt'02) as a tool to construct efficient chosen-ciphertext-secure encryption schemes. Since then, they have found many other applications, including password authenticated key exchange, oblivious transfer, and zero-knowledge arguments. One of the aspects that makes hash proof systems so interesting and powerful is that they can be seen as implicit proofs of membership for certain languages. As a result, by extending the family of languages that they can handle, one often obtains new applications or new ways to understand existing schemes. In this paper, we show how to construct hash proof systems for the disjunction of languages defined generically over cyclic, bilinear, and multilinear groups. Among other applications, this enables us to construct the most efficient one-time simulation-sound (quasi-adaptive) non-interactive zero-knowledge arguments for linear languages over cyclic groups, the first one-round group password-authenticated key exchange without random oracles, the most efficient threshold structure-preserving chosen-ciphertext-secure encryption scheme, and the most efficient one-round password authenticated key exchange in the UC framework. Join work with Michel Abdalla and David Pointcheval. Eprint 2014/483
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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