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.

scholarly journals An Efficient Code-Based Threshold Ring Signature Scheme with a Leader-Participant Model

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Guomin Zhou ◽  
Peng Zeng ◽  
Xiaohui Yuan ◽  
Siyuan Chen ◽  
Kim-Kwang Raymond Choo
Keyword(s):  
Quantum Computing ◽  
Digital Signature ◽  
Time Complexity ◽  
Signature Scheme ◽  
Decoding Algorithm ◽  
Signature Schemes ◽  
Ring Signature ◽  
Normal Code ◽  
Efficient Code

Digital signature schemes with additional properties have broad applications, such as in protecting the identity of signers allowing a signer to anonymously sign a message in a group of signers (also known as a ring). While these number-theoretic problems are still secure at the time of this research, the situation could change with advances in quantum computing. There is a pressing need to design PKC schemes that are secure against quantum attacks. In this paper, we propose a novel code-based threshold ring signature scheme with a leader-participant model. A leader is appointed, who chooses some shared parameters for other signers to participate in the signing process. This leader-participant model enhances the performance because every participant including the leader could execute the decoding algorithm (as a part of signing process) upon receiving the shared parameters from the leader. The time complexity of our scheme is close to Courtois et al.’s (2001) scheme. The latter is often used as a basis to construct other types of code-based signature schemes. Moreover, as a threshold ring signature scheme, our scheme is as efficient as the normal code-based ring signature.

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 Proposing a method to design secure digital signature scheme on the ring structure Zn

2022 ◽  
Vol 2 (14) ◽  
pp. 66-74
Author(s):  
Nguyen Dao Truong ◽  
Le Van Tuan
Keyword(s):  
Digital Signature ◽  
Ring Structure ◽  
Signature Scheme ◽  
Signature Schemes ◽  
Signature Generation ◽  
Digital Signature Scheme

Abstract—In this paper, we propose a method to design signature scheme on ring structure with residual classes modulo composite. At the same time, we develop several new digital signature schemes that are more secure, with faster signature generation than ElGamal digital signature scheme and its variants. Furthermore, our proposed signature scheme has overcome some weaknesses of some published signature scheme of the same type, which are built on ring structure. Tóm tắt—Trong bài báo này, chúng tôi đề xuất một phương pháp thiết kế lược đồ chữ ký trên cấu trúc vành các lớp thặng dự theo modulo hợp số, đồng thời phát triển một số lược đồ chữ ký số mới an toàn hơn, tốc độ sinh chữ ký nhanh hơn so với lược đồ chữ ký số ElGamal cùng với những biến thể của nó. Hơn nữa, lược đồ chữ ký do chúng tôi đề xuất cũng khắc phục được một số nhược điểm của một số lược đồ chữ ký cùng loại, được xây dựng trên cấu trúc vành.

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 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 Quantum Attacks on Bitcoin, and How to Protect Against Them

Ledger ◽  
2018 ◽  
Vol 3 ◽  
Author(s):  
Divesh Aggarwal ◽  
Gavin Brennen ◽  
Troy Lee ◽  
Miklos Santha ◽  
Marco Tomamichel
Keyword(s):  
At Risk ◽  
Quantum Computer ◽  
Alternative Proof ◽  
Quantum Computers ◽  
Signature Scheme ◽  
Area At Risk ◽  
Signature Schemes ◽  
Near Term ◽  
Financial Transactions ◽  
Large Quantum

The key cryptographic protocols used to secure the internet and financial transactions of today are all susceptible to attack by the development of a sufficiently large quantum computer. One particular area at risk is cryptocurrencies, a market currently worth over 100 billion USD. We investigate the risk posed to Bitcoin, and other cryptocurrencies, by attacks using quantum computers. We find that the proof-of-work used by Bitcoin is relatively resistant to substantial speedup by quantum computers in the next 10 years, mainly because specialized ASIC miners are extremely fast compared to the estimated clock speed of near-term quantum computers. On the other hand, the elliptic curve signature scheme used by Bitcoin is much more at risk, and could be completely broken by a quantum computer as early as 2027, by the most optimistic estimates. We analyze an alternative proof-of-work called Momentum, based on finding collisions in a hash function, that is even more resistant to speedup by a quantum computer. We also review the available post-quantum signature schemes to see which one would best meet the security and efficiency requirements of blockchain applications.

scholarly journals Scalable Revocable Identity-Based Signature Scheme with Signing Key Exposure Resistance from Lattices

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Congge Xie ◽  
Jian Weng ◽  
Jinming Wen
Keyword(s):  
Quantum Computing ◽  
Random Oracle Model ◽  
Random Oracle ◽  
Signature Scheme ◽  
Integer Solutions ◽  
Identity Based ◽  
Definition Of ◽  
Lattice Based Cryptography ◽  
Key Exposure

In 2014, a new security definition of a revocable identity-based signature (RIBS) with signing key exposure resistance was introduced. Based on this new definition, many scalable RIBS schemes with signing key exposure resistance were proposed. However, the security of these schemes is based on traditional complexity assumption, which is not secure against attacks in the quantum era. Lattice-based cryptography has many attractive features, and it is believed to be secure against quantum computing attacks. We reviewed existing lattice-based RIBS schemes and found that all these schemes are vulnerable to signing key exposure. Hence, in this paper, we propose the first lattice-based RIBS scheme with signing key exposure resistance by using the left-right lattices and delegation technology. In addition, we employ a complete subtree revocation method to ensure our construction meeting scalability. Finally, we prove that our RIBS scheme is selective-ID existentially unforgeable against chosen message attacks (EUF-sID-CMA) under the standard short integer solutions (SIS) assumption in the random oracle model.

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.

ID-Based Deniable Ring Signature with Constant-Size Signature

2011 ◽  
Vol 255-260 ◽  
pp. 2192-2196
Author(s):  
Cheng Yu Hu ◽  
Peng Tao Liu
Keyword(s):  
Bilinear Pairings ◽  
The Other ◽  
Ring Size ◽  
Signature Scheme ◽  
Signature Schemes ◽  
Ring Signature ◽  
Constant Size ◽  
Identity Based ◽  
Verification Process

The ring signature can guarantee the signer’s anonymity. Most proposed ring signature schemes have two problems: One is that the size of ring signature depends linearly on the ring size, and the other is that the signer can shift the blame to victims because of the anonymity. Some authors have studied the constant-size ring signature and deniable ring signature to solve these two problems. This paper shows that an identity-based ring signature scheme with constant size has some security problems by using an insecure accumulator and its verification process does not include the message m. Then we combine the concepts of “constant-size” and “deniable” to form an id-based deniable ring signature with constant-size signature. The new scheme with constant-size signature length is proposed based on an improved accumulator from bilinear pairings and it solves the problem of anonymity abuse.

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.

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