메뉴 건너뛰기




Volumn 52, Issue 9, 2006, Pages 4160-4170

On almost perfect nonlinear functions over F2n

Author keywords

Almost bent function; Almost perfect nonlinear (APN) function; Permutation polynomial; Power function

Indexed keywords

FINITE ELEMENT METHOD; FUNCTION EVALUATION; POLYNOMIALS; PRINCIPAL COMPONENT ANALYSIS; PROBABILITY;

EID: 33748579937     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2006.880036     Document Type: Article
Times cited : (114)

References (32)
  • 1
    • 0038072416 scopus 로고    scopus 로고
    • "Crooked functions, bent functions, and distance regular graphs"
    • T. Bending and D. F. Der Flass, "Crooked functions, bent functions, and distance regular graphs," Electron. J. Combin., vol. 5, no. 1, 1998, R34.
    • (1998) Electron. J. Combin. , vol.5 , Issue.1
    • Bending, T.1    Der Flass, D.F.2
  • 3
    • 38349034218 scopus 로고    scopus 로고
    • Almost perfect nonlinear functions
    • Res Rep. INRIA, RR-5774, [Online]. Available:
    • T. P. Berger, A. Canteaut, P. Charpin, and Y. Laigle-Chapuy, Almost perfect nonlinear functions Res. Rep. INRIA, RR-5774, 2005 [Online]. Available: Http://www.inria.fr/rrrt/
    • (2005)
    • Berger, T.P.1    Canteaut, A.2    Charpin, P.3    Laigle-Chapuy, Y.4
  • 4
    • 0026397734 scopus 로고
    • "Differential cryptanalysis of des-like cryptosystems"
    • E. Biham and A. Shamir, "Differential cryptanalysis of des-like cryptosystems," J. Cryptol., vol. 4, no. 1, pp. 3-72, 1991.
    • (1991) J. Cryptol. , vol.4 , Issue.1 , pp. 3-72
    • Biham, E.1    Shamir, A.2
  • 5
    • 33748527307 scopus 로고    scopus 로고
    • An Infinite Class of Quadratic APN Functions Which are not Equivalent to Power Mappings Cryptology ePrint Archive Rep
    • 2005/359, [Online]. Available:
    • L. Budaghyan, C. Carlet, P. Felke, and G. Leander, An Infinite Class of Quadratic APN Functions Which are not Equivalent to Power Mappings Cryptology ePrint Archive Rep. 2005/359, 2005 [Online]. Available: Http:/ /eprint.iacr.org/
    • (2005)
    • Budaghyan, L.1    Carlet, C.2    Felke, P.3    Leander, G.4
  • 6
    • 31744435261 scopus 로고    scopus 로고
    • "New constructions of almost bent and almost perfect nonlinear polynomials"
    • Bergen, Norway, Mar
    • L. Budaghyan, C. Carlet, and A. Pott, "New constructions of almost bent and almost perfect nonlinear polynomials," in Proc. Workshop on Coding and Cryptography - WCC 2005, Bergen, Norway, Mar. 2005, pp. 306-315.
    • (2005) Proc. Workshop on Coding and Cryptography - WCC 2005 , pp. 306-315
    • Budaghyan, L.1    Carlet, C.2    Pott, A.3
  • 7
    • 33748567562 scopus 로고    scopus 로고
    • "New classes of almost bent and almost perfect nonlinear polynomials"
    • Mar
    • L. Budaghyan, C. Carlet, and A. Pott, "New classes of almost bent and almost perfect nonlinear polynomials," IEEE Trans. Inf. Theory, vol. 52, no. 3, pp. 1141-1152, Mar. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.3 , pp. 1141-1152
    • Budaghyan, L.1    Carlet, C.2    Pott, A.3
  • 9
    • 0035334149 scopus 로고    scopus 로고
    • "On cryptographic properties of the cosets of R(1,m)"
