Solving systems of differential equations of addition

Lecture Notes in Computer Science

Volumn 3574, Issue , 2005, Pages 75-88

  Paul, Souradyuti ^a   Preneel, Bart ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; CRYPTOGRAPHY; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; PROBLEM SOLVING;

COMPLEXITY CLASSES; DIFFERENTIAL EQUATIONS OF ADDITION (DEA); SYMMETRIC CRYPTOGRAPHY;

DIFFERENTIAL EQUATIONS;

EID: 26444511997     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/11506157_7     Document Type: Conference Paper

References (24)

1. A. Aho, J. Hopcroft, J. Ullman, "The Design and Analysis of Computer Algorithms," Addison-Wesley, 1974.
2. I. A. Ajwa, Z. Liu, P. S. Wang, "Gröbner Bases Algorithm," ICM Technical Report, February 1995, Available Online at http://icm.mcs.kent. edu/reports/1995/gb.pdf.
3. 32 with Applications to MD5," Eurocrypt 1992 (R. A. Rueppel, ed.), vol. 658 of LNCS, pp. 71-80, Springer-Verlag, 1993.
4. C. Burwick, D. Coppersmith, E. D'Avignon, Y. Gennaro, S. Halevi, C. Jutla, S. M. Matyas Jr., L. O'Connor, M. Peyravian, D. Safford and N. Zunic, "MARS - A Candidate Cipher for AES," Available Online at http://www.research.ibm.com/security/mars.html, June 1998.
5. E. Biham, A. Shamir, "Differential Cryptanalysis of DES-like Cryptosystems," Crypto'90 (A. Menezes, S. A. Vanstone, eds.), vol. 537 of LNCS, pp. 2-21, Springer-Verlag, 1991.
6. T. H. Cormen, C. E. Leiserson, R. L. Rivest, "Introduction to Algorithms, " MIT Press.
7. 4)," Journal of Pure and Applied Algebra, vol. 139, pp. 61-88, 1999, Available Online at http://www.elsevier.com/locate/ jpaa.
8. R. Floyd, R. Beigel, "The Language of Machines," W. H. Freeman, 1994.
9. N. Ferguson, D. Whiting, B. Schneier, J. Kelsey, S. Lucks, T. Kohno, "Helix: Fast Encryption and Authentication in a Single Cryptographic Primitive," Fast Software Encryption 2003 (T. Johansson, ed.), vol. 2887 of LNCS, pp. 330-346, Springer-Verlag, 2003.
10. J. E. Hopcroft, R. Motwani, J. D. Ullman, "Introduction to Automata Theory, Languages and Computation," Second Edition, Pearson Education, 2004.
11. A. Klimov, A. Shamir, "Cryptographic Applications of T-Functions," Selected Areas in Cryptography 2003 (M. Matsui, R. J. Zuccherato, eds.), vol. 3006 of LNCS, pp. 248-261, Springer-Verlag, 2004.
12. A. Klimov, A. Shamir, "New Cryptographic Primitives Based on Multiword T-Functions," Fast Software Encryption 2004 (B. Roy, W. Meier, eds.), vol. 3017 of LNCS, pp. 1-15, Springer-Verlag, 2004.
13. A. Kipnis, A. Shamir, "Cryptanalysis of the HFE Public Key Cryptosystems by Relinearization," Crypto 1999 (M. Wiener, ed.), vol. 1666 of LNCS, pp. 19-30, Springer-Verlag, 1999.
14. X. Lai, J. L. Massey, S. Murphy, "Markov Ciphers and Differential Cryptanalysis," Eurocrypt'91 (W. Davis, ed.), vol. 547 of LNCS, pp. 17-38, Springer-Verlag, 1991.
15. H. Lipmaa, S. Moriai, "Efficient Algorithms for Computing Differential Properties of Addition," FSE 2001 (M. Matsui, ed.), vol. 2355 of LNCS, pp. 336-350, Springer-Verlag, 2002.
16. L. Lipmaa, J. Wallen, P. Dumas, "On the Additive Differential Probability of Exclusive-Or," Fast Software Encryption 2004 (B. Roy, W. Meier, eds.), vol. 3017 of LNCS, pp. 317-331, Springer-Verlag, 2004.
17. F. Muller, "Differential Attacks against the Helix Stream Cipher," Fast Software Encryption 2004 (B. Roy, W. Meier, eds.), vol. 3017 of LNCS, pp. 94-108, Springer-Verlag, 2004.
18. K. Nyberg, L. Knudsen, "Provable Security Against a Differential Attack," Journal of Cryptology, 8(1):27-37, 1991.
19. S. Paul, B. Preneel, "Solving Systems of Differential Equations of Addition," Cryptology ePrint Archive, Report 2004/294, Available Online at http://eprint.iacr.org/2004/294, 2004.
20. R. L. Rivest, M. Robshaw, R. Sidney, Y. L. Yin, "The RC6 Block Cipher," Available Online at http://theory.lcs.mit.edu/rivest/rc6.ps, June 1998.
21. B. Schneier, J. Kelsey, D. Whiting, D. Wagner, C.Hall, N. Ferguson, "The Twofish Encryption Algorithm: A 128-Bit Block Cipher," John Wiley & Sons, April 1999, ISBN: 0471353817.
22. O. Staffelbach, W. Meier, "Cryptographic Significance of the Carry for Ciphers Based on Integer Addition," Crypto'90 (A. Menezes, S. A. Vanstone, eds.), vol. 537 of LNCS, pp. 601-614, Springer-Verlag, 1991.
23. H. Yoshida, A. Biryukov, Christophe De Cannière, J. Lano, B. Preneel, "Non-randomness of the Full 4 and 5-Pass HAVAL," SCN 2004 (Carlo Blundo and Stelvio Cimato, eds.), vol. 3352 of LNCS, pp. 324-336, Springer-Verlag, 2004.
24. n," Fast Software Encryption 2003 (T. Johansson, ed.), vol. 2887 of LNCS, pp. 261-273, Springer-Verlag, 2003.