scholarly journals Efficient Implementations of Rainbow and UOV using AVX2

2021 ◽  
pp. 245-269
Author(s):  
Kyung-Ah Shim ◽  
Sangyub Lee ◽  
Namhun Koo
Keyword(s):  
Linear Systems ◽  
Digital Signature ◽  
Gaussian Elimination ◽  
Schur Complement ◽  
Matrix Inversion ◽  
Instruction Set ◽  
Signature Scheme ◽  
Secret Key ◽  
Quadratic Equations ◽  
Post Quantum Cryptography

A signature scheme based on multivariate quadratic equations, Rainbow, was selected as one of digital signature finalists for NIST Post-Quantum Cryptography Standardization Round 3. In this paper, we provide efficient implementations of Rainbow and UOV using the AVX2 instruction set. These efficient implementations include several optimizations for signing to accelerate solving linear systems and the Vinegar value substitution. We propose a new block matrix inversion (BMI) method using the Lower-Diagonal-Upper decomposition of blocks matrices based on the Schur complement that accelerates solving linear systems. Compared to UOV implemented with Gaussian elimination, our implementations with the BMI result in speedups of 12.36%, 24.3%, and 34% for signing at security categories I, III, and V, respectively. Compared to Rainbow implemented with Gaussian elimination, our implementations with the BMI result in speedups of 16.13% and 20.73% at the security categories III and V, respectively. We show that precomputation for the Vinegar value substitution and solving linear systems dramatically improve their signing. UOV with precomputation is 16.9 times, 35.5 times, and 62.8 times faster than UOV without precomputation at the three security categories, respectively. Rainbow with precomputation is 2.1 times, 2.2 times, and 2.8 times faster than Rainbow without precomputation at the three security categories, respectively. We then investigate resilience against leakage or reuse of the precomputed values in UOV and Rainbow to use the precomputation securely: leakage or reuse of the precomputed values leads to their full secret key recoveries in polynomial-time.

scholarly journals Analysis of security of post-quantum algorithm of Rainbow electronic signature against potential attacks

Radiotekhnika ◽  
2021 ◽  
pp. 85-93
Author(s):  
G.А. Maleeva
Keyword(s):  
Quantum Algorithm ◽  
Public Key Cryptography ◽  
Transformation Method ◽  
Accurate Estimate ◽  
Signature Scheme ◽  
Secret Key ◽  
Mathematical Basis ◽  
Electronic Signature ◽  
Post Quantum Cryptography ◽  
Band Separation

Multidimensional public key cryptography is a candidate for post-quantum cryptography, and it makes it possible  to generate particularly short signatures and quick verification. The Rainbow signature scheme proposed by J. Dean and D. Schmidt is such a multidimensional cryptosystem and it is considered to be protected against all known attacks. The need for research on Rainbow ES is justified by the fact that there is a need to develop and adopt a post-quantum national securities standard, and that in the process of the US NIST competition on the mathematical basis of cryptographic transformation method Rainbow, promising results. Therefore, it is considered important to take them into account and use them in Ukraine. The Rainbow signature scheme can be implemented simply and efficiently using linear algebra methods over a small finite field and, in particular, creates shorter signatures than those used in RSA and other post-quantum signatures [1]. In the 2nd round of NIST PQC, protected sets of Rainbow parameters are offered and several attacks on them are analyzed [1]. When comparing ES, preference is given to ES algorithms that have been selected according to unconditional criteria, as well as those that have better indicators for integral conditional criteria, because such a technique is more rational. In particular, the Rainbow-Band-Separation (RBS) attack [2] is the best known Rainbow attack with a certain set of parameters and is important. The Rainbow-Band-Separation attack restores the Rainbow secret key by solving certain systems of quadratic equations, and its complexity is measured by a well-known measure called the degree of regularity. However, as a rule, the degree of regularity is greater than the degree of solution in experiments, and it is impossible to obtain an accurate estimate. The paper proposes a new indicator of the complexity of the Rainbow-Band-Separation attack using  F4 algorithm, which gives a more accurate estimate compared to the indicator that uses the degree of regularity. The aim of the work is a comparative analysis of ES based on MQ-transformations on the criterion of stability-complexity and an attempt to understand the security of Rainbow against RBS attack using F4.

