Considerations of security of K(Xss)CBPKC, a post-quantum cryptosystem

V. K. Zadiraka, Антон Михайлович Кудін, I. A. Kudin +1 more

Syed Ismail Abdul Lathif, Priya Saxena, Priyanshi Singh

Revista, Zen, MATH, 10

The imminent threat posed by cryptographically relevant quantum computers necessitates a paradigm shift in public-key cryptography. Traditional schemes like RSA and Elliptic Curve Cryptography (ECC), the bedrock of modern secure communication, are vulnerable to quantum algorithms such as Shor's. This paper explores Module-LWE (Learning With Errors) cryptosystems as a compelling post-quantum replacement for RSA. We delve into the foundational mathematical properties of Module-LWE, highlighting its security rooted in the presumed intractability of hard lattice problems. A key focus is the concept of "tightly reduced hardness," which signifies that the security of a cryptographic scheme based on Module-LWE can be directly and efficiently linked to the worst-case hardness of an underlying lattice problem. This tight reduction allows for more aggressive parameter choices, leading to improved efficiency, smaller key and ciphertext sizes, and enhanced performance compared to generic LWE or other post-quantum candidates, without compromising security. We analyze the advantages of Module-LWE in terms of provable security, performance characteristics, and its suitability for key encapsulation mechanisms and digital signatures. The discussion encompasses its practical implications, implementation considerations, and its strong position within the NIST Post-Quantum Cryptography standardization effort, ultimately presenting Module-LWE as a robust, efficient, and future-proof alternative to RSA in a post-quantum world.

Anyu Wang, Dianyan Xiao, Yang Yu

Abstract The current widely used public‐key cryptosystems are vulnerable to quantum attacks. To prepare for cybersecurity in the quantum era, some projects have been launched to call for post‐quantum alternatives. Due to solid security and desirable performance, lattice‐based cryptosystems are viewed as promising candidates in the upcoming standardisation of post‐quantum cryptography. This study surveys the lattice‐based cryptosystems in the post‐quantum standardisation processes including the NIST Post‐Quantum Cryptography Standardisation and the Chinese Cryptographic Algorithm Design Competition, from both design and security aspects. We present generic design paradigms of lattice‐based schemes and describe several representative proposals and recent progress. We also recap some main cryptanalytic results and methods for estimating the concrete security of lattice‐based schemes.

Xenia Bogomolec, J. Gerhard

Madicke DIOP, Demba Sow

GenElGamal is an extension of the ElGamal public key encryption scheme, which modifies the key generation and encryption steps, proposed by Sow and Sow in [24]. With the rise of quantum computing, the security of public key cryptosystems based on the discrete logarithm problem, particularly GenElGamal, is threatened. In this paper, we propose a post-quantum version of the GenElGamal cryptosystem called PQ-GenElGamal using the difficult modulo 1 factoring problem (M1FP) that is resistant to post-quantum attacks. We describe our scheme and prove its security against both classical and post-quantum attacks.