François Arnault

François Arnault, Zoé Amblard

The Ekert quantum key distribution protocol uses pairs of entangled qubits and performs checks based on a Bell inequality to detect eavesdropping. The 3DEB protocol uses instead pairs of entangled qutrits to achieve better noise resistance than the Ekert protocol. It performs checks based on a Bell inequality for qutrits named CHSH-3. In this paper, we present a new protocol, which also uses pairs of entangled qutrits, but achieves even better noise resistance than 3DEB. This gain of performance is obtained by using another inequality called here hCHSH-3. As the hCHSH3 inequality involve products of observables which become incompatible when using quantum states, we show how the parties running the protocol can measure the violation of hCHSH3 in the presence of noise, to ensure the secrecy of the key.

François Arnault

Quadratic forms with embedded discriminants. Integral binary quadratic forms have multiple applications, for example in factorization or cryptography. The Nice family of cryptographic systems makes use of quadratic forms with different discriminants $\pm p$, and $\pm pq^2$ where $p$, $q$ are large primes. This paper shows the precise links between forms with $D$ discriminant and forms with $Df^2$ discriminant, which are crucial in the analysis of the systems Nice and theirs attacks. We also introduce the notion of semi-equivalence of binary quadratic forms, and give some characterizations of semi-equivalent forms, which are useful in the analysis of these attacks. ----- Les formes quadratiques binaires fournissent un moyen explicite pour manipuler des idéaux de corps quadratiques, et leurs applications pratiques sont multiples. De nombreux algorithmes de factorisation les utilisent. Elle sont aussi utilisées en cryptographie, en particulier pour les systèmes Nice. Les systèmes de chiffrement Nice utilisent des formes quadratiques de discriminants $\pm p$ et $\pm pq^2$ où $p$ et $q$ sont des nombres premiers. Cet article précise les liens entre les formes de discriminant $D$ et celles de discriminant $Df^2$, ce qui est essentiel pour l'analyse de Nice et de ses attaques. Il introduit aussi la notion de formes quadratiques semi-équivalentes et en explicite plusieurs caractérisations, utiles pour l'analyse de ces attaques.