scholarly journals A Digital Signature Scheme Based onMST3Cryptosystems

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Haibo Hong ◽  
Jing Li ◽  
Licheng Wang ◽  
Yixian Yang ◽  
Xinxin Niu
Keyword(s):  
Digital Signature ◽  
Encryption Scheme ◽  
Signature Scheme ◽  
Secret Key ◽  
Signature Schemes ◽  
Logarithmic Signatures ◽  
Public Key Cryptosystems ◽  
Cryptographic Keys ◽  
Main Components ◽  
Digital Signature Scheme

As special types of factorization of finite groups, logarithmic signature and cover have been used as the main components of cryptographic keys for secret key cryptosystems such asPGMand public key cryptosystems likeMST1,MST2, andMST3. Recently, Svaba et. al proposed a revisedMST3encryption scheme with greater security. Meanwhile, they put forward an idea of constructing signature schemes on the basis of logarithmic signatures and random covers. In this paper, we firstly design a secure digital signature scheme based on logarithmic signatures and random covers. In order to complete the task, we devise a new encryption scheme based onMST3cryptosystems.

scholarly journals A New Approach to Keep the Privacy Information of the Signer in a Digital Signature Scheme

Information ◽  
2020 ◽  
Vol 11 (5) ◽  
pp. 260
Author(s):  
Dung Hoang Duong ◽  
Willy Susilo ◽  
Viet Cuong Trinh
Keyword(s):  
Digital Signature ◽  
Group Signature ◽  
Encryption Scheme ◽  
Signature Scheme ◽  
Secret Key ◽  
New Approach ◽  
Designated Verifier ◽  
Designated Verifier Signature ◽  
Digital Signature Scheme ◽  
Responsible Person

In modern applications, such as Electronic Voting, e-Health, e-Cash, there is a need that the validity of a signature should be verified by only one responsible person. This is opposite to the traditional digital signature scheme where anybody can verify a signature. There have been several solutions for this problem, the first one is we combine a signature scheme with an encryption scheme; the second one is to use the group signature; and the last one is to use the strong designated verifier signature scheme with the undeniable property. In this paper, we extend the traditional digital signature scheme to propose a new solution for the aforementioned problem. Our extension is in the sense that only a designated verifier (responsible person) can verify a signer’s signature, and if necessary (in case the signer refuses to admit his/her signature) the designated verifier without revealing his/her secret key is able to prove to anybody that the signer has actually generated the signature. The comparison between our proposed solution and the three existing solutions shows that our proposed solution is the best one in terms of both security and efficiency.

scholarly journals Compact Dilithium Implementations on Cortex-M3 and Cortex-M4

2020 ◽  
pp. 1-24
Author(s):  
Denisa O. C. Greconici ◽  
Matthias J. Kannwischer ◽  
Daan Sprenkels
Keyword(s):  
Quantum Cryptography ◽  
Digital Signature ◽  
Flash Memory ◽  
Constant Time ◽  
Key Generation ◽  
Signature Scheme ◽  
Memory Footprint ◽  
Speed Up ◽  
Post Quantum Cryptography ◽  
Digital Signature Scheme

