Related papers: Insecure primitive elements in an ElGamal signatur…
We study the Sign_then_Encrypt, Commit_then_Encrypt_and_Sign, and Encrypt_then_Sign paradigms in the context of two cryptographic primitives, namely designated confirmer signatures and signcryption. Our study identifies weaknesses in those…
Fix a rational prime $r \geq 5$. In this article, we study the integer solutions of the generalized Fermat equation of signature $(2p,2q,r)$, namely $x^{2p}+y^{2q}=z^r$, where the primes $p,q \geq 5$ are varying. For each rational prime $r…
In this paper we propose a signature scheme based on two intractable problems, namely the integer factorization problem and the discrete logarithm problem for elliptic curves. It is suitable for applications requiring long-term security and…
Fully homomorphic encryption (FHE) allows anyone to perform computations on encrypted data, despite not having the secret decryption key. Since the Gentry's work in 2009, the primitive has interested many researchers. In this paper, we…
We describe a system, PEP3, for storage and retrieval of IP flow information in which the IP addresses are replaced by pseudonyms. Every eligible party gets its own set of pseudonyms. A single entity, the transcryptor, that is composed of…
The BMR16 circuit garbling scheme introduces gadgets that allow for ciphertext-free modular addition, while the multiplication of private inputs modulo a prime p can be done with 2(p - 1) ciphertexts as described in Malkin, Pastro, and…
In this paper, we extend the ElGamal cryptosystem to the third group of units of the ring $\Z_{n}$, which we prove to be more secure than the previous extensions. We describe the arithmetic needed in the new setting. We also provide some…
We show the following hold, unconditionally unless otherwise stated, relative to a random oracle: - There are NP search problems solvable by quantum polynomial-time machines but not classical probabilistic polynomial-time machines. - There…
This paper presents an overview of the use of elliptic curves in cryptography. The security of this cryptosystem is based on the discrete logarithm problem, which appears to be much harder compared to the discrete logarithm problem in other…
We propose public-key cryptosystems with public key a system of polynomial equations, algebraic or differential, and private key a single polynomial or a small-size ideal. We set up probabilistic encryption, signature, and signcryption…
Ring signature is a kind of group-oriented signature. It allows a member of a group to sign messages on behalf of the group without revealing his/her identity. Certificateless public key cryptography was first introduced by Al-Riyami and…
We consider a problem, which we call secure grouping, of dividing a number of parties into some subsets (groups) in the following manner: Each party has to know the other members of his/her group, while he/she may not know anything about…
This paper explores how reliable broadcast can be implemented without signatures when facing a dual adversary that can both corrupt processes and remove messages. More precisely, we consider an asynchronous $n$-process message-passing…
Diffie-Hellman groups are commonly used in cryptographic protocols. While most state-of-the-art, symbolic protocol verifiers support them to some degree, they do not support all mathematical operations possible in these groups. In…
Electronic documents are signed using private keys and verified using the corresponding digital certificates through the well-known public key infrastructure model. Private keys must be kept in a safe container so they can be reused. This…
Distributed immutable ledgers, or blockchains, allow the secure digitization of evidential transactions without relying on a trusted third-party. Evidential transactions involve the exchange of any form of physical evidence, such as money,…
Security protocols are used in many of our daily-life applications, and our privacy largely depends on their design. Formal verification techniques have proved their usefulness to analyse these protocols, but they become so complex that…
Although squaring integers is deterministic, squares modulo a prime, $p$, appear to be random. First, because they are all generated by the multiplicative linear congruential equation, $x_{i+1} = g^2 x_i \mod p$, where $x_0 = 1$ and $g$ is…
Chebyshev polynomials have been recently proposed for designing public-key systems. Indeed, they enjoy some nice chaotic properties, which seem to be suitable for use in Cryptography. Moreover, they satisfy a semi-group property, which…
We give an analogue of the ElGamal encryption system based on the Markovski algorithm [4; 5].