    • May
    • A. Canteaut, C. Carlet, P. Charpin, and C. Fontaine,, "On cryptographic properties of the cosets of R(1,m)," IEEE Trans. Inf. Theory, vol. 47, no. 4, pp. 1494-1513, May 2001.
    • (2001) IEEE Trans. Inf. Theory , vol.47 , Issue.4 , pp. 1494-1513
    • Canteaut, A.1    Carlet, C.2    Charpin, P.3    Fontaine, C.4
  • 10
    • 0033882818 scopus 로고    scopus 로고
    • "Binary m-sequences with three-valued crosscorrelation: A proof of welch conjecture"
    • Jan
    • A. Canteaut, P. Charpin, and H. Dobbertin, "Binary m-sequences with three-valued crosscorrelation: A proof of welch conjecture," IEEE Trans. Inf. Theory, vol. 46, no. 1, pp. 4-8, Jan. 2000.
    • (2000) IEEE Trans. Inf. Theory , vol.46 , Issue.1 , pp. 4-8
    • Canteaut, A.1    Charpin, P.2    Dobbertin, H.3
  • 11
    • 0000827003 scopus 로고    scopus 로고
    • "Weight divisibility of cyclic codes, highly nonlinear functions on GF(2 m) and crosscorrelation of maximum-length sequences"
    • A. Canteaut, P. Charpin, and H. Dobbertin, "Weight divisibility of cyclic codes, highly nonlinear functions on GF(2 m) and crosscorrelation of maximum-length sequences," SIAM J. Discr. Math., vol. 13, no. 1, pp. 105-138, 2000.
    • (2000) SIAM J. Discr. Math. , vol.13 , Issue.1 , pp. 105-138
    • Canteaut, A.1    Charpin, P.2    Dobbertin, H.3
  • 12
    • 0002251636 scopus 로고
    • "Partially-bent functions"
    • C. Carlet, "Partially-bent functions," Des., Codes, Cryptogr., no. 3, pp. 135-145, 1993
    • (1993) Des., Codes, Cryptogr. , Issue.3 , pp. 135-145
    • Carlet, C.1
  • 13
    • 0000805465 scopus 로고    scopus 로고
    • "Codes, bent functions and permutations suitable for DES-like cryptosystems"
    • C. Carlet, P. Charpin, and V. Zinoviev, "Codes, bent functions and permutations suitable for DES-like cryptosystems," Des., Codes, Cryptogr., vol. 15, no. 2, pp. 125-156, 1998.
    • (1998) Des., Codes, Cryptogr. , vol.15 , Issue.2 , pp. 125-156
    • Carlet, C.1    Charpin, P.2    Zinoviev, V.3
  • 14
    • 0003089993 scopus 로고
    • "Explicit evaluation of certain exponential sums"
    • L. Carlitz, "Explicit evaluation of certain exponential sums," Math. Scand., vol. 44, pp. 5-16, 1979.
    • (1979) Math. Scand. , vol.44 , pp. 5-16
    • Carlitz, L.1
  • 17
    • 0000380667 scopus 로고    scopus 로고
    • "On binary cyclic codes with minimum distance d = 3"
    • P. Charpin, A. Tietäväinen, and V. Zinoviev, "On binary cyclic codes with minimum distance d = 3," Probl. Inf. Transm., vol. 33, no. 4, pp. 287-296, 1997.
    • (1997) Probl. Inf. Transm. , vol.33 , Issue.4 , pp. 287-296
    • Charpin, P.1    Tietäväinen, A.2    Zinoviev, V.3
  • 18
    • 0037734831 scopus 로고    scopus 로고
    • n): A new class for n divisible by 5"
    • Berlin, Germany: Springer-Verlag
    • n): A new class for n divisible by 5," in Proc. Finite Fields and Applications Fq5. Berlin, Germany: Springer-Verlag, 2000, pp. 113-121.
    • (2000) Proc. Finite Fields and Applications Fq5 , pp. 113-121
    • Dobbertin, H.1
  • 19
    • 31744449110 scopus 로고    scopus 로고
    • "A new APN function which is not equivalent to a power mapping"
