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Volumn 4547 LNCS, Issue , 2007, Pages 177-188

The simplest method for constructing APN polynomials EA-inequivalent to power functions

Author keywords

Affine equivalence; Almost bent; Almost perfect nonlinear; CCZ equivalence; Differential uniformity; Nonlinearity; S box; Vectorial boolean function

Indexed keywords

CONFORMAL MAPPING; DIFFERENTIAL EQUATIONS; DISTRIBUTION FUNCTIONS; NONLINEAR EQUATIONS;

EID: 38149017156     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-73074-3_14     Document Type: Conference Paper
Times cited : (16)

References (32)
  • 1
    • 85028761102 scopus 로고
    • On almost perfect nonlinear permutations
    • Helleseth, T, ed, EUROCRYPT 1993, Springer, Heidelberg
    • Beth, T., Ding, C.: On almost perfect nonlinear permutations. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 65-76. Springer, Heidelberg (1993)
    • (1993) LNCS , vol.765 , pp. 65-76
    • Beth, T.1    Ding, C.2
  • 2
    • 0026397734 scopus 로고
    • Differential Cryptanalysis of DES-like Cryptosystems
    • Biham, E., Shamir, A.: Differential Cryptanalysis of DES-like Cryptosystems. Journal of Cryptology 4(1), 3-72 (1991)
    • (1991) Journal of Cryptology , vol.4 , Issue.1 , pp. 3-72
    • Biham, E.1    Shamir, A.2
  • 3
    • 38149013370 scopus 로고    scopus 로고
    • Budaghyan, L., Carlet, C.: Classes of Quadratic APN Trinomials and Hexanomials and Related Structures. Preprint, available at http://eprint.iacr. org/2007/098
    • Budaghyan, L., Carlet, C.: Classes of Quadratic APN Trinomials and Hexanomials and Related Structures. Preprint, available at http://eprint.iacr. org/2007/098
  • 5
    • 85088720143 scopus 로고    scopus 로고
    • 2n: the case n divisible by 4. In: Proceedings of the Workshop on Coding and Cryptography (2007) (To appear) available at http://eprint.iacr.org/2006/428.pdf
    • 2n: the case n divisible by 4. In: Proceedings of the Workshop on Coding and Cryptography (2007) (To appear) available at http://eprint.iacr.org/2006/428.pdf
  • 6
    • 51349134665 scopus 로고    scopus 로고
    • A class of quadratic APN binomials inequivalent to power functions
    • Submitted to, available at
    • Budaghyan, L., Carlet, C., Leander, G.: A class of quadratic APN binomials inequivalent to power functions. Submitted to IEEE Trans. Inform. Theory, available at http://eprint.iacr.org/2006/445.pdf
    • IEEE Trans. Inform. Theory
    • Budaghyan, L.1    Carlet, C.2    Leander, G.3
  • 8
    • 33748567562 scopus 로고    scopus 로고
    • New Classes of Almost Bent and Almost Perfect Nonlinear Functions
    • Budaghyan, L., Carlet, C., Pott, A.: New Classes of Almost Bent and Almost Perfect Nonlinear Functions. IEEE Trans. Inform. Theory 52(3), 1141-1152 (2006)
    • (2006) IEEE Trans. Inform. Theory , vol.52 , Issue.3 , pp. 1141-1152
    • Budaghyan, L.1    Carlet, C.2    Pott, A.3
  • 9
    • 31744435261 scopus 로고    scopus 로고
    • New Constructions of Almost Bent and Almost Perfect Nonlinear Functions
    • Charpin, P, Ytrehus, Ø, eds
    • Budaghyan, L., Carlet, C., Pott, A.: New Constructions of Almost Bent and Almost Perfect Nonlinear Functions. In: Charpin, P., Ytrehus, Ø., (eds.) Proceedings of the Workshop on Coding and Cryptography 2005, pp. 306-315 (2005)
    • (2005) Proceedings of the Workshop on Coding and Cryptography , pp. 306-315
