Biblio

An ideal lattice is defined over a ring learning with errors (Ring-LWE) problem. Polynomial multiplication over the ring is the most computational and time-consuming block in lattice-based cryptography. This paper presents the first hardware design of the polynomial multiplication for LAC, one of the Round-2 candidates of the NIST PQC Standardization Process, which has byte-level modulus p=251. The proposed architecture supports polynomial multiplications for different degree n (n=512/1024/2048). For designing the scheme, we used the Vivado HLS compiler, a high-level synthesis based hardware design methodology, which is able to optimize software algorithms into actual hardware products. The design of the scheme takes 274/280/291 FFs and 204/217/208 LUTs on the Xilinx Artix-7 family FPGA, requested by NIST PQC competition for hardware implementation. Multiplication core uses only 1/1/2 pieces of 18Kb BRAMs, 1/1/1 DSPs, and 90/94/95 slices on the board. Our timing result achieved in an alternative degree n with 5.052/4.3985/5.133ns.

Rapid advances in quantum computing, together with the announcement by the National Institute of Standards and Technology (NIST) to define new standards for digitalsignature, encryption, and key-establishment protocols, have created significant interest in post-quantum cryptographic schemes. This paper introduces Kyber (part of CRYSTALS - Cryptographic Suite for Algebraic Lattices - a package submitted to NIST post-quantum standardization effort in November 2017), a portfolio of post-quantum cryptographic primitives built around a key-encapsulation mechanism (KEM), based on hardness assumptions over module lattices. Our KEM is most naturally seen as a successor to the NEWHOPE KEM (Usenix 2016). In particular, the key and ciphertext sizes of our new construction are about half the size, the KEM offers CCA instead of only passive security, the security is based on a more general (and flexible) lattice problem, and our optimized implementation results in essentially the same running time as the aforementioned scheme. We first introduce a CPA-secure public-key encryption scheme, apply a variant of the Fujisaki-Okamoto transform to create a CCA-secure KEM, and eventually construct, in a black-box manner, CCA-secure encryption, key exchange, and authenticated-key-exchange schemes. The security of our primitives is based on the hardness of Module-LWE in the classical and quantum random oracle models, and our concrete parameters conservatively target more than 128 bits of postquantum security.

The paper contains the results of perspective digital signatures algorithms based on hash functions analysis. Several aspects of their implementation are presented. The comparative analysis was carried out by the method of hierarchies. Some problems of implementation in the existing infrastructure are described. XMSS algorithm implementation with Ukrainian hash function national standard is presented.

Symmetry ergodic matrices exponentiation (SEME) problem is to find x, given CxMDx, where C and D are the companion matrices of primitive polynomials and M is an invertible matrix over finite field. This paper proposes a new zero-knowledge identification scheme based on SEME problem. It is perfect zero-knowledge for honest verifiers. The scheme could provide a candidate cryptographic primitive in post quantum cryptography. Due to its simplicity and naturalness, low-memory, low-computation costs, the proposed scheme is suitable for using in computationally limited devices for identification such as smart cards.

Funded under the European Union's Horizon 2020 research and innovation programme, SAFEcrypto will provide a new generation of practical, robust and physically secure post-quantum cryptographic solutions that ensure long-term security for future ICT systems, services and applications. The project will focus on the remarkably versatile field of Lattice-based cryptography as the source of computational hardness, and will deliver optimised public key security primitives for digital signatures and authentication, as well identity based encryption (IBE) and attribute based encryption (ABE). This will involve algorithmic and design optimisations, and implementations of lattice-based cryptographic schemes addressing cost, energy consumption, performance and physical robustness. As the National Institute of Standards and Technology (NIST) prepares for the transition to a post-quantum cryptographic suite B, urging organisations that build systems and infrastructures that require long-term security to consider this transition in architectural designs; the SAFEcrypto project will provide Proof-of-concept demonstrators of schemes for three practical real-world case studies with long-term security requirements, in the application areas of satellite communications, network security and cloud. The goal is to affirm Lattice-based cryptography as an effective replacement for traditional number-theoretic public-key cryptography, by demonstrating that it can address the needs of resource-constrained embedded applications, such as mobile and battery-operated devices, and of real-time high performance applications for cloud and network management infrastructures.