Threshold-directed signature scheme based on hybrid number theoretic problems

2019 ◽  
Vol 13 (05) ◽  
pp. 2050098
Author(s):  
Mohd Saiful Adli Mohamad
Keyword(s):  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Signature Scheme ◽  
Integer Factorization ◽  
The Public ◽  
Designated Verifier ◽  
Single Number ◽  
Directed Signature ◽  
Cryptographic Attacks ◽  
Hybrid Number

Directed signature is a type of function-based signature with the property that the signature only can be verified by a designated verifier and at certain times, the verifier should be able to convince anyone about the validity of the signature without revealing any secret information about the signature to the public. Taking into consideration the involvement of group decision making, some threshold directed signature schemes based on single number theoretic problems, such as integer factorization, discrete logarithm problem, and elliptic curve discrete logarithm problem, have been developed by cryptographers. Although the single-problem-based schemes are still invincible because there is still no cryptanalyst to find the solution to the problems, in the future, if the enemy or attacker manages to get the polynomial algorithm to solve the single problems, the schemes will no longer be practiced and applied. For such reason, in this paper, we propose a new threshold-directed signature scheme based on integer factorization and discrete logarithm problems. The advantage of our scheme is based on the assumption that it is very unlikely to solve two hard number theoretic problems simultaneously. We also show that our scheme is secured against some cryptographic attacks and also significantly efficient compared with threshold signature scheme based on single problem.

scholarly journals Time-constrained strong multi-designated verifier signature suitable for Internet of things–based collaborative fog computing systems

2021 ◽  
Vol 17 (3) ◽  
pp. 155014772110017
Author(s):  
Han-Yu Lin
Keyword(s):  
Internet Of Things ◽  
Fog Computing ◽  
Discrete Logarithm ◽  
Signature Scheme ◽  
Computing Systems ◽  
Extended Technique ◽  
Diffie Hellman ◽  
Designated Verifier ◽  
Designated Verifier Signature ◽  
Cloud Servers

Fog computing is viewed as an extended technique of cloud computing. In Internet of things–based collaborative fog computing systems, a fog node aggregating lots of data from Internet of things devices has to transmit the information to distributed cloud servers that will collaboratively verify it based on some predefined auditing policy. However, compromised fog nodes controlled by an adversary might inject bogus data to cheat or confuse remote servers. It also causes the waste of communication and computation resources. To further control the lifetime of signing capability for fog nodes, an appropriate mechanism is crucial. In this article, the author proposes a time-constrained strong multi-designated verifier signature scheme to meet the above requirement. In particular, a conventional non-delegatable strong multi-designated verifier signature scheme with low computation is first given. Based on its constructions, we show how to transform it into a time-constrained variant. The unforgeability of the proposed schemes is formally proved based on the famous elliptic curve discrete logarithm assumption. The security requirement of strong signer ambiguity for our substantial constructions is also analyzed by utilizing the intractable assumption of decisional Diffie–Hellman. Moreover, some comparisons in terms of the signature size and computational costs for involved entities among related mechanisms are made.

scholarly journals Digital signature scheme on the 2 x 2 matrix algebra

2021 ◽  
Vol 17 (3) ◽  
pp. 254-261
Author(s):  
Nikolay A. Moldovyan ◽  
◽  
Alexandr A. Moldovyan ◽  
Keyword(s):  
Digital Signature ◽  
High Performance ◽  
Matrix Algebra ◽  
Multiplicative Group ◽  
Discrete Logarithm ◽  
Signature Scheme ◽  
The Public ◽  
Signature Generation ◽  
Commutative Subalgebras ◽  
Digital Signature Scheme

The article considers the structure of the 2x2 matrix algebra set over a ground finite field GF(p). It is shown that this algebra contains three types of commutative subalgebras of order p2, which differ in the value of the order of their multiplicative group. Formulas describing the number of subalgebras of every type are derived. A new post-quantum digital signature scheme is introduced based on a novel form of the hidden discrete logarithm problem. The scheme is characterized in using scalar multiplication as an additional operation masking the hidden cyclic group in which the basic exponentiation operation is performed when generating the public key. The advantage of the developed signature scheme is the comparatively high performance of the signature generation and verification algorithms as well as the possibility to implement a blind signature protocol on its base.

scholarly journals POST-QUANTUM BLIND SIGNATURE PROTOCOL ON NON-COMMUTATIVE ALGEBRAS

2021 ◽  
Vol 37 (4) ◽  
pp. 495-509
Author(s):  
Minh N.H ◽  
Moldovyan D.N, et al.
Keyword(s):  
Finite Field ◽  
Discrete Logarithm ◽  
Blind Signature ◽  
Discrete Logarithm Problem ◽  
Signature Scheme ◽  
Associative Algebras ◽  
Basic Properties ◽  
Commutative Algebras ◽  
Quantum Blind Signature

A method for constructing a blind signature scheme based on a hidden discrete logarithm problem defined in finite non-commutative associative algebras is proposed. Blind signature protocols are constructed using four-dimensional and six-dimensional algebras defined over a ground finite field GF(p) and containing a global two-sided unit as an algebraic support. The basic properties of the used algebra, which determine the choice of protocol parameters, are described.

scholarly journals Proposed Developments of Blind Signature Scheme based on The Elliptic Curve Discrete Logarithm Problem

2013 ◽  
Vol 2 (1) ◽  
pp. 151-160
Author(s):  
E.H. El Kinani ◽  
Fatima Amounas
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Discrete Logarithm ◽  
Mathematical Structure ◽  
Blind Signature ◽  
Discrete Logarithm Problem ◽  
Signature Scheme

In recent years, Elliptic Curve Cryptography (ECC) has attracted the attention of researchers due to its robust mathematical structure and highest security compared to other existing algorithm like RSA. Our main objective in this work was to provide a novel blind signature scheme based on ECC. The security of the proposed method results from the infeasibility to solve the discrete logarithm over an elliptic curve. In this paper we introduce a proposed to development the blind signature scheme with more complexity as compared to the existing schemes. Keyword: Cryptography, Blind Signature, Elliptic Curve, Blindness, Untraceability.DOI: 10.18495/comengapp.21.151160

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