ID-based threshold digital signature schemes on the elliptic curve discrete logarithm problem

Introduction: Development of practical post-quantum signature schemes is a current challenge in the applied cryptography. Recently, several different forms of the hidden discrete logarithm problem were proposed as primitive signature schemes resistant to quantum attacks. Purpose: Development of a new form of the hidden discrete logarithm problem set in finite commutative groups possessing multi-dimensional cyclicity, and a method for designing post-quantum signature schemes. Results: A new form of the hidden discrete logarithm problem is introduced as the base primitive of practical post-quantum digital signature algorithms. Two new four-dimensional finite commutative associative algebras have been proposed as algebraic support for the introduced computationally complex problem. A method for designing signature schemes on the base of the latter problem is developed. The method consists in using a doubled public key and two similar equations for the verification of the same signature. To generate a pair of public keys, two secret minimum generator systems <G, Q> and <H, V> of two different finite groups G<G, Q> and G<H, V> possessing two-dimensional cyclicity are selected at random. The first public key (Y, Z, U) is computed as follows: Y = Gy1Qy2a, Z = Gz1Qz2b, U = Gu1Qu2g, where the set of integers (y1, y2, a, z1, z2, b, u1, u2, g) is a private key. The second public key (Y¢, Z¢, U¢) is computed as follows: Y¢ = Hy1Vy2a, Z¢ = Hz1Vz2b, U¢ = Hu1Vu2g. Using the same parameters to calculate the corresponding elements belonging to different public keys makes it possible to calculate a single signature which satisfies two similar verification equations specified in different finite commutative associative algebras. Practical relevance: Due to a smaller size of the public key, private key and signature, as well as approximately equal performance as compared to the known analogues, the proposed digital signature scheme can be used in the development of post-quantum signature algorithms.

Download Full-text

A New Method for Designing Post-Quantum Signature Schemes

Journal of Communications ◽

10.12720/jcm.15.10.747-754 ◽

2020 ◽

pp. 747-754

Author(s):

Minh Nguyen Hieu ◽

◽

Moldovyan Alexander Andreevich ◽

Moldovyan Nikolay Andreevich ◽

Canh Hoang Ngoc

Keyword(s):

Digital Signature ◽

Quantum Computer ◽

Multiplicative Group ◽

Discrete Logarithm ◽

Quantum Signature ◽

Discrete Logarithm Problem ◽

New Method ◽

Signature Scheme ◽

Signature Schemes ◽

Computational Difficulty

The current standards of the digital signature algorithms are based on computational difficulty of the discrete logarithm and factorization problems. Expected appearance in near future of the quantum computer that is able to solve in polynomial time each of the said computational puts forward the actual task of the development of the post-quantum signature algorithms that resist the attacks using the quantum computers. Recently, the signature schemes based on the hidden discrete logarithm problem set in finite non-commutative associative algebras had been proposed. The paper is devoted to a further development of this approach and introduces a new practical post-quantum signature scheme possessing small size of public key and signature. The main contribution of the paper is the developed new method for defining the hidden discrete logarithm problem that allows applying the finite commutative groups as algebraic support of the post-quantum digital signature schemes. The method uses idea of applying multipliers that mask the periodicity connected with the value of discrete logarithm of periodic functions set on the base of the public parameters of the signature scheme. The finite 4-dimensional commutative associative algebra the multiplicative group of which possesses 4-dimensional cyclicity is used as algebraic support of the developed signature scheme.

