Related papers: The Mathematical Foundation of Post-Quantum Crypto…
This paper presents a comprehensive cryptographic analysis of the security parameters of the LINEture post-quantum digital signature scheme, which is constructed using matrix algebra over elementary abelian 2-groups. We investigate the…
In recent years, quantum computers and Shor quantum algorithm have posed a threat to current mainstream asymmetric cryptography methods (e.g. RSA and Elliptic Curve Cryptography (ECC)). Therefore, it is necessary to construct a Post-Quantum…
Due to recent development in quantum computing, the invention of a large quantum computer is no longer a distant future. Quantum computing severely threatens modern cryptography, as the hard mathematical problems beneath classic public-key…
With the development of Shor's algorithm, some nondeterministic polynomial (NP) time problems (e.g. prime factorization problems and discrete logarithm problems) may be solved in polynomial time. In recent years, although some homomorphic…
The long-term security of public blockchains strictly depends on the hardness assumptions of the underlying digital signature schemes. In the current scenario, most deployed cryptocurrencies and blockchain platforms rely on elliptic-curve…
In recent years, with the advancement of quantum computing, mainstream asymmetric cryptographic methods in the current Public Key Infrastructure (PKI) systems are gradually being threatened. Therefore, this study explores X.509 security…
Quantum computers are expected to break today's public key cryptography within a few decades. New cryptosystems are being designed and standardised for the post-quantum era, and a significant proportion of these rely on the hardness of…
Blockchain is a Distributed Ledger Technology (DLT) that offers numerous benefits including decentralization, transparency, efficiency, and reduced costs. Hence, blockchain has been included in many fields. Blockchain relies on…
Modern web traffic relies on 2048-bit RSA encryption to secure our data in transit. Rapid advances in Quantum Computing pose a grave challenge by allowing hackers to break this encryption in hours. In August of 2024, the National Institute…
Lattices are discrete mathematical objects with widespread applications to integer programs as well as modern cryptography. A fundamental problem in both domains is the Closest Vector Problem (popularly known as CVP). It is well-known that…
Finding the shortest vector in a lattice is a problem that is believed to be hard both for classical and quantum computers. Many major post-quantum secure cryptosystems base their security on the hardness of the Shortest Vector Problem…
Trust is the core building block of secure systems, and it is enforced through methods to ensure that a specific system is properly configured and works as expected. In this context, a Root of Trust (RoT) establishes a trusted environment,…
Shor's algorithm efficiently solves factoring and discrete logarithm problems using quantum computers, compromising all public key schemes used today. These schemes rely on assumptions on their computational complexity, which quantum…
In this work, we exhibit a hierarchy of polynomial time algorithms solving approximate variants of the Closest Vector Problem (CVP). Our first contribution is a heuristic algorithm achieving the same distance tradeoff as HSVP algorithms,…
We review new frontiers in information security technologies in communications and distributed storage technologies with the use of classical, quantum, hybrid classical-quantum, and post-quantum cryptography. We analyze the current…
Recent advancements in post-quantum cryptographic algorithms have led to their standardization by the National Institute of Standards and Technology (NIST) to safeguard information security in the post-quantum era. These algorithms,…
In this paper we discuss the Hidden Subgroup Problem (HSP) in relation to post-quantum group-based cryptography. We review the relationship between HSP and other computational problems discuss an optimal solution method, and review the…
Chosen-ciphertext security, which guarantees confidentiality of encrypted messages even in the presence of a decryption oracle, has become the defacto notion of security for public-key encryption under active attack. In this manuscript, for…
We give a deterministic algorithm for solving the (1+eps)-approximate Closest Vector Problem (CVP) on any n dimensional lattice and any norm in 2^{O(n)}(1+1/eps)^n time and 2^n poly(n) space. Our algorithm builds on the lattice point…
We present a lattice-based scheme for homomorphic evaluation of quantum programs and proofs that remains secure against quantum adversaries. Classical homomorphic encryption is lifted to the quantum setting by replacing composite-order…