Post-quantum digital signature schemes: setting a hidden group with two-dimensional cyclicity

2020 ◽  
Vol 4 ◽  
pp. 75-82
Author(s):  
D.Yu. Guryanov ◽  
◽  
D.N. Moldovyan ◽  
A. A. Moldovyan ◽  
Keyword(s):  
Associative Algebra ◽  
Digital Signature ◽  
Quantum Signature ◽  
Commutative Group ◽  
Two Dimensional ◽  
Signature Scheme ◽  
Signature Schemes ◽  
Fixed Element ◽  
Commutative Associative Algebra ◽  
Quantum Digital Signature

For the construction of post-quantum digital signature schemes that satisfy the strengthened criterion of resistance to quantum attacks, an algebraic carrier is proposed that allows one to define a hidden commutative group with two-dimensional cyclicity. Formulas are obtained that describe the set of elements that are permutable with a given fixed element. A post-quantum signature scheme based on the considered finite non-commutative associative algebra is described.

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 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.

A Blind Proxy Re-Signatures Scheme Based on Random Oracle

2011 ◽  
Vol 204-210 ◽  
pp. 1062-1065 ◽  
Author(s):  
Yu Qiao Deng
Keyword(s):  
Digital Signature ◽  
Digital Signatures ◽  
Random Oracle ◽  
Proxy Signature ◽  
Public Key ◽  
Signature Scheme ◽  
Signature Schemes

Digital signature schemes allow a signer to transform any message into a signed message, such that anyone can verify the validity of the signed message using the signer’s public key, but only the signer can generate signed messages. A proxy re-signature, which is a type of digital signatures, has significant applications in many areas. Proxy signature scheme was first introduced by Blaze, Bleumer, and Strauss, but that scheme is inefficient and with limited features. After that, some Proxy re-signature schemes were proposed by researchers. This paper constructs a blind proxy re-signatures scheme. Comparing to the previous proxy re-signature schemes, the scheme adds a message blinded feature, and then the security of the scheme is proven.

scholarly journals A Fully Adaptively Secure Threshold Signature Scheme Based on Dual-Form Signatures Technology

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yuanju Gan
Keyword(s):  
Digital Signature ◽  
Vector Spaces ◽  
Signature Scheme ◽  
Threshold Signature ◽  
Signature Schemes ◽  
Dual Form ◽  
The Standard Model ◽  
Chosen Message Attack ◽  
Security Notion ◽  
Attack Models

In t , n threshold signature schemes, any subset of t participants out of n can produce a valid signature, but any fewer than t participants cannot. Meanwhile, a threshold signature scheme should remain robust and unforgeable against up to t − 1 corrupted participants. This nonforgeability property is that even an adversary breaking into up to t − 1 participants should be unable to generate signatures on its own. Existential unforgeability against adaptive chosen message attacks is widely considered as a standard security notion for digital signature, and threshold signature should also follow this accordingly. However, there are two special attack models in a threshold signature scheme: one is the static corruption attack and the other is the adaptive corruption attack. Since the adaptive corruption model appears to better capture real threats, designing and proving threshold signature schemes secure in the adaptive corruption model has been focused on in recent years. If a threshold signature is secure under adaptive chosen message attack and adaptive corruption attack, we say it is fully adaptively secure. In this paper, based on the dual pairing vector spaces technology, we construct a threshold signature scheme and use Gerbush et al.’s dual-form signatures technology to prove our scheme, which is fully adaptively secure in the standard model, and then compare it to other schemes in terms of the efficiency and computation.

scholarly journals Enhanced quantum signature scheme using quantum amplitude amplification operators

PLoS ONE ◽  
2021 ◽  
Vol 16 (10) ◽  
pp. e0258091
Author(s):  
Basma Elias ◽  
Ahmed Younes
Keyword(s):  
Quantum Computing ◽  
Quantum Signature ◽  
Quantum States ◽  
Bell States ◽  
Signature Scheme ◽  
Signature Schemes ◽  
Diffusion Operator ◽  
Quantum Amplitude ◽  
Preparation Phase ◽  
Amplitude Amplification

Quantum signature is the use of the principles of quantum computing to establish a trusted communication between two parties. In this paper, a quantum signature scheme using amplitude amplification techniques will be proposed. To secure the signature, the proposed scheme uses a partial diffusion operator and a diffusion operator to hide/unhide certain quantum states during communication. The proposed scheme consists of three phases, preparation phase, signature phase and verification phase. To confuse the eavesdropper, the quantum states representing the signature might be hidden, not hidden or encoded in Bell states. It will be shown that the proposed scheme is more secure against eavesdropping when compared with relevant quantum signature schemes.

scholarly journals Time of signing in the Estonian digital signature scheme

2019 ◽  
pp. 40-50
Author(s):  
Tõnu Mets ◽  
Arnis Parsovs
Keyword(s):  
European Union ◽  
Digital Signature ◽  
Digital Signatures ◽  
Signature Scheme ◽  
Signature Schemes ◽  
Electronic Documents ◽  
Legal Requirement ◽  
The Public ◽  
Digital Signature Scheme ◽  
Legal Consequences

There is a widespread misconception among some lawyers, technologists and the public that the Estonian digital signature scheme provides reliable proof of the time when a document was digitally signed. In this article Tõnu Mets and Arnis Parsovs show that the legal requirement to establish the time of signing is not met in practice. The related legal requirement that the validation of the digital signature should confirm that the certificate was valid at the time of signing is also not met. The authors analyse the legal consequences of this, and discuss possible solutions for the issues that arise. They note that digital signature schemes used in other countries implementing Regulation (EU) No 910/2014 of the European Parliament and the Council of 23 July 2014 (eIDAS) are likely to share the problems discussed in this article. Index words: Estonia, European Union, Digital signatures, Electronic documents

Hardware Architectures for Post-Quantum Digital Signature Schemes

2021 ◽  
Author(s):  
Deepraj Soni ◽  
Kanad Basu ◽  
Mohammed Nabeel ◽  
Najwa Aaraj ◽  
Marc Manzano ◽  
...  
Keyword(s):  
Digital Signature ◽  
Signature Schemes ◽  
Hardware Architectures ◽  
Quantum Digital Signature

scholarly journals Digital Signatures in a Quantum World: Evaluating The Trade-off Between Performance and Security for GeMSS

2019 ◽  
Author(s):  
Paulo Ricardo Reis ◽  
Fábio Borges
Keyword(s):  
Quantum Computing ◽  
Digital Signature ◽  
Quantum Computer ◽  
Signature Scheme ◽  
Signature Schemes ◽  
Trade Off ◽  
Signature Generation ◽  
Security Parameter ◽  
Verification Process ◽  
Definition Of

With the advent of quantum computing, it urges the definition of a cryptographic standard algorithm that can resist attacks from a quantum computer. Inside this context is GeMSS, a multivariate quadratic signature scheme based on the HFEvconstruct. Schemes of this type have shown great potential throughout the last two decades. This paper traces a comparison of performance and security between GeMSS and other relevant digital signature schemes, showing that despite of its slow signature generation and large key pair, it has a very quick verification process and tiny signatures. It also proposes a method for deriving the size of keys from the security parameter evaluated.

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