Post-quantum cryptography: lattice signatures

Ravinder Kaur

Maria Nuțu, Răzvan Bocu, Maksim Iavich

With the development of large-scale quantum computers, classical cryptographic algorithms such as RSA or ECC can easily be broken by Shor’s algorithm. Consequently, the cryptography community is shifting its focus toward Post-Quantum Cryptography (PQC), developing primitives that are secure against both classical and quantum attacks. In this paper, we propose a novel Verkle-Polynomial Signature (VPS) scheme by combining the lattice-based polynomial commitment scheme of Cini et al. with Verkle trees and a lattice-based One-Time Signature (OTS) engine to achieve post-quantum security. We demonstrate that while sacrificing the operational efficiency and structural maturity of traditional hash-based signatures, our framework provides robust post-quantum security guarantees inherited from standard lattice assumptions.

G. Sunil, B. Girirajan, Manda Sai Anjani

Frank Nauheimer

Digital signatures are used to ensure authentication. Blind signature schemes are a special form of digital signatures and important in scenarios which depend on anonymous and secure authentication. (e.g. e-voting) The common digital blind signature schemes are based on asymmetric cryptography with underlying hard problems like integer factorization or discrete logarithm. These hard problems will become weak with the development of quantum computers. To avoid the uselessness of classic cryptography in the post quantum era, it will be important to find alternative methods based on other hard problems. This book deals with the attempt of developing a new blind signature scheme based on lattice signature schemes.

Sean Patrick Murphy, Rachel Player

Abstract The need for developing post-quantum cryptography, that is to say cryptographic schemes that are believed to remain secure if large-scale quantum computers are developed, is demonstrated by a discussion of the classical and the quantum algorithms for solving the factorization problem. The ongoing process by the US standards body NIST to standardize post-quantum public-key encryption and digital signatures is described. Lattice-based cryptography is introduced as a prominent area of post-quantum cryptography. Lattice problems, including the Learning with Errors (LWE) problem, are introduced. The AGCD cryptosystem, based on the approximate greatest common divisor (AGCD) problem, is described.