Alternative signature generation procedures in the digital signature schemes based on the hidden discrete logarithm problem

2020 ◽  
pp. 100-107
Author(s):  
D.N. Moldovyan ◽  
A.A. Moldovyan ◽  
D.Yu. Guryanov
Keyword(s):  
Quantum Algorithms ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Public Key ◽  
Practical Significance ◽  
Signature Schemes ◽  
Factorization Problem ◽  
Private Key ◽  
Signature Generation ◽  
Computational Difficulty

Public-key cryptographic algorithms and protocols based on computational difficulty of the factorization problem and on the discrete logarithm problem are widely used in information-telecommunication systems. Currently the problem of construction of the post-quantum algorithms and protocols, i.e. cryptoschemes that are secure to potential attacks using quantum computers, represents a challenge in the area of applied and theoretic cryptography. In the literature the postquantum signature schemes based on the hidden discrete logarithm problem that is formulated in the finite non-commutativeassociative algebras were proposed. A disadvantage of such signature schemes is comparatively large size of the private key. The goal of the study is to develop an alternative signature generation procedures that will allow to reduce significantly the size of the private key. To achieve the goal, it is using the elements of the public key to compute the fixation vector at the first step of the signature formation procedure. As a result, there are designed alternative signature generation procedures in two known signature schemes based on the computational difficulty of the hidden discrete logarithm problem. Application of the proposed procedures gives possibility to reduce the size of the private key. The practical significance of the study is reduction the size of the protected memory in the electronic devices used for computation of the digital signatures.

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.

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.

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.

scholarly journals A post-quantum digital signature scheme on groups with four-dimensional cyclicity

2021 ◽  
pp. 43-51
Author(s):  
Nikolay Moldovyan ◽  
Dmitry Moldovyan
Keyword(s):  
Digital Signature ◽  
Discrete Logarithm ◽  
Quantum Signature ◽  
Discrete Logarithm Problem ◽  
Public Key ◽  
Associative Algebras ◽  
Signature Schemes ◽  
Public Keys ◽  
Digital Signature Scheme ◽  
Quantum Digital Signature

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.

scholarly journals A New Method for Designing Post-Quantum Signature Schemes

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.

scholarly journals Penerapan skema tanda tangan Schnorr pada pembuatan tanda tangan digital

2017 ◽  
Vol 12 (1) ◽  
pp. 57
Author(s):  
Herdita Fajar Isnaini ◽  
Karyati Karyati
Keyword(s):  
Digital Signature ◽  
Hash Function ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Public Key ◽  
Key Generation ◽  
Signature Scheme ◽  
Private Key ◽  
Message Digest ◽  
Schnorr Signature

Tanda tangan digital dapat dijadikan sebagai salah satu cara untuk menjamin keaslian pesan atau informasi yang diterima. Salah satu skema yang dapat digunakan dalam membentuk tanda tangan adalah skema tanda tangan Schnorr. Skema tanda tangan ini berdasarkan pada masalah logaritma diskret. Skema ini memerlukan penggunaan fungsi hash yang akan menghasilkan nilai hash pesan untuk pembuatan tanda tangan, yang menjadi salah satu alasan keamanan dari skema ini. Skema tanda tangan Schnorr terdiri dari tiga proses, yaitu: pembentukan kunci, pembuatan tanda tangan serta verifikasi. Kajian ini akan membahas mengenai skema tanda tangan Schnorr dalam membentuk tanda tangan digital sebagai pengaman keaslian informasi, yang dibahas per prosesnya, meliputi: pembentukan kunci, pembuatan tanda tangan yang disertai perhitungan nilai hash serta verifikasi. Hasil dari kajian ini adalah didapatkan algoritma – algoritma dari skema tanda tangan Schnorr, yaitu algoritma pembentukan kunci publik dan kunci privat, algoritma pembuatan tanda tangan, serta algoritma verifikasi tanda tangan.Kata Kunci: tanda tangan digital, skema tanda tangan Schnorr, nilai hash, kunci publik, kunci privat. Implementation of Schnorr Signature Scheme in The Form of  Digital Signature AbstractDigital signature can be used as a way to ensure the authenticity of a received message or information. There is a scheme that can be used to form a signature called Schnorr signature scheme. This signature scheme is based on discrete logarithm problem. This scheme requires the use of hash function that will result to a message digest to form the signature, which is the reason of this scheme’s security. Schnorr signature scheme consists of three processes, namely: the key generation, signature formation, and verification. This study will discuss the Schnorr signature scheme in the form of digital signatures as a safeguard of an information’s authenticity, which is discussed process by process, including: the key generation, signature formation as well as the calculation of message digest and verification. The results of this study obtained algorithms - algorithms of Schnorr signature scheme, which is an algorithm of a public key and a private key generation, an algorithm of the signature formation, and an algorithm of signature verification.Keywords: digital signature, Schnorr signature scheme, message digest, public key, privat key

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

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.

scholarly journals Collective Signature Protocols for Signing Groups based on Problem of Finding Roots Modulo Large Prime Number

2021 ◽  
Vol 13 (04) ◽  
pp. 59-69
Author(s):  
Tuan Nguyen Kim ◽  
Duy Ho Ngoc ◽  
Nikolay A. Moldovyan
Keyword(s):  
Elliptic Curve ◽  
Prime Number ◽  
Digital Signature ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Public Key ◽  
Prime Factorization ◽  
Factorization Problem ◽  
Hybrid Combination ◽  
Different Types

Generally, digital signature algorithms are based on a single difficult computational problem like prime factorization problem, discrete logarithm problem, elliptic curve problem. There are also many other algorithms which are based on the hybrid combination of prime factorization problem and discrete logarithm problem. Both are true for different types of digital signatures like single digital signature, group digital signature, collective digital signature etc. In this paper we propose collective signature protocols for signing groups based on difficulty of problem of finding roots modulo large prime number. The proposed collective signatures protocols have significant merits one of which is connected with possibility of their practical using on the base of the existing public key infrastructures.

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.

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