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

scholarly journals Algebraic Supports and New Forms of the Hidden Discrete Logarithm Problem for Post-quantum Public-key Cryptoschemes

2021 ◽  
Vol 18 (3) ◽  
Author(s):  
Dmitriy Moldovyan ◽  
Nashwan Al-Majmar ◽  
Alexander Moldovyan
Keyword(s):  
Key Agreement ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Public Key ◽  
Large Set ◽  
Associative Algebras ◽  
Dimensional Algebra ◽  
The Public ◽  
Private Key ◽  
Quantum Public Key

This paper introduces two new forms of the hidden discrete logarithm problem defined over a finite non-commutative associative algebras containing a large set of global single-sided units. The proposed forms are promising for development on their base practical post-quantum public key-agreement schemes and are characterized in performing two different masking operations over the output value of the base exponentiation operation that is executed in framework of the public key computation. The masking operations represent homomorphisms and each of them is mutually commutative with the exponentiation operation. Parameters of the masking operations are used as private key elements. A 6-dimensional algebra containing a set of p3 global left-sided units is used as algebraic support of one of the hidden logarithm problem form and a 4-dimensional algebra with p2 global right-sided units is used to implement the other form of the said problem. The result of this paper is the proposed two methods for strengthened masking of the exponentiation operation and two new post-quantum public key-agreement cryptoschemes. Mathematics subject classification: 94A60, 16Z05, 14G50, 11T71, 16S50.

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 Diffie-Hellman Key Agreement with Elliptic Curve Discrete Logarithm Problem

2015 ◽  
Vol 129 (12) ◽  
pp. 25-27 ◽  
Author(s):  
Samta Gajbhiye ◽  
Sanjeev Karmakar ◽  
Monisha Sharma
Keyword(s):  
Elliptic Curve ◽  
Key Agreement ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Diffie Hellman

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.

scholarly journals A Novel Provably Secure Key-Agreement Using Secret Subgroup Generator

2021 ◽  
Author(s):  
Abdelhaliem Babiker
Keyword(s):  
Key Agreement ◽  
Cyclic Subgroup ◽  
Discrete Logarithm ◽  
Key Exchange ◽  
Discrete Logarithm Problem ◽  
Secret Key ◽  
Shared Secret ◽  
Shared Secret Key ◽  
Provably Secure

Abstract In this paper, a new key-agreement scheme is proposed and analyzed. In addition to being provably secure in shared secret key indistinguishability model, the scheme has an interesting feature: while using exponentiation over a cyclic subgroup to establish the key-agreement, the generator of that subgroup is hidden to secure the scheme against adversaries that are capable of solving the Discrete Logarithm Problem, which means that the scheme might be candidate as a post-quantum key exchange scheme.

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.

Improvement of a Structured Multi-Signature Scheme

2010 ◽  
Vol 439-440 ◽  
pp. 401-406
Author(s):  
Jun Zhang
Keyword(s):  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Public Key ◽  
Signature Scheme ◽  
Forgery Attack ◽  
Signature Schemes ◽  
Insider Attack ◽  
Public Keys

Structured multi-signatures is a special multi-signature which multiple signer can sign the same message and it provided co-signers with different position have different authorization capability. There are lots of structured multi-signature schemes such as Harn’s scheme and Burmester’s scheme, etc. Though Harn’s scheme was relatively safer, yet this scheme was not safety enough because it was very easily aggressed by the forgery attack. This paper shows the scheme can not resist the forgery attack. Then the paper proposed a new structure multi-signature scheme based on the difficulty of the discrete logarithm problem with verifying signature parameter and signers’ public keys. By verifying public-key, the new scheme can resist lots of outsider attack and insider attack. The validity of the new scheme can be verified, and it is a secure structured multi-signature scheme.

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