References
[1] FAUGERE J C. A new efficient algorithm for computing Grobner bases (F4). Journal of Pure and Applied Algebra, 1999, 139(1/2/3): 61 -88.
[2] FAUGERE J C. A new efficient algorithm for computing Grobner bases without reduction to zero (F5). Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation (ISSAC'02), 2002, Jul 7 -10, 2002, Lille, France. New York, NY, USA: ACM, 2002: 75 -83.
[3] GAO X S, HUANG Z Y. Characteristic set algorithms for equation solving in finite fields. Journal of Symbolic Computation, 2012, 47(6): 655 -679.
[4] GAO X S, VAN DER HOEVEN J, YUAN C M, et al. Characteristic set method for differential-difference polynomial
systems. Journal of Symbolic Computation, 2009, 44(9): 1137 -1163.
[5] BARD G V. Algorithms for solving linear and polynomial systems of equations over finite fields, with applications to cryptanalysis. Ph D Thesis. College Park, MD, USA: University of Maryland, 2007.
[6] BARD G V, COURTOIS N T, JEFFERSON C. Efficient methods for conversion and solution of sparse systems of low-degree multivariate polynomials over GF(2) via SAT-solvers. International Association for Cryptologic Research (IACR)
Cryptology ePrint Archive, Paper 2007/024, 2007.
[7] HARROW A W, HASSIDIM A, LLOYD S. Quantum algorithm for linear systems of equations. Physical Review Letters, 2009, 103(15): Article 150502.
[8] AMBAINIS A. Variable time amplitude amplification and a faster quantum algorithm for solving systems of linear equations. Proceedings of the 29th International Symposium on Theoretical Aspects of Computer Science (STACS'12), 2012, Feb 29 - Mar 3, Paris, France. Schloss Dagstuhl, Germany: Leibniz-Center for Informatics, 2012: 636 -647.
[9] CHILDS A M, KOTHARI R, SOMMA R D. Quantum algorithm for systems of linear equations with exponentially improved dependence on precision. SIAM Journal on Computing, 2017, 46(6): 1920 -1950.
[10] CHEN Y A, GAO X S. Quantum algorithm for Boolean equation solving and quantum algebraic attack on cryptosystems. Journal of Systems Science and Complexity, 2022, 35(1): 373 -412.
[11] DING J T, GHEORGHIU V, GILYEN A, et al. Limitations of the Macaulay matrix approach for using the HHL algorithm to solve multivariate polynomial systems. ArXiv Preprint, arXiv: 2111. 00405, 2021.
[12] HASTAD J. Satisfying degree-d equations over GF[2]n. Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques: Proceedings of the 14th International Workshop on Approximation Algorithms for Combinatorial Optimization (APPROX'11) and 15th International Workshop on Randomization and Approximation Techniques in Computer Science (RANDOM'11), 2011, Aug 17 - 19, Princeton, NJ, USA. LNTCS 6845. Berlin, Germany: Springer, 2011: 242 -253.
[13] ZHAO S W, GAO X S. Minimal achievable approximation ratio for MAX-MQ in finite fields. Theoretical Computer Science, 2009, 410(21/22/23): 2285 -2290.
[14] ALBRECHT M, CID C. Cold boot key recovery by solving polynomial systems with noise. Applied Cryptography and
Network Security: Proceedings of the 9th International Conference on Applied Cryptography and Network Security (ACNS'11), 2011, Jun 7 -10, Nerja (Malaga), Spain. LNSC 6715. Berlin, Germany: Springer, 2011: 57 -72.
[15] HUANG Z Y, LIN D D. A new method for solving polynomial systems with noise over F2 and its applications in cold boot key recovery. Selected Areas in Cryptography: Proceedings of the 19th Selected Areas in Cryptography (SAC'12), 2012, Aug 15 - 16, Windsor, Canada. LNSC 7707. Berlin, Germany: Springer, 2013: 16 -33.
[16] CHEN Y A, GAO X S, YUAN C M. Quantum algorithms for optimization and polynomial systems solving over finite fields. ArXiv Preprint, arXiv: 1802. 03856, 2018.
[17] BLUM A, KALAI A, WASSERMAN H. Noise-tolerant learning, the parity problem, and the statistical query model. Journal of the ACM, 2003, 50(4): 506 -519.
[18] LEVIEIL E, FOUQUE P A. An improved LPN algorithm. Security and Cryptography for Networks: Proceedings of the 5th International Conference on Security and Cryptography for Networks (SCN'06), 2006, Sept 6 - 8, Maiori, Italy. LNSC
4116. Berlin, Germany: Springer, 2006: 348 -359.
[19] GUO Q, JOHANSSON T, LONDAHL C. Solving LPN using covering codes. Advances in Cryptology: Proceedings of the 20th International Conference on the Theory and Application of Cryptology and Information Security (ASIACRYPT'14): Part I, 2014, Dec 7 - 11, Kaoshiung, China. LNSC 8873. Berlin, Germany: Springer, 2014: 1 -20.
[20] BOGOS S, VAUDENAY S. Optimization of LPN solving algorithms. Advances in Cryptology: Proceedings of the 22nd
International Conference on the Theory and Application of Cryptology and Information Security (ASIACRYPT'16): Part I,
2016, Dec 4 - 8, Hanoi, Vietnam. LNCS 10031. Berlin, Germany: Springer, 2016: 703 -728.
[21] ZHANG B, GONG X X. New algorithms for solving LPN. International Association for Cryptologic Research (IACR)
Cryptology ePrint Archive, Paper 2007/780, 2017.
[22] MICCIANCIO D. Improving lattice based cryptosystems using the Hermite normal form. Cryptography and Lattices: Proceedings of the 2001 International Cryptography and Lattices Conference (CaLC'01), 2001, Mar 29 -30, Providence, RI, USA. LNCS 2146. Berlin, Germany: Springer, 2001: 126 -145.
[23] BERRY D W, AHOKAS G, CLEVE R, et al. Efficient quantum algorithms for simulating sparse Hamiltonians. Communications in Mathematical Physics, 2007, 270(2): 359 -371.
|
