Permutation Polynomials Modulo 2w

Finite Fields and their Applications

Volumn 7, Issue 2, 2001, Pages 287-292

  Rivest, Ronald L ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

latin square; multipermutation; Permutation polynomial

Indexed keywords

EID: 0042334853     PISSN: 10715797     EISSN: None     Source Type: Journal    
DOI: 10.1006/ffta.2000.0282     Document Type: Article

References (17)

1. Euler L. Recherches sur une nouvelle espece des quarrés magiques. Verh. Zeeuwsch Genenot. Wetensch. Vliss. 9:1782;85-239.
2. Hall M. Jr. Combinatorial Theory. 1967;Blaisdell, Boston.
3. Hardy G. H., Wright E. M. An Introduction to the Theory of Numbers. 1975;Clarendon, Oxford.
4. Lidl R., Niederreiter H. Finite Fields. 1983;Addison-Wesley, Reading.
5. Lidl R., Mullen G. L. When does a polynomial over a finite field permute the elements of the field? Amer. Math. Monthly. 95:1988;243-246.
6. Lidl R., Mullen G. L. When does a polynomial over a finite field permute the elements of the field? II. Amer. Math. Monthly. 100:1993;71-74.
7. Lidl R., Müller W. B. Permutation polynomials in RSA-cryptosystems. Chaum D. Proc. CRYPTO 83. 1984;293-301 Plenum, New York.
8. Ma K., von zur Gathen J. The computational complexity of recognizing permutation functions. Proceedings of the 26th ACM Symposium on the Theory of Computing. 1994;ACM, Montreal. p. 392-401.
9. k over a finite field. Proc. Amer. Math. Soc. 120:1994;47-51.
10. Mullen G., Stevens H. Polynomial functions (mod m). Acta Math. Hungar. 44:1984;237-241.
11. p. Fibonacci Quart. 18:1980;104-107.
12. R. L. Rivest, M. J. B. Robshaw, R. Sidney, and, Y. L. Yin, The RC6 block cipher, submitted;, available at, http://theory.lcs.mit.edu/~rivest/rc6.pdf , or, http://csrc.nist.gov/encryption/aes/.
13. Rivest R. L., Shamir A., Adleman L. M. A method for obtaining digital signatures and public-key cryptosystems. Comm. ACM. 21:1978;120-126.
14. Schnorr C. P., Vaudenay S. Black box cryptanalysis of hash networks based on multipermutations. Santis De. Proc. EUROCRYPT'94. 950:1994;47-57 Springer-Verlag, New York.
15. Shannon C. E. Communication theory of secrecy systems. Bell Sys. Tech. J. 28:1949;657-715.
16. Vaudenay S. On the need for multipermutations: cryptanalysis of MD4 and SAFER. Preneel B. Fast Software Encryption. 1008:1994;286-297 Springer-Verlag, Berlin/New York.
17. von zur Gathen J. Tests for permutation polynomials, SIAM J. Comput. 20:1991;591-602.