An algorithm for simultaneous nonsymmetric algebraic Riccati equations over finite fields
Tài liệu tham khảo
Garey, 1979
Fraenkel, 1979, Complexity of problems in games, graphs and algebraic equations, Discrete Appl Math, 1, 15, 10.1016/0166-218X(79)90012-X
Wolf C, Preneel B. Taxonomy of public-key schemes based on the problem of multivariate quadratic equations. Cryptology eprint archive, report 2005/077, 2005.
Wang, 2006, A medium-field multivariate public key encryption scheme, vol. 3860, 132
Billet, 2009, Overview of cryptanalysis techniques in multivariate public key cryptography, 263
Ding, 2009, Multivariate public key cryptography, 193
Tao, 2013, Simple matrix scheme for encryption, vol. 7932, 231
Ding, 2017, Current state of multivariate cryptography, IEEE Secur Privacy, 15, 28, 10.1109/MSP.2017.3151328
2015
2016
Chen, 2009, SSE Implementation of multivariate PKCs on modern x86 CPUs, 33
Czypek, 2012, Efficient implementation of MQPKS on constrained devices, 374
Beullens, 2017, Field lifting for smaller UOV public keys, 227
Petzoldt, 2013
Doyle, 1988, State-space solutions to standard H2 and H∞ control problems, 1691
Sampei, 1990, An algebraic approach to H∞ output feedback control problems, Systems Control Lett, 14, 13, 10.1016/0167-6911(90)90075-6
Scherer, 1990
Rosenthal, 1997, Some interesting problems in systems theory which are of fundamental importance in coding theory, 4574
Rosenthal, 1996, On behaviors and convolutional codes, IEEE Trans Inform Theory, 42, 1881, 10.1109/18.556682
Chen, 2020
Peretz, 2016, On multivariable encryption schemes based on simultaneous algebraic riccati equations over finite fields, Finite Fields Appl, 39, 1, 10.1016/j.ffa.2016.01.002
Shih, 2018, Cryptanalysis of riccati equation encryption schemes TP-I and TP-II, Finite Fields Appl, 54, 30, 10.1016/j.ffa.2018.07.004
Faugère, 1999, A new efficient algorithm for computing Gröbner bases, J Pure Appl Algebra, 139, 61, 10.1016/S0022-4049(99)00005-5
Faugère, 2002, A new efficient algorithm for computingGröbner bases without reduction to zero, 75
Courtois N, Klimov A, Patarin J, Shamir A. Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations. In: Proc. of EUROCRYPT 2000, Vol. LNCS 1807. 2000, p. 392–407.
Bouillaguet C, Chen HC, Cheng CM, Chou T, Niederhagen R, Shamir A, et al. Fast exhaustive search for polynomial systems in F2. In: Cryptographic hardware and embedded systems, CHES 2010, 12’th international workshop. Santa Barbara, USA; 2010, p. 203–18.
Bardet, 2013, On the complexity of solving quadratic Boolean systems, Elsevier J Complexity, 29, 53, 10.1016/j.jco.2012.07.001
Joux, 2017, A crossbred algorithm for solving boolean polynomial systems, 3
von zur Gathen, 2001, Factoring polynomials over finite fields: A survey, J Symbolic Comput, 31, 3, 10.1006/jsco.1999.1002
