scholarly journals A novel method for developing post-quantum cryptoschemes and a practical signature algorithm

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nikolay Andreevich Moldovyan ◽  
Dmitriy Nikolaevich Moldovyan
Keyword(s):  
Digital Signature ◽  
Practical Purpose ◽  
Multiplicative Group ◽  
Quantum Signature ◽  
Public Key ◽  
Signature Scheme ◽  
Associative Algebras ◽  
Content Type ◽  
The Public ◽  
Public Keys

PurposeThe practical purpose of this research is to propose a candidate for post-quantum signature standard that is free of significant drawback of the finalists of the NIST world competition, which consists in the large size of the signature and the public key. The practical purpose is to propose a fundamentally new method for development of algebraic digital signature algorithms.Design/methodology/approachThe proposed method is distinguished by the use of two different finite commutative associative algebras as a single algebraic support of the digital signature scheme and setting two different verification equation for a single signature. A single public key is computed as the first and the second public keys, elements of which are computed exponentiating two different generators of cyclic groups in each of the algebras.FindingsAdditionally, a scalar multiplication by a private integer is performed as final step of calculation of every element of the public key. The same powers and the same scalar values are used to compute the first and the second public keys by the same mathematic formulas. Due to such design, the said generators are kept in secret, providing resistance to quantum attacks. Two new finite commutative associative algebras, multiplicative group of which possesses four-dimensional cyclicity, have been proposed as a suitable algebraic support.Originality/valueThe introduced method is novel and includes new techniques for designing algebraic signature schemes that resist quantum attacks. On its base, a new practical post-quantum signature scheme with relatively small size of signature and public key is developed.

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 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 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.

A Mobile Coalition Key-Evolving Digital Signature Scheme for Wireless/Mobile Networks

2011 ◽  
pp. 285-311
Author(s):  
Quanxing Zhang ◽  
Chwan-Hwa Wu ◽  
J. David Irwin
Keyword(s):  
Mobile Networks ◽  
Digital Signature ◽  
Mobile Ip ◽  
Public Key ◽  
Signature Scheme ◽  
The Public ◽  
New States ◽  
Dynamic Path ◽  
The Individual ◽  
Digital Signature Scheme

A scheme is proposed in this chapter to apply a secure digital signature scheme in a mobile-IP environment and treats the three entities in a dynamic path as either foreign agents (FA), home agents (HA) or mobile agents (MA), such that a coalition is formed containing each of the individual agents. Each agent has a pair of keys: one private and one public. The private key is evolving with time, and the public key is signed by a certification authority (CA). All the private keys of the three agents in the coalition are needed to sign a signature. Furthermore, all the messages are signed and verified. The signature is verified against a public key, computed as the product of the public keys of all three agents, and readily generated when a new dynamic path is formed. In addition, the key-evolving scheme prevents an adversary from forging past signatures under any circumstances. As a result of the schemes’ proactive refresh capability, an adversary must simultaneously compromise each MA, FA and HA in order to forge future signatures. When a new dynamic path is formed or private keys evolve to new states, an interactive, proactive synchronization scheme is employed among the agents. Thus, the loss of a mobile device, or its information, will cause minimal information damage.

Certificates and Public Key Infrastructure

2008 ◽  
pp. 217-245
Author(s):  
Manuel Mogollon
Keyword(s):  
Access Control ◽  
Digital Signature ◽  
Public Key Infrastructure ◽  
Public Key ◽  
Comprehensive System ◽  
Public Key Encryption ◽  
Control Data ◽  
The Public ◽  
Digital Certificates ◽  
Public Keys

In public-key encryption, the secrecy of the public key is not required, but the authenticity of the public key is necessary to guarantee its integrity and to avoid spoofing and playback attacks. A user’s public key can be authenticated (signed) by a certificate authority that verifies that a public key belongs to a specific user. In this chapter, digital certificates, which are used to validate public keys, and certificate authorities are discussed. When public-key is used, it is necessary to have a comprehensive system that provides public key encryption and digital signature services to ensure confidentiality, access control, data integrity, authentication, and non-repudiation. That system, public-key infrastructure or PKI, is also discussed in this chapter.

scholarly journals DiLizium: A Two-Party Lattice-Based Signature Scheme

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 989
Author(s):  
Jelizaveta Vakarjuk ◽  
Nikita Snetkov ◽  
Jan Willemson
Keyword(s):  
Quantum Signature ◽  
Public Key ◽  
Full Detail ◽  
Design Rationale ◽  
Signature Scheme ◽  
Future Studies ◽  
The Public ◽  
Security Proof ◽  
Learning With Errors ◽  
Performance Estimates