    • Feb
    • Y. Edel, G. Kyureghyan, and A. Pott, "A new APN function which is not equivalent to a power mapping," IEEE Trans. Inf. Theory, vol. 52, no. 2, pp. 744-747, Feb. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.2 , pp. 744-747
    • Edel, Y.1    Kyureghyan, G.2    Pott, A.3
  • 20
    • 0000447674 scopus 로고
    • "Some results about the cross-correlation function between two maximal linear sequences"
    • T. Helleseth, "Some results about the cross-correlation function between two maximal linear sequences," Discr. Math., vol. 16, pp. 209-232, 1976.
    • (1976) Discr. Math. , vol.16 , pp. 209-232
    • Helleseth, T.1
  • 23
    • 0025432647 scopus 로고
    • "The weights of the Orthogonals of the extended quadratic binary Goppa codes"
    • May
    • G. Lachaud and J. Wolfmann, "The weights of the Orthogonals of the extended quadratic binary Goppa codes," IEEE Trans. Inf. Theory, vol. 36, no. 3, pp. 686-692, May 1990.
    • (1990) IEEE Trans. Inf. Theory , vol.36 , Issue.3 , pp. 686-692
    • Lachaud, G.1    Wolfmann, J.2
  • 26
    • 84948979030 scopus 로고
    • "S-boxes and round functions with controllable linearity and differential uniformity"
    • Berlin, Germany: Springer-Verlag
    • K. Nyberg, "S-boxes and round functions with controllable linearity and differential uniformity," in Fast Software Encryption - FSE'94 (Lecture Notes in Computer Science). Berlin, Germany: Springer-Verlag, 1995, vol. 1008, pp. 111-130.
    • (1995) Fast Software Encryption - FSE'94 (Lecture Notes in Computer Science) , vol.1008 , pp. 111-130
    • Nyberg, K.1
  • 28
    • 0029632010 scopus 로고
    • "Provable security against a differential attack"
    • K. Nyberg and L. R. Knudsen, "Provable security against a differential attack," J. Cryptol., vol. 8, no. 1, 1995.
    • (1995) J. Cryptol. , vol.8 , Issue.1
    • Nyberg, K.1    Knudsen, L.R.2
  • 29
    • 0010665268 scopus 로고
    • "A complete determination of translation ovoids in finite Desarguian planes"
    • Nov
    • S. E. Payne, "A complete determination of translation ovoids in finite Desarguian planes," Lincei - Rend. Sc. Fis. Mat. E Nat., vol. LI, Nov. 1971.
    • (1971) Lincei - Rend. Sc. Fis. Mat. E Nat. , vol.51
    • Payne, S.E.1
  • 30
    • 0041552981 scopus 로고    scopus 로고
    • Codes, Graphs, and Schemes from Nonlinear Functions
    • Tilburg Univ., Tilburg, The Netherlands, Tech. Rep., Res. Memo., FEW 790, May
    • E. R. V. Dam and D. F. D. Flass, Codes, Graphs, and Schemes from Nonlinear Functions, Tilburg Univ., Tilburg, The Netherlands, Tech. Rep., Res. Memo., FEW 790, May 2000.
    • (2000)
    • Dam, E.R.V.1    Flass, D.F.D.2
  • 31
    • 0000720010 scopus 로고
    • "GAC - The criterion for global avalanche characterics of cryptographic functions"
    • X.-M. Zhang and Y. Zheng, "GAC - The criterion for global avalanche characterics of cryptographic functions," J. Universal Comp. Sci., vol. 1, no. 5, pp. 320-337, 1995.
    • (1995) J. Universal Comp. Sci. , vol.1 , Issue.5 , pp. 320-337
    • Zhang, X.-M.1    Zheng, Y.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.