The tower variant of the number field sieve (TNFS) is known to be asymptotically the most efficient algorithm to solve the discrete logarithm problem in finite fields of medium characteristics, when the extension degree is composite. A major ...${\mathbb{}}_{{}^{\mathrm{}}}$

The Number Field Sieve and its numerous variants is the best algorithm to compute discrete logarithms in medium and large characteristic finite fields. When the extension degree n is composite and the characteristic p is of medium size, the Tower ...${}_{{}^{}}\mathrm{}\mathrm{}{}_{{}^{}}\mathrm{}\mathrm{}$

• A novel approach of constructing post-quantum DS algorithms with a hidden group is proposed.
• Use FNAA as an algebraic support and based on computational complexity of finding a solution of a system of many quadratic equations with many ...

A recently proposed new concept for constructing algebraic signature schemes with a hidden group is used to develop two new post-quantum signature algorithms on four-dimensional and six-dimensional finite noncommutative associative algebras. As ...

Shor presented a quantum algorithm to factor large integers and compute discrete logarithms in polynomial time. As a result, public key cryptosystems, such as RSA, ElGamal and ECC, which are based on these computational assumptions will become ...

This paper proposes a fully homomorphic computational model for secret sharing. The backbone of the proposed model is Chinese remainder theorem. The proposed model achieves non-threshold secret sharing. The homomorphism has been achieved using ...

The strength of many security protocols lies on the computational intractability of the integer factorization and discrete logarithm problems. Currently, the best-known techniques employed are number field sieve (NFS) family of algorithms. They ...

Logical cryptanalysis, first introduced by Massacci in 2000, is a viable alternative to common algebraic cryptanalysis techniques over boolean fields. With xor operations being at the core of many cryptographic problems, recent research in this ...

The distributed discrete logarithm (DDL) problem was introduced by Boyle, Gilboa and Ishai at CRYPTO 2016. A protocol solving this problem was the main tool used in the share conversion procedure of their homomorphic secret sharing (HSS) scheme ...$\mathbb{}$${}^{}$$$${}^{}{}^{}$${}^{\mathrm{}}$${}^{\mathrm{}}$${}^{\mathrm{}\mathrm{}}$$\sqrt{}$

Recent algorithmic improvements of discrete logarithm computation in special extension fields threaten the security of pairing-friendly curves used in practice. A possible answer to this delicate situation is to propose alternative curves that are ...$\mathrm{}$$\mathrm{}$$\mathrm{}$

This paper proposes an extended RSA digital signature scheme and extended ElGamal digital signature schemes with appendix and with message recovery over the algebraic integer ring Z[e2πi/5] of the cyclotomic field Q[e2πi/5]. In these digital signature ...

Recent progress on NFS imposed a new estimation of the security of pairings. In this work we study the best attacks against some of the most popular pairings and propose new key sizes using an analysis which is more precise than the analysis in a ...

Each finite binary sequence (s _h ) is associated with a Boolean function B. The correlation measure of order k and the r-th order nonlinearity are figures of merit for the unpredictability of (s _h ) and B, respectively. We estimate the r-th order ...

Computing discrete logarithms is generically a difficult problem. For divisor class groups of curves defined over extension fields, a variant of the Index-Calculus called decomposition attack is used, and it can be faster than generic approaches. In ...

The distributed discrete logarithm (DDL) problem was introduced by Boyle et al. at CRYPTO 2016. A protocol solving this problem was the main tool used in the share conversion procedure of their homomorphic secret sharing (HSS) scheme which allows ...

Carlitz rank and index are two important measures for the complexity of a permutation polynomial f(x) over the finite field Fq. In particular, for cryptographic applications we need both, a high Carlitz rank and a high index. In this article we study ...

Generating coset representatives of PGL 2 ( F q ) in PGL 2 ( F q 2 ) is a key ingredient in certain algorithms of determining primitive elements and computing discrete logarithms in finite fields of small characteristic. In this paper, we describe a ...

In 2004, Bellare et al. formalized the notion for identity-based identification (IBI) schemes and proposed many schemes based on their transformation from standard identification schemes. However the authors left the security under active/concurrent ...

The signcryption scheme should withstand various leakage attacks in practical applications. This paper presents a new leakage-resilient certificateless signcryption (LR-CLSC) scheme without bilinear pairing. The security of this scheme is based on the ...

Being able to compute efficiently a low-weight multiple of a given binary polynomial is often a key ingredient of correlation attacks to LFSR-based stream ciphers. The best known general purpose algorithm is based on the generalized birthday problem. We ...

The security of pairing-based crypto-systems relies on the difficulty to compute discrete logarithms in finite fields $${\mathbb F}_{p^n}$$ where n is a small integer larger than 1. The state-of-art algorithm is the number field sieveï źNFS together ...