Improved Interpolation Attacks on Cryptographic Primitives of Low Algebraic Degree

2020 ◽  
pp. 171-193 ◽  
Author(s):  
Chaoyun Li ◽  
Bart Preneel
Keyword(s):  
Algebraic Degree ◽  
Cryptographic Primitives

Improved Secure Transaction Scheme With Certificateless Cryptographic Primitives for IoT-Based Mobile Payments

2021 ◽  
pp. 1-9
Author(s):  
Zirui Qiao ◽  
Qiliang Yang ◽  
Yanwei Zhou ◽  
Mingwu Zhang
Keyword(s):  
Cryptographic Primitives ◽  
Mobile Payments

scholarly journals The Algebraic Degree of Phase-Type Distributions

2010 ◽  
Vol 47 (03) ◽  
pp. 611-629
Author(s):  
Mark Fackrell ◽  
Qi-Ming He ◽  
Peter Taylor ◽  
Hanqin Zhang
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Polynomial Algorithm ◽  
Algebraic Degree ◽  
Nonnegative Matrices ◽  
Stieltjes Transform ◽  
Special Cases ◽  
Phase Type ◽  
Phase Type Distributions ◽  
The Matrix

This paper is concerned with properties of the algebraic degree of the Laplace-Stieltjes transform of phase-type (PH) distributions. The main problem of interest is: given a PH generator, how do we find the maximum and the minimum algebraic degrees of all irreducible PH representations with that PH generator? Based on the matrix exponential (ME) order of ME distributions and the spectral polynomial algorithm, a method for computing the algebraic degree of a PH distribution is developed. The maximum algebraic degree is identified explicitly. Using Perron-Frobenius theory of nonnegative matrices, a lower bound and an upper bound on the minimum algebraic degree are found, subject to some conditions. Explicit results are obtained for special cases.

scholarly journals Conjugacy Systems Based on Nonabelian Factorization Problems and Their Applications in Cryptography

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Lize Gu ◽  
Shihui Zheng
Keyword(s):  
Performance Analysis ◽  
Quantum Algorithm ◽  
Integer Factorization ◽  
Algebraic Structures ◽  
Cryptographic Primitives ◽  
Factorization Problem ◽  
Integer Factorization Problem ◽  
Modern Cryptography ◽  
Nonabelian Groups

To resist known quantum algorithm attacks, several nonabelian algebraic structures mounted upon the stage of modern cryptography. Recently, Baba et al. proposed an important analogy from the integer factorization problem to the factorization problem over nonabelian groups. In this paper, we propose several conjugated problems related to the factorization problem over nonabelian groups and then present three constructions of cryptographic primitives based on these newly introduced conjugacy systems: encryption, signature, and signcryption. Sample implementations of our proposal as well as the related performance analysis are also presented.

scholarly journals Cryptographic primitives in blockchains

2019 ◽  
Vol 127 ◽  
pp. 43-58 ◽  
Author(s):  
Licheng Wang ◽  
Xiaoying Shen ◽  
Jing Li ◽  
Jun Shao ◽  
Yixian Yang
Keyword(s):  
Cryptographic Primitives
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