An efficient ID-based cryptographic encryption based on discrete logarithm problem and integer factorization problem

2015 ◽  
Vol 115 (2) ◽  
pp. 351-358 ◽  
Author(s):  
Chandrashekhar Meshram
Keyword(s):  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Integer Factorization ◽  
Factorization Problem ◽  
Integer Factorization Problem

Problems in Cryptography and Cryptanalysis

2018 ◽  
pp. 23-39
Author(s):  
Kannan Balasubramanian ◽  
Rajakani M.
Keyword(s):  
Elliptic Curve ◽  
Optimization Problems ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Random Number Generators ◽  
Factorization Problem ◽  
Diffie Hellman ◽  
Integer Factorization Problem ◽  
Diffie Hellman Key Exchange ◽  
Membership Problems

The integer factorization problem used in the RSA cryptosystem, the discrete logarithm problem used in Diffie-Hellman Key Exchange protocol and the Elliptic Curve Discrete Logarithm problem used in Elliptic Curve Cryptography are traditionally considered the difficult problems and used extensively in the design of cryptographic algorithms. We provide a number of other computationally difficult problems in the areas of Cryptography and Cryptanalysis. A class of problems called the Search problems, Group membership problems, and the Discrete Optimization problems are examples of such problems. A number of computationally difficult problems in Cryptanalysis have also been identified including the Cryptanalysis of Block ciphers, Pseudo-Random Number Generators and Hash functions.

Problems in Cryptography and Cryptanalysis

2021 ◽  
pp. 837-853
Author(s):  
Kannan Balasubramanian ◽  
Rajakani M.
Keyword(s):  
Elliptic Curve ◽  
Optimization Problems ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Random Number Generators ◽  
Factorization Problem ◽  
Diffie Hellman ◽  
Integer Factorization Problem ◽  
Diffie Hellman Key Exchange ◽  
Membership Problems

The integer factorization problem used in the RSA cryptosystem, the discrete logarithm problem used in Diffie-Hellman Key Exchange protocol and the Elliptic Curve Discrete Logarithm problem used in Elliptic Curve Cryptography are traditionally considered the difficult problems and used extensively in the design of cryptographic algorithms. We provide a number of other computationally difficult problems in the areas of Cryptography and Cryptanalysis. A class of problems called the Search problems, Group membership problems, and the Discrete Optimization problems are examples of such problems. A number of computationally difficult problems in Cryptanalysis have also been identified including the Cryptanalysis of Block ciphers, Pseudo-Random Number Generators and Hash functions.

scholarly journals Practical IBC using Hybrid-Mode Problems: Factoring and Discrete Logarithm

2015 ◽  
Vol 4 (1) ◽  
pp. 73-82 ◽  
Author(s):  
Chandrashekhar Meshram
Keyword(s):  
Discrete Logarithm ◽  
Public Key ◽  
Integer Factorization ◽  
Hybrid Mode ◽  
Factorization Problem ◽  
The Public ◽  
Public Key Cryptosystems ◽  
Integer Factorization Problem ◽  
Security Challenges

Shamir proposed the concept of the ID-based cryptosystem (IBC) in 1984. Instead of generating and publishing a public key for each user, the ID-based scheme permits each user to choose his name or network address as his public key. This is advantageous to public-key cryptosystems because the public-key verification is so easy and direct. In such a way, a large public key file is not required. Since new cryptographic schemes always face security challenges and many integer factorization problem and discrete logarithm based cryptographic systems have been deployed, therefore, the purpose of this paper is to design practical IBC using hybrid mode problems factoring and discrete logarithm. We consider the security against a conspiracy of some entities in the proposed system and show the possibility of establishing a more secure system.

