scholarly journals Use of Signed Permutations in Cryptography

2020 ◽  
pp. 23-38
Author(s):  
Iharantsoa Vero Raharinirina
Keyword(s):  
Discrete Logarithm ◽  
Public Key ◽  
Natural Numbers ◽  
Hyperoctahedral Group ◽  
Public Key Cryptosystems ◽  
Signed Permutations ◽  
Negative Point ◽  
Large Memory ◽  
One To One

In this paper we consider cryptographic applications of the arithmetic on the hyperoctahedral group. On an appropriate subgroup of the latter, we particularly propose to construct public key cryptosystems based on the discrete logarithm. The fact that the group of signed permutations has rich properties provides fast and easy implementation and makes these systems resistant to attacks like the Pohlig-Hellman algorithm. The only negative point is that storing and transmitting permutations need large memory. Using together the hyperoctahedral enumeration system and what is called subexceedant functions, we define a one-to-one correspondence between natural numbers and signed permutations with which we label the message units.

An alternative practical public-key cryptosystems based on the Dependent RSA Discrete Logarithm Problems

2021 ◽  
Vol 164 ◽  
pp. 114047
Author(s):  
Shailendra Kumar Tripathi ◽  
Bhupendra Gupta ◽  
K.K. Soundra Pandian
Keyword(s):  
Discrete Logarithm ◽  
Public Key ◽  
Public Key Cryptosystems

scholarly journals MPKC-based Threshold Proxy Signcryption Scheme

2019 ◽  
Vol 17 (2) ◽  
pp. 196-206
Author(s):  
Li Huixian ◽  
Gao Jin ◽  
Wang Lingyun ◽  
Pang Liaojun2
Keyword(s):  
Quantum Computer ◽  
Discrete Logarithm ◽  
Random Oracle Model ◽  
Random Oracle ◽  
Public Key ◽  
Group Signature ◽  
Large Integer ◽  
Efficient Technology ◽  
Public Key Cryptosystems ◽  
Signcryption Scheme

The threshold proxy signcryption can implement signature and encryption simultaneously in one logical step, and can be used to realize the decentralized protection of the group signature key, so it is an efficient technology for network security. Currently, most of the existing threshold proxy signcryption schemes are designed based on the traditional public key cryptosystems, and their security mainly depends on the difficulty of the large integer decomposition and the discrete logarithm. However, the traditional public key cryptosystems cannot resist the quantum computer attack, which makes the existing threshold proxy signcryption schemes based on traditional public key cryptosystems insecure against quantum attacks. Motivated by these concerns, we proposed a threshold proxy signcryption scheme based on Multivariate Public Key Cryptosystem (MPKC) which is one of the quantum attack-resistent public key algorithms. Under the premise of satisfying the threshold signcryption requirements of the threshold proxy, our scheme can not only realize the flexible participation of the proxy signcrypters but also resist the quantum computing attack. Finally, based on the assumption of Multivariate Quadratic (MQ) problem and Isomorphism Polynomial (IP) problem, the proof of the confidentiality and the unforgeability of the proposed scheme under the random oracle model is given.

Blind Signature Based on Discrete Logarithm Type Cryptosystem

2011 ◽  
Vol 204-210 ◽  
pp. 1318-1321
Author(s):  
Xuan Wu Zhou ◽  
Yan Fu
Keyword(s):  
Elliptic Curves ◽  
Discrete Logarithm ◽  
Blind Signature ◽  
Discrete Logarithm Problem ◽  
Public Key ◽  
Security Level ◽  
Signature Schemes ◽  
Public Key Cryptosystems ◽  
Trapdoor Function ◽  
Asymmetric Cryptosystem

Discrete logarithm problem is an important trapdoor function to design asymmetric cryptosystem, and some fast public key cryptosystems have been designed based on it. In the paper, we introduced fast asymmetric cryptosystem into the designing and analyzing of blind signature, and presented improved blind signature schemes based on ECC (Elliptic Curves Cryptosystem). The trapdoor function of the blind signatures is based on ECDLP (Elliptic Curves Discrete Logarithm Problem), and the algorithms of the scheme make full use of the superiority of ECC, such as high efficiency and short key length. The improved blind signature schemes can achieve the same security level with less storing space, smaller communication band-width and less overheads regarding software and hardware application. Furthermore, the algorithms in the schemes can be generalized into other public key cryptosystems based on discrete logarithm problem without any influence to efficiency or security.

Provable Security for Public Key Cryptosystems

2016 ◽  
pp. 317-341
Author(s):  
Syed Taqi Ali
Keyword(s):  
Provable Security ◽  
Ad Hoc ◽  
Discrete Logarithm ◽  
Random Oracle Model ◽  
Public Key ◽  
Public Key Cryptosystem ◽  
Public Key Cryptosystems ◽  
Security Proofs ◽  
Security Proof ◽  
The One

In the early years after the invention of public key cryptography by Diffie and Hellman in 1976, the design and evaluation of public key cryptosystems has been done merely in ad-hoc manner based on trial and error. The public key cryptosystem said to be secure as long as there is no successful cryptanalytic attack on it. But due to various successful attacks on the cryptosystems after development, the cryptographic community understood that this ad-hoc approach might not be good enough. The paradigm of provable security is an attempt to get rid of ad hoc design. The goals of provable security are to define appropriate models of security on the one hand, and to develop cryptographic designs that can be proven to be secure within the defined models on the other. There are two general approaches for structuring the security proof. One is reductionist approach and other is game-based approach. In these approaches, the security proofs reduce a well known problem (such as discrete logarithm, RSA) to an attack against a proposed cryptosystem. With this approach, the security of public key cryptosystem can be proved formally under the various models viz. random oracle model, generic group model and standard model. In this chapter, we will briefly explain these approaches along with the security proofs of well known public key cryptosystems under the appropriate model.

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.

scholarly journals Provable Security for Public Key Cryptosystems

Cryptography ◽  
2020 ◽  
pp. 214-238
Author(s):  
Syed Taqi Ali
Keyword(s):  
Provable Security ◽  
Ad Hoc ◽  
Discrete Logarithm ◽  
Random Oracle Model ◽  
Public Key ◽  
Public Key Cryptosystem ◽  
Public Key Cryptosystems ◽  
Security Proofs ◽  
Security Proof ◽  
The One

In the early years after the invention of public key cryptography by Diffie and Hellman in 1976, the design and evaluation of public key cryptosystems has been done merely in ad-hoc manner based on trial and error. The public key cryptosystem said to be secure as long as there is no successful cryptanalytic attack on it. But due to various successful attacks on the cryptosystems after development, the cryptographic community understood that this ad-hoc approach might not be good enough. The paradigm of provable security is an attempt to get rid of ad hoc design. The goals of provable security are to define appropriate models of security on the one hand, and to develop cryptographic designs that can be proven to be secure within the defined models on the other. There are two general approaches for structuring the security proof. One is reductionist approach and other is game-based approach. In these approaches, the security proofs reduce a well known problem (such as discrete logarithm, RSA) to an attack against a proposed cryptosystem. With this approach, the security of public key cryptosystem can be proved formally under the various models viz. random oracle model, generic group model and standard model. In this chapter, we will briefly explain these approaches along with the security proofs of well known public key cryptosystems under the appropriate model.

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