    • Budaghyan, L.1    Carlet, C.2    Pott, A.3
  • 10
    • 84957612451 scopus 로고    scopus 로고
    • Canteaut, A., Charpin, P., Dobbertin, H.: A new characterization of almost bent functions. In: Knudsen, L.R. (ed.) FSE 1999. LNCS, 1636, pp. 186-200. Springer, Heidelberg (1999)
    • Canteaut, A., Charpin, P., Dobbertin, H.: A new characterization of almost bent functions. In: Knudsen, L.R. (ed.) FSE 1999. LNCS, vol. 1636, pp. 186-200. Springer, Heidelberg (1999)
  • 11
    • 0033882818 scopus 로고    scopus 로고
    • Binary m-sequences with three-valued crosscorrelation: A proof of Welch's conjecture
    • Canteaut, A., Charpin, P., Dobbertin, H.: Binary m-sequences with three-valued crosscorrelation: A proof of Welch's conjecture. IEEE Trans. Inform. Theory 46(1), 4-8 (2000)
    • (2000) IEEE Trans. Inform. Theory , vol.46 , Issue.1 , pp. 4-8
    • Canteaut, A.1    Charpin, P.2    Dobbertin, H.3
  • 14
    • 0000805465 scopus 로고    scopus 로고
    • Codes, bent functions and permutations suitable for DES-like cryptosystems
    • Carlet, C., Charpin, P., Zinoviev, V.: Codes, bent functions and permutations suitable for DES-like cryptosystems. Designs, Codes and Cryptography 15(2), 125-156 (1998)
    • (1998) Designs, Codes and Cryptography , vol.15 , Issue.2 , pp. 125-156
    • Carlet, C.1    Charpin, P.2    Zinoviev, V.3
  • 15
    • 84948990962 scopus 로고
    • Links between differential and linear cryptanalysis
    • De Santis, A, ed, EUROCRYPT 1994, Springer, Heidelberg
    • Chabaud, F., Vaudenay, S.: Links between differential and linear cryptanalysis. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 356-365. Springer, Heidelberg (1995)
    • (1995) LNCS , vol.950 , pp. 356-365
    • Chabaud, F.1    Vaudenay, S.2
  • 17
    • 69249147785 scopus 로고    scopus 로고
    • APN Polynomials and Related Codes
    • Banff International Research Station November
    • Dillon, J.F.: APN Polynomials and Related Codes. Polynomials over Finite Fields and Applications, Banff International Research Station (November 2006)
    • (2006) Polynomials over Finite Fields and Applications
    • Dillon, J.F.1
  • 21
    • 0037734831 scopus 로고    scopus 로고
    • n): A new case for n divisible by 5
    • Jungnickel, D, Niederreiter, H, eds, Germany, pp, Springer, Heidelberg
    • n): a new case for n divisible by 5. In: Jungnickel, D., Niederreiter, H. (eds.) Proceedings of Finite Fields and Applications FQ5, Augsburg, Germany, pp. 113-121. Springer, Heidelberg (2000)
    • (2000) Proceedings of Finite Fields and Applications FQ5, Augsburg , pp. 113-121
    • Dobbertin, H.1
  • 22
    • 31744449110 scopus 로고    scopus 로고
    • A new APN function which is not equivalent to a power mapping
    • Edel, Y., Kyureghyan, G., Pott, A.: A new APN function which is not equivalent to a power mapping. IEEE Trans. Inform. Theory 52(2), 744-747 (2006)
    • (2006) IEEE Trans. Inform. Theory , vol.52 , Issue.2 , pp. 744-747
    • Edel, Y.1    Kyureghyan, G.2    Pott, A.3
  • 23
    • 84937741493 scopus 로고
    • Maximal recursive sequences with 3-valued recursive crosscorrelation functions
    • Gold, R.: Maximal recursive sequences with 3-valued recursive crosscorrelation functions. IEEE Trans. Inform. Theory 14, 154-156 (1968)
    • (1968) IEEE Trans. Inform. Theory , vol.14 , pp. 154-156
    • Gold, R.1
  • 24
    • 0038410824 scopus 로고    scopus 로고
