MutantXL: Solving Multivariate Polynomial Equations for Cryptanalysis

Dagstuhl Seminar Proceedings

Volumn 9031, Issue , 2009, Pages

  Buchmann, Johannes ^a   Ding, Jintai ^b   Mohamed, Mohamed Saied Emam ^a   Mohamed, Wael Said Abd Elmageed ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

^b UNIVERSITY OF CINCINNATI   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM FOR SOLVING; MULTIVARIATE POLYNOMIAL; MULTIVARIATE SYSTEMS; POLYNOMIALS EQUATION; SYSTEM OF POLYNOMIAL EQUATIONS;

EID: 85175267765     PISSN: 18624405     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (13)

1. Matsumoto, T., Imai, H.: Public Quadratic Polynomial-Tuples for Efficient Signature-Verification and Message-Encryption. In: Workshop on the Theory and Application of of Cryptographic Techniques Advances in Cryptology- EUROCRYPT. Volume 330 of Lecture Notes in Computer Science., Davos, Switzerland, Springer (1988) 419-453
2. Patarin, J.: Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): two new families of Asymmetric Algorithms. In: Proceeding of International Conference on the Theory and Application of Cryptographic Techniques Advances in Cryptology- Eurocrypt. Volume 1070 of Lecture Notes in Computer Science., Saragossa, Spain, Springer (1996) 33-48
3. + and HM: Variations Around Two Schemes of T. Matsumoto and H. Imai. In: Proceeding of International Conference on the Theory and Application of Cryptology and Information Security Advances in Cryptology ASIACRYPT. Volume 1514 of Lecture Notes in Computer Science., Beijing, China, Springer (1998) 35-50
4. Moh, T.: A Public Key System With Signature And Master Key Functions. In: Communications in Algebra. (1999) 2207-2222
5. Courtois, N., Klimov, A., Patarin, J., Shamir, A.: Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations. In: Proceedings of International Conference on the Theory and Application of Cryptographic Techniques(EUROCRYPT). Volume 1807 of Lecture Notes in Computer Science., Bruges, Belgium, Springer (2000) 392-407
6. Ding, J., Buchmann, J., Mohamed, M.S.E., Moahmed, W.S.A., Weinmann, R.P.: MutantXL. In: Proceedings of the 1st international conference on Symbolic Computation and Cryptography (SCC08), Beijing, China, LMIB (2008) 16-22
7. Ding, J.: Mutants and its impact on polynomial solving strategies and algorithms. (Privately distributed research note, University of Cincinnati and Technical University of Darmstadt, 2006)
8. Mohamed, M.S.E., Mohamed, W.S.A.E., Ding, J., Buchmann, J.: MXL2: Solving Polynomial Equations over GF(2) using an Improved Mutant Strategy. In: Proceedings of The Second international Workshop on Post-Quantum Cryptography, (PQCrypto08). Lecture Notes in Computer Science, Cincinnati, USA, Springer-Verlag, Berlin (2008) 203-215
9. Faugère, J.C.: A new efficient algorithm for computing Gröbner bases (F4). Pure and Applied Algebra 139 (1999) 61-88
10. Mohamed, M.S.E., Ding, J., Buchmann, J.: Algebraic Cryptanalysis of MQQ Public Key Cryptosystem by MutantXL. Technical Report 2008/451, Cryptology ePrint Archive (2008)
11. Courtois, N.T.: Experimental Algebraic Cryptanalysis of Block Ciphers. http://www.cryptosystem.net/aes/toyciphers.html (2007)
12. Albrecht, M., Bard, G.: M4RI - Linear Algebra over GF(2). http://m4ri.sagemath.org/index.html (2008)
13. chung Wang, L., hwang Chang, F.: Tractable rational map cryptosystem (2005)