An Existential Unforgeable Signature Scheme Based on Multivariate Quadratic Equations

2017 ◽  
pp. 37-64 ◽  
Author(s):  
Kyung-Ah Shim ◽  
Cheol-Min Park ◽  
Namhun Koo
Keyword(s):  
Signature Scheme ◽  
Quadratic Equations

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.

Extended Algorithm for Solving Underdefined Multivariate Quadratic Equations

2014 ◽  
Vol E97.A (6) ◽  
pp. 1418-1425 ◽  
Author(s):  
Hiroyuki MIURA ◽  
Yasufumi HASHIMOTO ◽  
Tsuyoshi TAKAGI
Keyword(s):  
Quadratic Equations

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.

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