A Proxy Signature Based on the Difficulty of Solving Equations of Higher on Quaternion Ring

2014 ◽  
Vol 513-517 ◽  
pp. 1951-1954
Author(s):  
Hui Shao ◽  
Fan Zhang ◽  
Xiao Zhuan Yuan ◽  
Chuan Da Qi
Keyword(s):  
Digital Signature ◽  
Discrete Logarithm ◽  
Proxy Signature ◽  
Discrete Logarithm Problem ◽  
Signature Scheme ◽  
Multivariate Functions ◽  
Actual Application ◽  
Solving Equations ◽  
Computational Difficulty ◽  
High Degree

At present, all the applied schemes of the digital signature schemes based on the research of the factoring problem, discrete logarithm problem, and discrete logarithm problem on the elliptic curve cant meet the demand of actual application. This paper introduces the knowledge to the digital signature and studies the signature scheme based on the quaternion ring. The scheme introduces the multivariate functions of high degree to non-commutative quaternion ring, and its safety based on the computational difficulty to solve the the multivariate equations of high degree. The article applies this thought to proxy signature and designs a proxy signature scheme. Finally, it gives the safety analysis of the new scheme.

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 Constructing the 2-Element AGDS Protocol based on the Discrete Logarithm Problem

2021 ◽  
Vol 13 (04) ◽  
pp. 13-22
Author(s):  
Tuan Nguyen Kim ◽  
Duy Ho Ngoc ◽  
Nikolay A. Moldovyan
Keyword(s):  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Group Signature ◽  
Signature Scheme ◽  
Fixed Size ◽  
Electronic Documents ◽  
Computational Difficulty

It is considered a group signature scheme in frame of which different sets of signers sign electronic documents with hidden signatures and the head of the signing group generates a group signature of fixed size. A new mechanism for imbedding the information about signers into a group signature is proposed. The method provides possibilities for reducing the signature size and to construct collective signature protocols for signing groups. New group signature and collective signature protocols based on the computational difficulty of discrete logarithm are proposed.

Proxy-Protected Proxy Multi-Signature Based on Elliptic Curve

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.

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

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