scholarly journals Integer factorization and discrete logarithm problems

2014 ◽  
Vol 4 (1) ◽  
pp. 1-20
Author(s):  
Pierrick Gaudry
Keyword(s):  
Discrete Logarithm ◽  
Integer Factorization

scholarly journals Analysis Review on Public Key Cryptography Algorithms

2018 ◽  
Vol 12 (2) ◽  
pp. 447 ◽  
Author(s):  
Jasmin Ilyani Ahmad ◽  
Roshidi Din ◽  
Mazida Ahmad
Keyword(s):  
Elliptic Curve ◽  
Digital Signature ◽  
Coding Theory ◽  
Discrete Logarithm ◽  
Public Key Cryptography ◽  
Hybrid Algorithms ◽  
Public Key ◽  
Integer Factorization

This paper presents several Public Key Cryptography (PKC) algorithms based on the perspective of researchers’ effort since it was invented in the last four decades. The categories of the algorithms had been analyzed which are Discrete Logarithm, Integer Factorization, Coding Theory, Elliptic Curve, Lattices, Digital Signature and Hybrid algorithms. This paper reviewed the previous schemes in different PKC algorithms. The aim of this paper is to present the comparative trends of PKC algorithms based on number of research for each algorithm in last four decades, the roadmap of PKC algorithms since they were invented and the most chosen algorithms among previous researchers. Finally, the strength and drawback of proposed schemes and algorithms also presented in this paper.

scholarly journals A new RSA public key encryption scheme with chaotic maps

2020 ◽  
Vol 10 (2) ◽  
pp. 1430
Author(s):  
Nedal Tahat ◽  
Ashraf A. Tahat ◽  
Maysam Abu-Dalu ◽  
Ramzi B. Albadarneh ◽  
Alaa E. Abdallah ◽  
...  
Keyword(s):  
Information Exchange ◽  
Chaotic Maps ◽  
Discrete Logarithm ◽  
Public Key Cryptography ◽  
Public Key ◽  
Original Text ◽  
Public Key Encryption ◽  
Integer Factorization ◽  
Computational Ability ◽  
New System

Public key cryptography has received great attention in the field of information exchange through insecure channels. In this paper, we combine the Dependent-RSA (DRSA) and chaotic maps (CM) to get a new secure cryptosystem, which depends on both integer factorization and chaotic maps discrete logarithm (CMDL). Using this new system, the scammer has to go through two levels of reverse engineering, concurrently, so as to perform the recovery of original text from the cipher-text has been received. Thus, this new system is supposed to be more sophisticated and more secure than other systems. We prove that our new cryptosystem does not increase the overhead in performing the encryption process or the decryption process considering that it requires minimum operations in both. We show that this new cryptosystem is more efficient in terms of performance compared with other encryption systems, which makes it more suitable for nodes with limited computational ability.

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.

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