Section: New Results

Euclidean Lattice Reduction and Applications

Lattice algorithms and hardness proofs

X.-W. Chang (McGill), D. Stehlé and G. Villard [17] proposed the first fully rigorous perturbation analysis of the R-factor of LLL-reduced matrices under column-wise perturbations. This study is very useful to devise LLL-type algorithms relying on floating-point approximations.

L. Luzzi (ENSEA), C. Ling (Imperial College) and D. Stehlé improved [20] the analyses of efficient Bounded Distance Decoding algorithms for lattices, and investigated the consequences for lattice-coded multiple-input multiple-output (MIMO) systems.

A. Langlois and D. Stehlé [54] introduced the Module-SIS and Module-LWE average-case lattice problems and reduced worst-case lattice problems to them. This provides a progressive transformation from the non-structured average-case lattices problems SIS and LWE, to the quite restricted but efficient average-case lattices problems Ring-SIS and Ring-LWE.

Cryptography

S. Ling (Nanyang Technological University, Singapore) and D. Stehlé [55] described the first public-key traitor tracing encryption scheme with security relying on the hardness of standard worst-case problems on Euclidean lattices.

J.-C. Belfiore (Telecom Paritech), L. Luzzi (ENSEA), C. Ling (Imperial College) and D. Stehlé [53] proved that nested lattice codes can achieve semantic security and strong secrecy over the Gaussian wiretap channel.

S. Ling (Nanyang Technological University, Singapore), K. Nguyen (NTU), H. Wang (NTU) and D. Stehlé [40] generalized Stern's zero-knowledge proof of knowledge protocol to obtain a statistical zero-knowledge proof of knowledge for the Inhomogeneous Small Integer Solution ISIS problem (in the infinity norm). This scheme is the first one that comes with no norm loss in the knowledge extraction procedure, leading to cryptographic constructions with tighter security proofs.

N. Attrapadung (AIST, Japan), J. Herranz (UPC, Spain), F. Laguillaumie, B. Libert (UCL, Belgium), E. de Panafieu (ENS Cachan), C. Ràfols (UPC, Spain) [15] proposed the first attribute-based encryption (ABE) schemes allowing for truly expressive access structures and with constant ciphertext size.

G. Castagnos (IMB) and F. Laguillaumie [38] gave a generic approach to design homomorphic encryption schemes, which extends Gjosteen’s framework. A specific scheme allows an arbitrary number of multiplications in the groups, as well as a pairing evaluation on the underlying plaintexts.

J. Herranz (UPC, Spain), F. Laguillaumie, B. Libert (UCL, Belgium) and C. Ràfols (URV, Catalonia)  [34] proposed the first two attribute-based (for threshold predicates) signature schemes with constant size signatures. Their security is proven in the selective-predicate and adaptive-message setting, in the standard model, under chosen message attacks.

S. Canard (Orange Labs), G. Fuchsbauer (University of Bristol, UK), A. Gouget (Gemalto), F. Laguillaumie  [30] defined a new cryptographic primitive called plaintext-checkable encryption, which extends public-key encryption by the following functionality: given a plaintext, a ciphertext and a public key, it is universally possible to check whether the ciphertext encrypts the plaintext under the key. They provide efficient generic random-oracle constructions based on any probabilistic or deterministic encryption scheme as well as a practical construction in the standard model.