Public-Key Cryptosystems Based on the Discrete Logarithm Problem

2010 ◽  
pp. 205-238 ◽  
Author(s):  
Christof Paar ◽  
Jan Pelzl
Keyword(s):  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Public Key ◽  
Public Key Cryptosystems

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.

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

Public Key-Agreement Schemes Based on the Hidden Discrete Logarithm Problem

2020 ◽  
Vol 26 (10) ◽  
pp. 577-585
Author(s):  
R. S. Fahrutdinov ◽  
◽  
A. Yu. Mirin ◽  
D. N. Moldovyan ◽  
A. A. Kostina ◽  
...  
Keyword(s):  
Key Agreement ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Public Key

Efficient Convertible User Designating Confirmer Partially Blind Signature with Provable Security

2011 ◽  
Vol 282-283 ◽  
pp. 307-311
Author(s):  
Li Zhen Ma
Keyword(s):  
Provable Security ◽  
Discrete Logarithm ◽  
Random Oracle Model ◽  
Random Oracle ◽  
Blind Signature ◽  
Discrete Logarithm Problem ◽  
Public Key ◽  
Signature Schemes ◽  
Partially Blind Signature ◽  
Provably Secure

Any one who knows the signer’s public key can verify the validity of a given signature in partially blind signature schemes. This verifying universality may be used by cheats if the signed message is sensitive or personal. To solve this problem, a new convertible user designating confirmer partially blind signature, in which only the designated confirmer (designated by the user) and the user can verify and confirm the validity of given signatures and convert given signatures into publicly verifiable ones, is proposed. Compared with Huang et al.’s scheme, the signature size is shortened about 25% and the computation quantity is reduced about 36% in the proposed scheme. Under random oracle model and intractability of Discrete Logarithm Problem the proposed scheme is provably secure.

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.

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.

Structure and Analysis of Certificateless Proxy Blind Signature Scheme without Bilinear Pairing

2013 ◽  
Vol 734-737 ◽  
pp. 3194-3198
Author(s):  
Yi Wang
Keyword(s):  
Finite Field ◽  
Discrete Logarithm ◽  
Public Key Cryptography ◽  
Bilinear Pairing ◽  
Blind Signature ◽  
Discrete Logarithm Problem ◽  
Public Key ◽  
Signature Scheme ◽  
Proxy Blind Signature ◽  
Certificateless Public Key Cryptography

Combined with certificateless public key cryptography and proxy blind signature, an efficient certificateless proxy blind signature scheme is proposed. Its security is based on the discrete logarithm problem. Compared with the existed certificateless proxy blind signature scheme, because without bilinear pairing, it have higher efficiency. According to the different attacker and all kinds of attacks, the scheme is proved to be correct and security under the hardness of discrete logarithm problem in the finite field.

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