Download Full-text

Proxy-Protected Proxy Multi-Signature Based on Elliptic Curve

International Journal of Informatics and Communication Technology (IJ-ICT) ◽

10.11591/ijict.v3i1.pp67-72 ◽

2014 ◽

Vol 3 (1) ◽

pp. 67

Author(s):

Manoj Kumar Chande ◽

Balwant Singh Thakur

Keyword(s):

Low Power ◽

Elliptic Curve ◽

Digital Signature ◽

Discrete Logarithm ◽

Proxy Signature ◽

Entire Group ◽

Signature Scheme ◽

Signature Schemes ◽

Basic Properties ◽

Digital Signature Algorithm

In this work, we propose a proxy-protected proxy multi-signature scheme based on EllipticCurve Digital Signature Algorithm (ECDSA), which aims at providing data authenticity,integrity, and non-repudiation to satisfy the basic properties of partial delegation proxy signaturedescribed by Mambo et al. as well as strong proxy signature properties defined byLee et. al. The proposed signing/verifying scheme combines the advantages of proxyprotectedsignature and multi-signature scheme. The security of the proposed schemes isbased on the difficulty of breaking the elliptic curve discrete logarithm problem (ECDLP).The scheme proposed is faster and secure than the multi-signature based on factoring ordiscrete logarithm problem (DLP). The final multi-signature of a message can be verifiedindividually for each signer or collectively for a subgroup or entire group as well. Finally,the proposed proxy-protected proxy multi-signature schemes can be used in E-commerceand E-government application, which can be implemented using low power and small processingdevices.

Download Full-text

Improvement of digital signature with message recovery and its variants based on elliptic curve discrete logarithm problem

Computer Standards & Interfaces ◽

10.1016/s0920-5489(04)00039-x ◽

2004 ◽

Author(s):

Z SHAO

Keyword(s):

Elliptic Curve ◽

Digital Signature ◽

Discrete Logarithm ◽

Discrete Logarithm Problem ◽

Message Recovery

Download Full-text

Secure Signature Schemes Based on Interactive Protocols

BRICS Report Series ◽

10.7146/brics.v1i29.21637 ◽

1994 ◽

Vol 1 (29) ◽

Cited By ~ 1

Author(s):

Ronald Cramer ◽

Ivan B. Damgård

Keyword(s):

Digital Signature ◽

Discrete Logarithm ◽

Discrete Logarithm Problem ◽

Signature Schemes

A method is proposed for constructing from interactive protocols digital signature schemes secure against adaptively chosen message attacks. Our main result is that practical secure signature schemes can now also be based on computationally difficult problems other than factoring, such as the discrete logarithm problem.

Download Full-text

A novel method for development of post-quantum digital signature schemes

Information and Control Systems ◽

10.31799/1684-8853-2020-6-21-29 ◽

2020 ◽

pp. 21-29

Author(s):

Dmitry Moldovyan ◽

Alexandr Moldovyan ◽

Nikolay Moldovyan

Keyword(s):

Digital Signature ◽

Discrete Logarithm ◽

Practical Interest ◽

Quantum Signature ◽

Discrete Logarithm Problem ◽

Public Key ◽

Associative Algebras ◽

Signature Schemes ◽

The Public ◽

Quantum Digital Signature

Introduction: Development of post-quantum digital signature standards represents a current challenge in the area of cryptography. Recently, the signature schemes based on the hidden discrete logarithm problem had been proposed. Further development of this approach represents significant practical interest, since it provides possibility of designing practical signature schemes possessing small size of public key and signature. Purpose: Development of the method for designing post-quantum signature schemes and new forms of the hidden discrete logarithm problem, corresponding to the method. Results: A method for designing post-quantum signature schemes is proposed. The method consists in setting the dependence of the publickey elements on masking multipliers that eliminates the periodicity connected with the value of discrete logarithm of periodic functions constructed on the base of the public parameters of the cryptoscheme. Two novel forms for defining the hidden discrete logarithm problem in finite associative algebras are proposed. The first (second) form has allowed to use the finite commutative (non-commutative) algebra as algebraic support of the developed signature schemes. Practical relevance: Due to significantly smaller size of public key and signature and approximately equal performance in comparison with the known analogues, the developed signature algorithms represent interest as candidates for practical post-quantum cryptoschemes.

Download Full-text