scholarly journals Integer Factorization: Solution via Algorithm for Constrained Discrete Logarithm Problem

2009 ◽  
Vol 5 (9) ◽  
pp. 674-679 ◽  
Author(s):  
Boris S. Verkhov
Keyword(s):  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Integer Factorization

Threshold-directed signature scheme based on hybrid number theoretic problems

2019 ◽  
Vol 13 (05) ◽  
pp. 2050098
Author(s):  
Mohd Saiful Adli Mohamad
Keyword(s):  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Signature Scheme ◽  
Integer Factorization ◽  
The Public ◽  
Designated Verifier ◽  
Single Number ◽  
Directed Signature ◽  
Cryptographic Attacks ◽  
Hybrid Number

Directed signature is a type of function-based signature with the property that the signature only can be verified by a designated verifier and at certain times, the verifier should be able to convince anyone about the validity of the signature without revealing any secret information about the signature to the public. Taking into consideration the involvement of group decision making, some threshold directed signature schemes based on single number theoretic problems, such as integer factorization, discrete logarithm problem, and elliptic curve discrete logarithm problem, have been developed by cryptographers. Although the single-problem-based schemes are still invincible because there is still no cryptanalyst to find the solution to the problems, in the future, if the enemy or attacker manages to get the polynomial algorithm to solve the single problems, the schemes will no longer be practiced and applied. For such reason, in this paper, we propose a new threshold-directed signature scheme based on integer factorization and discrete logarithm problems. The advantage of our scheme is based on the assumption that it is very unlikely to solve two hard number theoretic problems simultaneously. We also show that our scheme is secured against some cryptographic attacks and also significantly efficient compared with threshold signature scheme based on single problem.

A new public key scheme based on DRSA and generalized GDLP

2016 ◽  
Vol 08 (04) ◽  
pp. 1650057 ◽  
Author(s):  
Pinkimani Goswami ◽  
Madan Mohan Singh ◽  
Bubu Bhuyan
Keyword(s):  
Multiplicative Group ◽  
Discrete Logarithm ◽  
Randomized Algorithm ◽  
Discrete Logarithm Problem ◽  
Public Key ◽  
Integer Factorization ◽  
New Public ◽  
Encryption Decryption ◽  
Group Modulo

In this paper, we propose a new public key scheme, which is a combination of RSA variant namely the DRSA and the generalization of generalized discrete logarithm problem (generalized GDLP). The security of this scheme depends equally on the integer factorization of [Formula: see text] and the discrete logarithm problem (DLP) on [Formula: see text], where [Formula: see text] is the product of two large primes and [Formula: see text] is the multiplicative group modulo [Formula: see text]. The scheme is a randomized algorithm. It is at least as secure as the DRSA and ElGamal schemes. We also compare the encryption–decryption performance of the proposed scheme with the RSA and DRSA schemes.

scholarly journals On the first fall degree of summation polynomials

2019 ◽  
Vol 13 (3-4) ◽  
pp. 229-237
Author(s):  
Stavros Kousidis ◽  
Andreas Wiemers
Keyword(s):  
Elliptic Curve ◽  
Gröbner Basis ◽  
Discrete Logarithm ◽  
Polynomial Systems ◽  
Discrete Logarithm Problem ◽  
Grobner Basis ◽  
Weil Descent ◽  
Degree Bound

Abstract We improve on the first fall degree bound of polynomial systems that arise from a Weil descent along Semaev’s summation polynomials relevant to the solution of the Elliptic Curve Discrete Logarithm Problem via Gröbner basis algorithms.

Sign in / Sign up

Export Citation Format

Share Document