Cryptography

Computational Methods

  1. Gwénolé Ars, Jean-Charles Faugère, Hideki Imai, Mitsuru Kawazoe, and Makoto Sugita, Comparison between XL and Gröbner basis algorithms, Advances in Cryptology—Asiacrypt 2004, Lecture Notes in Comput. Sci., vol. 3329, Springer, Berlin, 2004, pp. 338–353.[MR]
  2. Roberto Maria Avanzi, Another look at square roots (and other less common operations) in fields of even characteristic, Selected Areas in Cryptography, Lecture Notes in Computer Science, vol. 4876/2007, Springer Berlin / Heidelberg, 2007, pp. 138–154.[eprint]
  3. M. Barbosa, R. Noad, D. Page, and N. P. Smart, First steps toward a cryptography-aware language and compiler, IACR, 45 pages.[eprint]
  4. Gregory V. Bard, Nicolas T. Courtois, and Chris Jefferson, Efficient methods for conversion and solution of sparse systems of low-degree multivariate polynomials over GF(2) via SAT-solvers, IACR (2007), 14 pages.[eprint]
  5. Aurélie Bauer and Antoine Joux, Toward a rigorous variation of Coppersmith's algorithm on three variables, Advances in cryptology—EUROCRYPT 2007, Lecture Notes in Comput. Sci., vol. 4515, Springer, Berlin, 2007, pp. 361–378.[MR]
  6. Stanislav Bulygin and Michael Brickenstein, Obtaining and solving systems of equations in key variables only for the small variants of AES, IACR (2008), 26 pages.[eprint]
  7. Wouter Castryck, Hendrik Hubrechts, and Frederik Vercauteren, Computing zeta functions in families of Ca, b curves using deformation, Algorithmic Number Theory, Lecture Notes in Computer Science, vol. 5011, Springer, 2008, pp. 296-311.
  8. Chia-Hsin Owen Chen, Ming-Shing Chen, Jintai Ding, Fabian Werner, and Bo-Yin Yang, Odd-char multivariate hidden field equations, IACR eprint2008:543 (2008), 18 pages.
  9. Jiun-Ming Chen and Bo-Yin Yang, All in the XL family: theory and practice, Information Security and Cryptology. ICISC 2004: 7th International Conference, Seoul, Korea, December 2–3, 2004, Lecture Notes in Comput. Sci., vol. 3506, Springer, Berlin, 2005, pp. 296.
  10. Jean-Charles Faugére and Ludovic Perret, Algebraic cryptanalysis of Curry and Flurry using correlated messages, IACR (2008), 14 pages.[eprint]
  11. Antoine Joux, David Naccache, and Emmanuel Thomé, When e-th roots become easier than factoring, Advances in Cryptology - ASIACRYPT 2007, Lecture Notes in Computer Science, vol. 4833/2007, Springer Berlin / Heidelberg, 2007, pp. 13–28.
  12. David R. Kohel, The AGM-X0(N) Heegner point lifting algorithm and elliptic curve point counting, Advances in Cryptology—Asiacrypt 2003, Lecture Notes in Comput. Sci., vol. 2894, Springer, Berlin, 2003, pp. 124–136.[MR]
  13. Czesław Kościelny, Computing in the composite GF(qm) of characteristic 2 formed by means of an irreducible binomial, Appl. Math. Comput. Sci. 8 (1998), no. 3, 671–680.[MR]
  14. Kazuto Matsuo, Jinhui Chao, and Shigeo Tsujii, An improved baby step giant step algorithm for point counting of hyperelliptic curves over finite fields, Algorithmic Number Theory (Sydney, 2002), Lecture Notes in Comput. Sci., vol. 2369, Springer, Berlin, 2002, pp. 461–474.[MR]
  15. Mohamed Saied Emam Mohamed, Wael Said Abd Elmageed Mohamed, Jintai Ding, and Johannes Buchmann, MXL2: solving polynomial equations over GF(2) using an improved mutant strategy, Post-Quantum Cryptography, Lecture Notes in Comput. Sci., vol. 5299, Springer, Berlin, 2008, pp. 203–215.
  16. Naoki Ogura and Shigenori Uchiyama, Cryptanalysis of the birational permutation signature scheme over a non-commutative ring, IACR (2009), 13 pages.[eprint]
  17. Mikael Olofsson, Vlsi Aspects on Inversion in Finite Fields, PhD Thesis, Linköpings Universitet, Linköping, Sweden, 2002.
  18. Håvard Raddum and Igor Semaev, Solving multiple right hand sides linear equations, Des. Codes Cryptogr. 49 (2008), no. 1-3, 147–160.[MR/eprint]
  19. A. J. M. Segers, Algebraic Attacks from a Gröbner Basis Perspective, PhD Thesis, Technische Universiteit Eindhoven, 2004.
  20. Igor Semaev, Sparse boolean equations and circuit lattices, IACR (2009), 15 pages.[eprint]
  21. B. Smith, Isogenies and the discrete logarithm problem in Jacobians of genus 3 hyperelliptic curves, J. Cryptology 22 (2009), no. 4, 505–529.
  22. Makoto Sugita, Mitsuru Kawazoe, and Hideki Imai, Relation between the XL algorithm and Groebner basis algorithms, IEICE Trans. Fundamentals E89-A (2006), no. 1, 11–18.
  23. Kenneth Koon-Ho Wong, Gregory V. Bard, and Robert H. Lewis, Partitioning multivariate polynomial equations via vertex separators for algebraic cryptanalysis and mathematical applications, IACR (2009), 33 pages.[eprint]