Related papers: Module Lattice Security (Part IV): Probabilistic P…
The McEliece cryptosystem based on quasi-cyclic moderate-density parity-check (QC-MDPC) codes is first purposed in 2013\cite{QCMDPC} and is considered a promising contender in the post-quantum era. Understanding its security is hence…
Learning with Errors is one of the fundamental problems in computational learning theory and has in the last years become the cornerstone of post-quantum cryptography. In this work, we study the quantum sample complexity of Learning with…
This study proposes post-quantum encrypted control systems based on dynamic-key Learning with Errors (LWE) encryption schemes. The proposed method develops update maps that simultaneously update the private key and ciphertexts within the…
Another threat is the development of large quantum computers, which have a high likelihood of breaking the high popular security protocols because it can use both Shor and Grover algorithms. In order to fix this looming threat,…
We discuss a new attack, termed a dimension or linear decomposition attack, on several known group-based cryptosystems. This attack gives a polynomial time deterministic algorithm that recovers the secret shared key from the public data in…
In this paper, we propose a new variant of the McEliece cryptosystem using two families of quasi-cyclic codes: low density parity check codes (QC-LDPC) and moderate density parity check codes (QC-MDPC). Due to the low weight codewords in…
Unconditional security proofs of various quantum key distribution (QKD) protocols are built on idealized assumptions. One key assumption is: the sender (Alice) can prepare the required quantum states without errors. However, such an…
Public key encryption with equality test (PKEET) supports to check whether two ciphertexts encrypted under different public keys contain the same message or not. PKEET has many interesting applications such as keyword search on encrypted…
We discuss the advantages and limitations of cyclotomic fields to have fast polynomial arithmetic within homomorphic encryption, and show how these limitations can be overcome by replacing cyclotomic fields by a family that we refer to as…
We present a polynomial-time quantum algorithm for the Hidden Subgroup Problem over $\mathbb{D}_{2^n}$. The usual approach to the Hidden Subgroup Problem relies on harmonic analysis in the domain of the problem, and the best known algorithm…
High-speed long polynomial multiplication is important for applications in homomorphic encryption (HE) and lattice-based cryptosystems. This paper addresses low-latency hardware architectures for long polynomial modular multiplication using…
It was recently demonstrated that the Matrix Action Key Exchange (MAKE) algorithm, a new type of key exchange protocol using the semidirect product of matrix groups, is vulnerable to a linear algebraic attack if the matrices are over a…
Quantum key distribution (QKD) promises provably secure communications. In order to improve the secret key rate, combining a biased basis choice with the decoy-state method is proposed. Concomitantly, there is a basis-independent detection…
In modern cryptography, block encryption is a fundamental cryptographic primitive. However, it is impossible for block encryption to achieve the same security as one-time pad. Quantum mechanics has changed the modern cryptography, and lots…
Post-quantum cryptography currently rests on a small number of hardness assumptions, posing significant risks should any one of them be compromised. This vulnerability motivates the search for new and cryptographically versatile assumptions…
Motivated by the recent experimental demonstrations of quantum supremacy, proving the hardness of the output of random quantum circuits is an imperative near term goal. We prove under the complexity theoretical assumption of the…
I construct a secure multi-party scheme to compute a classical function by a succinct use of a specially designed fault-tolerant random polynomial quantum error correction code. This scheme is secure provided that (asymptotically) strictly…
We study the problem of determining the probability that m vectors selected uniformly at random from the intersection of the full-rank lattice L in R^n and the window [0,B)^n generate $\Lambda$ when B is chosen to be appropriately large.…
Lattices have many significant applications in cryptography. In 2021, the $p$-adic signature scheme and public-key encryption cryptosystem were introduced. They are based on the Longest Vector Problem (LVP) and the Closest Vector Problem…
We introduce a simple, practical approach with probabilistic information-theoretic security to solve one of quantum key distribution's major security weaknesses: the requirement of an authenticated classical channel to prevent…