Description
Providing security proofs instead of arguing lack of existing relevant attacks is a quite new approach when it comes to cryptography. In the last thirty years, a lot of work has been done to formalize security of systems and prove of the achievement of security criteria. It has resulted in the design of a great number of proofs under various hypotheses. Though a step in the right direction, these pencil-and-paper proofs are so numerous, involved and technical that the community has difficulty to carefully check them. The well-known example of the encryption scheme OAEP whose security proof, apparently correct, was corrected seven years after its publication illustrates that security-dedicated verification tools need to be designed. Our work takes place in the so-called computational model, where messages are considered to be bitstrings, and system adversaries are probabilistic Turing machines. A proof of security is then a complexity-theoretic reduction argument: the probability of success of an adversary in solving a security challenge is reduced to its ability to solve a known difficult problem (given a fixed amount of resources). Firstly, we provide some intuition on usual security requirements, and common sketches of security proofs. Then, we present a semantics and a logic to formalize security proofs. One could say there are several levels in automatic proving: computer-aided verification of proofs, computer-aided design of proofs, and automatic generation of proofs. We show how our inference rules can be used to derive proofs and verify them automatically, or sometimes perform a proof search using some additional inputs.
Prochains exposés
-
Verification of Rust Cryptographic Implementations with Aeneas
Orateur : 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
Orateur : 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
Orateur : 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
-