摘要: We give an exact characterization of permutation polynomials modulo n=2w, w?2: a polynomial P(x)=a0+a1x +···+adxd with integral coefficients is n if and only a1 odd, (a2+a4+a6+···) even, (a3+a5+a7+···) even. also characterize defining latin squares but prove that multipermutations (that is, pair orthogonal squares) n=2wdo not exist.
core.ac.uk
elsevier.com
sci-hub.se 参考文章(16)
Serge Vaudenay, On the need for multipermutations: Cryptanalysis of MD4 and SAFER fast software encryption. ,vol. 1008, pp. 286- 297 ,(1994) , 10.1007/3-540-60590-8_22
C. P. Schnorr, S. Vaudenay, Black box cryptanalysis of hash networks based on multipermutations theory and application of cryptographic techniques. ,vol. 950, pp. 47- 57 ,(1994) , 10.1007/BFB0053423
Rudolf Lidl, Winfried B. Müller, Permutation Polynomials in RSA-Cryptosystems Advances in Cryptology. pp. 293- 301 ,(1984) , 10.1007/978-1-4684-4730-9_23
Rex Matthews, Permutation properties of the polynomials 1++\cdots+^{} over a finite field Proceedings of the American Mathematical Society. ,vol. 120, pp. 47- 51 ,(1994) , 10.1090/S0002-9939-1994-1165062-2
R. L. Rivest, A. Shamir, L. Adleman, A method for obtaining digital signatures and public-key cryptosystems Communications of the ACM. ,vol. 26, pp. 96- 99 ,(1983) , 10.1145/357980.358017
G. Mullen, H. Stevens, Polynomial functions (modm) Acta Mathematica Hungarica. ,vol. 44, pp. 237- 241 ,(1984) , 10.1007/BF01950276
Keju Ma, Joachim von zur Gathen, The computational complexity of recognizing permutation functions Proceedings of the twenty-sixth annual ACM symposium on Theory of computing - STOC '94. pp. 392- 401 ,(1994) , 10.1145/195058.195204
Joachim van zur Gathen, Tests for permutation polynomials SIAM Journal on Computing. ,vol. 20, pp. 591- 602 ,(1991) , 10.1137/0220037
Rudolf Lidl, Gary L. Mullen, When does a polynomial over a finite field permute the elements of the fields American Mathematical Monthly. ,vol. 95, pp. 243- 246 ,(1988) , 10.2307/2323626
G. H. Hardy, An Introduction to the Theory of Numbers ,(1938)