Description
Group encryption (GE) is the natural encryption analogue of group signatures in that it allows verifiably encrypting messages for some anonymous member of a group while providing evidence that the receiver is a properly certified group member. Should the need arise, an opening authority is capable of identifying the receiver of any ciphertext. As intro- duced by Kiayias, Tsiounis and Yung (Asiacrypt’07), GE is motivated by applications in the context of oblivious retriever storage systems, anony- mous third parties and hierarchical group signatures. This paper provides the first realization of group encryption under lattice assumptions. Our construction is proved secure in the standard model (assuming interac- tion in the proving phase) under the Learning-With-Errors (LWE) and Short-Integer-Solution (SIS) assumptions. As a crucial component of our system, we describe a new zero-knowledge argument system allowing to demonstrate that a given ciphertext is a valid encryption under some hid- den but certified public key, which incurs to prove quadratic statements about LWE relations. Specifically, our protocol allows arguing knowledge of witnesses consisting of X ∈ ℤ_q^{m×n}, s ∈ ℤ_q^n and a small-norm e ∈ ℤ^m which underlie a public vector b = X · s + e ∈ ℤ_q^m while simultaneously proving that the matrix X ∈ ℤ_q^{m×n} has been correctly certified. We believe our proof system to be useful in other applications involving zero-knowledge proofs in the lattice setting. lien: rien
Next sessions
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Random lattices that are modules over the ring of integers
Speaker : Nihar Gargava - Institut de Mathématiques d'Orsay
We investigate the average number of lattice points within a ball where the lattice is chosen at random from the set of unit determinant ideal or modules lattices of some cyclotomic number field. The goal is to consider the space of such lattice as a probabilistic space and then study the distribution of lattice point counts. This is inspired by the connections of this problem to lattice-based[…]-
Cryptography
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Schéma de signature à clé publique : Frobénius-UOV
Speaker : Gilles Macario-Rat - Orange
L'exposé présente un schéma de signature à clé publique post-quantique inspiré du schéma UOV et introduisant un nouvel outil : les formes de Frobénius. L'accent est mis sur le rôle et les propriétés des formes de Frobénius dans ce nouveau schéma : la simplicité de description, la facilité de mise en oeuvre et le gain inédit sur les tailles de signature et de clé qui bat RSA-2048 au niveau de[…] -
Yoyo tricks with a BEANIE
Speaker : Xavier Bonnetain - Inria
TBD-
Cryptography
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Symmetrical primitive
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