Reduction of the integer factorization complexity upper bound to the complexity of the Diffie–Hellman problem

2021 ◽  
Vol 31 (1) ◽  
pp. 1-4
Author(s):  
Mikhail A. Cherepnev
Keyword(s):  
Upper Bound ◽  
Polynomial Algorithm ◽  
Integer Factorization ◽  
Factorization Problem ◽  
Diffie Hellman ◽  
Integer Factorization Problem

Abstract We construct a probabilistic polynomial algorithm that solves the integer factorization problem using an oracle solving the Diffie–Hellman problem.

scholarly journals Conjugacy Systems Based on Nonabelian Factorization Problems and Their Applications in Cryptography

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Lize Gu ◽  
Shihui Zheng
Keyword(s):  
Performance Analysis ◽  
Quantum Algorithm ◽  
Integer Factorization ◽  
Algebraic Structures ◽  
Cryptographic Primitives ◽  
Factorization Problem ◽  
Integer Factorization Problem ◽  
Modern Cryptography ◽  
Nonabelian Groups

To resist known quantum algorithm attacks, several nonabelian algebraic structures mounted upon the stage of modern cryptography. Recently, Baba et al. proposed an important analogy from the integer factorization problem to the factorization problem over nonabelian groups. In this paper, we propose several conjugated problems related to the factorization problem over nonabelian groups and then present three constructions of cryptographic primitives based on these newly introduced conjugacy systems: encryption, signature, and signcryption. Sample implementations of our proposal as well as the related performance analysis are also presented.

scholarly journals Connections on Valuated Binary Tree and Their Applications in Factoring Odd Integers

2021 ◽  
pp. 134-153
Author(s):  
Xingbo Wang ◽  
Jinfeng Luo ◽  
Ying Tian ◽  
Li Ma
Keyword(s):  
Binary Tree ◽  
Numerical Experiments ◽  
Mathematical Reasoning ◽  
Binary Trees ◽  
Integer Factorization ◽  
Parallel Connection ◽  
Central Lines ◽  
Factorization Problem ◽  
Integer Factorization Problem

This paper makes an investigation on geometric relationships among nodes of the valuated binary trees, including parallelism, connection and penetration. By defining central lines and distance from a node to a line, some intrinsic connections are discovered to connect nodes between different subtrees. It is proved that a node out of a subtree can penetrate into the subtree along a parallel connection. If the connection starts downward from a node that is a multiple of the subtree’s root, then all the nodes on the connection are multiples of the root. Accordingly composite odd integers on such connections can be easily factorized. The paper proves the new results with detail mathematical reasoning and demonstrates several numerical experiments made with Maple software to factorize rapidly a kind of big odd integers that are of the length from 59 to 99 decimal digits. It is once again shown that the valuated binary tree might be a key to unlock the lock of the integer factorization problem.

scholarly journals A New LSB Attack on Special-Structured RSA Primes

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 838
Author(s):  
Amir Hamzah Abd Ghafar ◽  
Muhammad Rezal Kamel Ariffin ◽  
Muhammad Asyraf Asbullah
Keyword(s):  
Polynomial Time ◽  
Public Key Cryptosystem ◽  
Integer Factorization ◽  
Partial Knowledge ◽  
Rsa Cryptosystem ◽  
Factorization Problem ◽  
Integer Factorization Problem ◽  
Positive Integers ◽  
Vital Element ◽  
Great Danger

Asymmetric key cryptosystem is a vital element in securing our communication in cyberspace. It encrypts our transmitting data and authenticates the originality and integrity of the data. The Rivest–Shamir–Adleman (RSA) cryptosystem is highly regarded as one of the most deployed public-key cryptosystem today. Previous attacks on the cryptosystem focus on the effort to weaken the hardness of integer factorization problem, embedded in the RSA modulus, N = p q . The adversary used several assumptions to enable the attacks. For examples, p and q which satisfy Pollard’s weak primes structures and partial knowledge of least significant bits (LSBs) of p and q can cause N to be factored in polynomial time, thus breaking the security of RSA. In this paper, we heavily utilized both assumptions. First, we assume that p and q satisfy specific structures where p = a m + r p and q = b m + r q for a , b are positive integers and m is a positive even number. Second, we assume that the bits of r p and r q are the known LSBs of p and q respectively. In our analysis, we have successfully factored N in polynomial time using both assumptions. We also counted the number of primes that are affected by our attack. Based on the result, it may poses a great danger to the users of RSA if no countermeasure being developed to resist our attack.

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