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 Modification of Traditional RSA into Symmetric-RSA Cryptosystems

Cryptography ◽  
2020 ◽  
pp. 120-128
Author(s):  
Prerna Mohit ◽  
G. P. Biswas
Keyword(s):  
Digital Signature ◽  
Discrete Logarithm ◽  
Prime Numbers ◽  
Public Key ◽  
Key Exchange Protocol ◽  
Factorization Problem ◽  
Rsa Algorithm ◽  
Diffie Hellman ◽  
Diffie Hellman Key Exchange ◽  
Rsa Cryptography

This paper addresses the modification of RSA cryptography namely Symmetric-RSA, which seem to be equally useful for different cryptographic applications such as encryption, digital signature, etc. In order to design Symmetric-RSA, two prime numbers are negotiated using Diffie-Hellman key exchange protocol followed by RSA algorithm. As the new scheme uses Diffie-Hellman and RSA algorithm, the security of the overall system depends on discrete logarithm as well as factorization problem and thus, its security is more than public-key RSA. Finally, some new cryptographic applications of the proposed modifications are described that certainly extend the applications of the existing RSA.

scholarly journals The Equivalence between the DHP and DLP for Elliptic Curves Used in Practical Applications

2004 ◽  
Vol 7 ◽  
pp. 50-72 ◽  
Author(s):  
A. Muzereau ◽  
N. P. Smart ◽  
F. Vercauteren
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Precise Estimate ◽  
Practical Applications ◽  
Diffie Hellman ◽  
Exact Security

AbstractIn this paper, the authors re-examine the reduction of Maurer and Wolf of the discrete logarithm problem to the Diffie-Hellman problem. They give a precise estimate for the number of operations required in the reduction, and then use this to estimate the exact security of the elliptic curve variant of the Diffie-Hellman protocol for various elliptic curves defined in standards.

Modification of Traditional RSA into Symmetric-RSA Cryptosystems

2017 ◽  
Vol 13 (1) ◽  
pp. 66-73
Author(s):  
Prerna Mohit ◽  
G. P. Biswas
Keyword(s):  
Digital Signature ◽  
Discrete Logarithm ◽  
Prime Numbers ◽  
Public Key ◽  
Key Exchange Protocol ◽  
Factorization Problem ◽  
Rsa Algorithm ◽  
Diffie Hellman ◽  
Diffie Hellman Key Exchange ◽  
Rsa Cryptography

This paper addresses the modification of RSA cryptography namely Symmetric-RSA, which seem to be equally useful for different cryptographic applications such as encryption, digital signature, etc. In order to design Symmetric-RSA, two prime numbers are negotiated using Diffie-Hellman key exchange protocol followed by RSA algorithm. As the new scheme uses Diffie-Hellman and RSA algorithm, the security of the overall system depends on discrete logarithm as well as factorization problem and thus, its security is more than public-key RSA. Finally, some new cryptographic applications of the proposed modifications are described that certainly extend the applications of the existing RSA.

scholarly journals Collective Signature Protocols for Signing Groups based on Problem of Finding Roots Modulo Large Prime Number

2021 ◽  
Vol 13 (04) ◽  
pp. 59-69
Author(s):  
Tuan Nguyen Kim ◽  
Duy Ho Ngoc ◽  
Nikolay A. Moldovyan
Keyword(s):  
Elliptic Curve ◽  
Prime Number ◽  
Digital Signature ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Public Key ◽  
Prime Factorization ◽  
Factorization Problem ◽  
Hybrid Combination ◽  
Different Types

Generally, digital signature algorithms are based on a single difficult computational problem like prime factorization problem, discrete logarithm problem, elliptic curve problem. There are also many other algorithms which are based on the hybrid combination of prime factorization problem and discrete logarithm problem. Both are true for different types of digital signatures like single digital signature, group digital signature, collective digital signature etc. In this paper we propose collective signature protocols for signing groups based on difficulty of problem of finding roots modulo large prime number. The proposed collective signatures protocols have significant merits one of which is connected with possibility of their practical using on the base of the existing public key infrastructures.

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