    • A proof of the Welch and Niho conjectures on crosscor-relations of binary m-sequences
    • Hollmann, H., Xiang, Q.: A proof of the Welch and Niho conjectures on crosscor-relations of binary m-sequences. Finite Fields and Their Applications 7, 253-286 (2001)
    • (2001) Finite Fields and Their Applications , vol.7 , pp. 253-286
    • Hollmann, H.1    Xiang, Q.2
  • 25
    • 85026907169 scopus 로고
    • 3 in char. 2 and some applications to cyclic codes
    • Moreno, O, Cohen, G, Mora, T, eds, AAECC-10, Springer, Heidelberg
    • 3 in char. 2 and some applications to cyclic codes. In: Moreno, O., Cohen, G., Mora, T. (eds.) AAECC-10. LNCS, vol. 673, pp. 180-194. Springer, Heidelberg (1993)
    • (1993) LNCS , vol.673 , pp. 180-194
    • Janwa, H.1    Wilson, R.2
  • 26
    • 0001059304 scopus 로고
    • The weight enumerators for several classes of subcodes of the second order binary Reed-Muller codes
    • Kasami, T.: The weight enumerators for several classes of subcodes of the second order binary Reed-Muller codes. Inform, and Control 18, 369-394 (1971)
    • (1971) Inform, and Control , vol.18 , pp. 369-394
    • Kasami, T.1
  • 27
    • 0025432647 scopus 로고
    • The Weights of the Orthogonals of the Extended Quadratic Binary Goppa Codes
    • Lachaud, G., Wolfmann, J.: The Weights of the Orthogonals of the Extended Quadratic Binary Goppa Codes. IEEE Trans. Inform. Theory 36, 686-692 (1990)
    • (1990) IEEE Trans. Inform. Theory , vol.36 , pp. 686-692
    • Lachaud, G.1    Wolfmann, J.2
  • 28
    • 85025704284 scopus 로고
    • Linear cryptanalysis method for DES cipher
    • Helleseth, T, ed, EUROCRYPT 1993, Springer, Heidelberg
    • Matsui, M.: Linear cryptanalysis method for DES cipher. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 386-397. Springer, Heidelberg (1994)
    • (1994) LNCS , vol.765 , pp. 386-397
    • Matsui, M.1
  • 29
    • 38149133803 scopus 로고    scopus 로고
    • A construction of differentially 4-uniform functions from commutative semifields of characteristic 2
    • Proceedings of WAIFI
    • Nakagawa, N., Yoshiara, S.: A construction of differentially 4-uniform functions from commutative semifields of characteristic 2. In: Proceedings of WAIFI 2007, LNCS (2007)
    • (2007) LNCS
    • Nakagawa, N.1    Yoshiara, S.2
  • 30
    • 84962968104 scopus 로고
    • Differentially uniform mappings for cryptography
    • Helleseth, T, ed, EUROCRYPT 1993, Springer, Heidelberg
    • Nyberg, K.: Differentially uniform mappings for cryptography. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 55-64. Springer, Heidelberg (1994)
    • (1994) LNCS , vol.765 , pp. 55-64
    • Nyberg, K.1
  • 31
    • 84948979030 scopus 로고
    • S-boxes and Round Functions with Controllable Linearity and Differential Uniformity
    • Preneel, B, ed, Fast Software Encryption, Springer, Heidelberg
    • Nyberg, K.: S-boxes and Round Functions with Controllable Linearity and Differential Uniformity. In: Preneel, B. (ed.) Fast Software Encryption. LNCS, vol. 1008, pp. 111-130. Springer, Heidelberg (1995)
    • (1995) LNCS , vol.1008 , pp. 111-130
    • Nyberg, K.1
  • 32
    • 0000977083 scopus 로고
    • On mutual correlation of sequences
    • Sidelnikov, V.: On mutual correlation of sequences. Soviet Math. Dokl. 12, 197-201 (1971)
    • (1971) Soviet Math. Dokl , vol.12 , pp. 197-201
    • Sidelnikov, V.1


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