In this paper, we propose DiLizium: a new lattice-based two-party signature scheme. Our scheme is constructed from a variant of the Crystals-Dilithium post-quantum signature scheme. This allows for more efficient two-party implementation compared with the original but still derives its post-quantum security directly from the Module Learning With Errors and Module Short Integer Solution problems. We discuss our design rationale, describe the protocol in full detail, and provide performance estimates and a comparison with previous schemes. We also provide a security proof for the two-party signature computation protocol against a classical adversary. Extending this proof to a quantum adversary is subject to future studies. However, our scheme is secure against a quantum attacker who has access to just the public key and not the two-party signature creation protocol.

scholarly journals Candidate for practical post-quantum signature scheme

2020 ◽  
Vol 16 (4) ◽  
pp. 455-461
Author(s):  
Nikolay A. Moldovyan ◽  
◽  
Alexandr A. Moldovyan ◽  
Keyword(s):  
Discrete Logarithm ◽  
Quantum Signature ◽  
Public Key ◽  
Signature Verification ◽  
Signature Scheme ◽  
The Public ◽  
Cyclic Groups ◽  
Commutative Associative Algebra ◽  
Computational Intractability ◽  
New Criterion

A new criterion of post-quantum security is used to design a practical signature scheme based on the computational complexity of the hidden discrete logarithm problem. A 4-dimensional finite non-commutative associative algebra is applied as algebraic support of the cryptoscheme. The criterion is formulated as computational intractability of the task of constructing a periodic function containing a period depending on the discrete logarithm value. To meet the criterion, the hidden commutative group possessing the 2-dimensional cyclicity is exploited in the developed signature scheme. The public-key elements are computed depending on two vectors that are generators of two different cyclic groups contained in the hidden group. When computing the public key two types of masking operations are used: i) possessing the property of mutual commutativity with the exponentiation operation and ii) being free of such property. The signature represents two integers and one vector S used as a multiplier in the verification equation. To prevent attacks using the value S as a fitting element the signature verification equation is doubled.

scholarly journals Anonymous Payment in a Kiosk Centric Model Using Digital Signature Scheme with Message Recovery and Low Computational Power Devices

2006 ◽  
Vol 1 (2) ◽  
pp. 1-11
Author(s):  
Jesús Isaac ◽  
José Camara ◽  
Antonio Manzanares ◽  
Joaquín Márquez
Keyword(s):  
Public Space ◽  
Digital Signature ◽  
Signature Scheme ◽  
Computational Power ◽  
Power Devices ◽  
Signature Schemes ◽  
The Public ◽  
Message Recovery ◽  
Public Keys ◽  
Digital Signature Scheme

In this paper we present an anonymous protocol for a mobile payment system based on a Kiosk Centric Case Mobile Scenario where the customer cannot communicate with the issuer due to absence of Internet access with her mobile device and the costs of implementing other mechanism of communication between both of them are high. Our protocol protects the real identity of the clients during the purchase and employs a digital signature scheme with message recovery using self-certified public keys that reduces the public space and the communication cost in comparison with the certificate-based signature schemes. Moreover, our proposed protocol requires low computational power that makes it suitable for mobile devices. As a result, our proposal illustrates how a portable device equipped with a short range link (such Bluetooth, Infrared or Wi-Fi) and low computational power should be enough to interact with a vendor machine in order to buy goods or services in a secure way.

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 Digital Signature Scheme with Hidden Group Possessing Two-Dimensional Cyclicity

2021 ◽  
Vol 7 (2) ◽  
pp. 85-93
Author(s):  
D. Moldovyan ◽  
R. Fahrutdinov ◽  
A. Mirin ◽  
A. Kostina
Keyword(s):  
Digital Signature ◽  
Discrete Logarithm ◽  
Public Key ◽  
Two Dimensional ◽  
Signature Scheme ◽  
The Public ◽  
Multiplication Operation ◽  
Signature Generation ◽  
Cryptographic Primitive ◽  
Digital Signature Scheme

A method is proposed for constructing digital signature schemes based on the hidden discrete logarithm problem, which meet ageneral criterion of post-quantum resistance. The method provides a relatively small size of the public key and signature. Based on the method, a practical digital signature scheme has been developed, in which the exponentiation operation in a hidden group with two-dimensional cyclicity is the basic cryptographic primitive. The algebraic support of a cryptoscheme is a four-dimensional finite non-commutative algebra with associative multiplication operation. By specifying algebra using abasis vector multiplication table with half of empty cells, the performance of signature generation and authentication procedures is improved. A public key is a triple of four-dimensional vectors calculated as images of elements of a hidden group which are mapped using two types of masking operations: 1) mutually commutative with the exponentiation operation and 2) not having this property.

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