Related papers: Insecure primitive elements in an ElGamal signatur…

Most cryptosystems are defined over finite algebraic structures where arithmetic operations are performed modulo natural numbers. This applies to private key as well as to public key ciphers. No secure cryptosystems defined over the field…

The session initiation protocol (SIP) is a powerful signaling protocol that controls communication on the Internet, establishing, maintaining, and terminating the sessions. The services that are enabled by SIP are equally applicable in the…

Digital signatures guarantee the authenticity and transferability of messages, and are widely used in modern communication. The security of currently used classical digital signature schemes, however, relies on computational assumptions. In…

We consider a new model for the testing of untrusted quantum devices, consisting of a single polynomial-time bounded quantum device interacting with a classical polynomial-time verifier. In this model we propose solutions to two tasks - a…

We describe a novel type of weak cryptographic private key that can exist in any discrete logarithm based public-key cryptosystem set in a group of prime order $p$ where $p-1$ has small divisors. Unlike the weak private keys based on…

We propose a quantum authentication and digital signature protocol whose security is founded on the Quantum Merlin Arthur~(QMA)-completeness of the consistency of local density matrices. The protocol functions as a true public-key…

We consider a private distributed multiplication problem involving N computation nodes and T colluding nodes. Shamir's secret sharing algorithm provides perfect information-theoretic privacy, while requiring an honest majority, i.e., N \ge…

This paper presents a new method for quantum identity authentication (QIA) protocols. The logic of classical zero-knowledge proofs (ZKPs) due to Schnorr is applied in quantum circuits and algorithms. This novel approach gives an exact way…

We extend many results on Selmer groups for elliptic curves and modular forms to the non-ordinary setting. More precisely, we study the signed Selmer groups defined using the machinery of Wach modules over $\mathbf{Z}_p$-cyclotomic…

We prove an analogue of the celebrated Hall-Higman theorem, which gives a lower bound for the degree of the minimal polynomial of any semisimple element of prime power order $p^{a}$ of a finite classical group in any nontrivial irreducible…

We show that every construction of one-time signature schemes from a random oracle achieves black-box security at most $2^{(1+o(1))q}$, where $q$ is the total number of oracle queries asked by the key generation, signing, and verification…

In this paper we review and comment on "A novel protocol-authentication algorithm ruling out a man-in-the-middle attack in quantum cryptography", [M. Peev et al., Int. J. Quant. Inform., 3, 225, (2005)]. In particular, we point out that the…

Secure key leasing (a.k.a. key-revocable cryptography) enables us to lease a cryptographic key as a quantum state in such a way that the key can be later revoked in a verifiable manner. We propose a simple framework for constructing…

Signature-based algorithms have brought large improvements in the performances of Gr\"obner bases algorithms for polynomial systems over fields. Furthermore, they yield additional data which can be used, for example, to compute the module…

In this paper, we present a variant of Waters' Identity-Based Encryption scheme with a much smaller public-key size (only a few kilobytes). We show that this variant is semantically secure against passive adversaries in the standard…

In this paper, we prove that the supersingular isogeny problem (Isogeny), endomorphism ring problem (EndRing) and maximal order problem (MaxOrder) are equivalent under probabilistic polynomial time reductions, unconditionally. Isogeny-based…

Preserving data confidentiality in clouds is a key issue. Secret Sharing, a cryptographic primitive for the distribution of a secret among a group of $n$ participants designed so that only subsets of shareholders of cardinality $0 < t \leq…

Weber's conjecture (1886) governs three aspects of lattice-based cryptography: the solvability of the Principal Ideal Problem, the freeness of modules over rings of integers, and the tightness of worst-case-to-average-case reductions in…

For $q=p^m$ with $p$ prime and $k\mid q-1$, we consider the generalized Paley graph $\Gamma(k,q) = Cay(\mathbb{F}_q, R_k)$, with $R_k=\{ x^k : x \in \mathbb{F}_q^* \}$, and the irreducible $p$-ary cyclic code $\mathcal{C}(k,q) =…

We reconsider a classical theorem by Bican and El Bashir, which guarantees the existence of non-trivial relatively pure submodules in a module category over a ring with unit. Our aim is to generalize the theorem to module categories over…