We present implementations of the lattice-based digital signature scheme Dilithium for ARM Cortex-M3 and ARM Cortex-M4. Dilithium is one of the three signature finalists of the NIST post-quantum cryptography competition. As our Cortex-M4 target, we use the popular STM32F407-DISCOVERY development board. Compared to the previous speed records on the Cortex-M4 by Ravi, Gupta, Chattopadhyay, and Bhasin we speed up the key operations NTT and NTT−1 by 20% which together with other optimizations results in speedups of 7%, 15%, and 9% for Dilithium3 key generation, signing, and verification respectively. We also present the first constant-time Dilithium implementation on the Cortex-M3 and use the Arduino Due for benchmarks. For Dilithium3, we achieve on average 2 562 kilocycles for key generation, 10 667 kilocycles for signing, and 2 321 kilocycles for verification.Additionally, we present stack consumption optimizations applying to both our Cortex- M3 and Cortex-M4 implementation. Due to the iterative nature of the Dilithium signing algorithm, there is no optimal way to achieve the best speed and lowest stack consumption at the same time. We present three different strategies for the signing procedure which allow trading more stack and flash memory for faster speed or viceversa. Our implementation of Dilithium3 with the smallest memory footprint uses less than 12kB. As an additional output of this work, we present the first Cortex-M3 implementations of the key-encapsulation schemes NewHope and Kyber.

A Black-Box Construction of Strongly Unforgeable Signature Scheme in the Leakage Setting

2017 ◽  
Vol 28 (06) ◽  
pp. 761-780 ◽  
Author(s):  
Jianye Huang ◽  
Qiong Huang ◽  
Chunhua Pan
Keyword(s):  
Digital Signature ◽  
Building Blocks ◽  
Black Box ◽  
Signature Scheme ◽  
Secret Key ◽  
Cryptographic Primitives ◽  
Leakage Model ◽  
Leakage Resilient ◽  
Input Model ◽  
Auxiliary Input

Traditional cryptography considers the security of cryptosystems when the attackers have no access to the secret key. However, due to the imperfect implementation of cryptosystems, the attackers are able to obtain partial secret state of the systems via side-channel attacks, which are not considered in the traditional security notions of cryptographic primitives, including digital signature, and thus break their security. Leakage-resilient cryptography was then proposed to solve the problem. Recently, Wang et al. showed that any signature scheme can be transformed to a strongly unforgeable one in the leakage setting. However, their transformation requires to change the key pair of the scheme. In this paper, we present a key-modification-free solution in both the bounded leakage model and the auxiliary input model. Specifically, we propose a black-box construction of strongly unforgeable signature scheme in the leakage setting, and show that if the underlying building blocks are leakage-resilient, so is the resulting scheme.

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 Quantum Dual Signature with Coherent States Based on Chained Phase-Controlled Operations

2020 ◽  
Vol 10 (4) ◽  
pp. 1353 ◽  
Author(s):  
Jinjing Shi ◽  
Shuhui Chen ◽  
Jiali Liu ◽  
Fangfang Li ◽  
Yanyan Feng ◽  
...  
Keyword(s):  
Coherent States ◽  
Security Analysis ◽  
Encryption Algorithm ◽  
High Fidelity ◽  
Signature Scheme ◽  
Secret Key ◽  
Simulation Experiments ◽  
Quantum Devices ◽  
Shared Secret ◽  
Cnot Operation

A novel encryption algorithm called the chained phase-controlled operation (CPCO) is presented in this paper, inspired by CNOT operation, which indicates a stronger correlation among message states and each message state depending on not only its corresponding key but also other message states and their associated keys. Thus, it can prevent forgery effectively. According to the encryption algorithm CPCO and the classical dual signature protocols, a quantum dual signature scheme based on coherent states is proposed in this paper. It involves three participants, the customer Alice, the merchant Bob and the bank Trent. Alice expects to send her order message and payment message to Bob and Trent, respectively. It is required that the two messages must be linked to guarantee the payment is paid for the corresponding order. Thus, Alice can generate a quantum dual signature to achieve the goal. In detail, Alice firstly signs her two messages with the shared secret key. Then She connects the two signatures into a quantum dual signature. Finally, Bob and Trent severally verify the signatures of the order message and the payment message. Security analysis shows that our scheme can ensure its security against forgery, repudiation and denial. In addition, simulation experiments based on the Strawberry Fields platform are performed to valid the feasibility of CPCO. Experimental results demonstrate that CPCO is viable and the expected coherent states can be acquired with high fidelity, which indicates that the encryption algorithm of the scheme can be implemented on quantum devices effectively.

Sign in / Sign up

Export Citation Format

Share Document