Compositions and parities of complete mappings and of orthomorphisms

Aragona, 2018, Primitivity of PRESENT and other lightweight ciphers, J. Algebra Appl., 17, 10.1142/S0219498818501153 Aragona, 2014, On the group generated by the round functions of translation based ciphers over arbitrary finite fields, Finite Fields Appl., 25, 293, 10.1016/j.ffa.2013.10.005 Aragona, 2017, The group generated by the round functions of a GOST-like cipher, Ann. Mat. Pura Appl. (4), 196, 1, 10.1007/s10231-016-0559-6 Aragona, 2021, On invariant subspaces in the Lai-Massey scheme and a primitivity reduction, Mediterr. J. Math., 18, 10.1007/s00009-021-01781-x Bateman, 1950, A remark on infinite groups, Am. Math. Mon., 57, 623, 10.2307/2308116 Beals, 1991, Harmonious groups, J. Comb. Theory, Ser. A, 56, 223, 10.1016/0097-3165(91)90034-E Besche, 2002, A millennium project: constructing small groups, Int. J. Algebra Comput., 12, 623, 10.1142/S0218196702001115 Bóna, 2012, Combinatorics of Permutations Bors, 2022, Coset-wise affine functions and cycle types of complete mappings, Finite Fields Appl., 83, 10.1016/j.ffa.2022.102088 Bray, 2020, The Hall-Paige conjecture, and synchronization for affine and diagonal groups, J. Algebra, 545, 27, 10.1016/j.jalgebra.2019.02.025 Caranti, 2009, An application of the O'Nan-Scott theorem to the group generated by the round functions of an AES-like cipher, Des. Codes Cryptogr., 52, 293, 10.1007/s10623-009-9283-1 Caranti, 2009, On some block ciphers and imprimitive groups, Appl. Algebra Eng. Commun. Comput., 20, 339, 10.1007/s00200-009-0100-x Coppersmith, 1975, Generators for certain alternating groups with applications to cryptography, SIAM J. Appl. Math., 29, 624, 10.1137/0129051 Daemen, 2002, The Design of Rijndael. AES – The Advanced Encryption Standard Eberhard, 2022, An asymptotic for the Hall-Paige conjecture, Adv. Math., 404 Evans, 1992, Orthomorphism Graphs of Groups, vol. 1535 Evans, 1992, The existence of complete mappings of finite groups, vol. 90, 65 Evans, 2009, The admissibility of sporadic simple groups, J. Algebra, 321, 105, 10.1016/j.jalgebra.2008.09.028 Evans, 2018, Orthogonal Latin Squares Based on Groups, vol. 57 Even, 1983, DES-like functions can generate the alternating group, IEEE Trans. Inf. Theory, 29, 863, 10.1109/TIT.1983.1056752 Feng, 2011, Loiss: a byte-oriented stream cipher, vol. 6639, 109 Francetić, 2018, Parity of sets of mutually orthogonal Latin squares, J. Comb. Theory, Ser. A, 155, 67, 10.1016/j.jcta.2017.10.006 Friedlander, 1978, On a group sequencing problem of Ringel, vol. XXI, 307 Hall, 1955, Complete mappings of finite groups, Pac. J. Math., 5, 541, 10.2140/pjm.1955.5.541 Hornauer, 1994, Markov ciphers and alternating groups, vol. 765, 453 Hsu, 1984, Generalized complete mappings, neofields, sequenceable groups and block designs. I, Pac. J. Math., 111, 317, 10.2140/pjm.1984.111.317 Işik, 2017, Complete mappings and Carlitz rank, Des. Codes Cryptogr., 85, 121, 10.1007/s10623-016-0293-5 Junod, 2005, FOX: a new family of block ciphers, vol. 3357, 114 Kaliski, 1988, Is the data encryption standard a group? (Results of cycling experiments on DES), J. Cryptol., 1, 3, 10.1007/BF00206323 Kotlar, 2012, Parity types, cycle structures and autotopisms of Latin squares, Electron. J. Comb., 19, P10, 10.37236/2538 Liebeck, 1988, On the O'Nan-Scott theorem for finite primitive permutation groups, J. Aust. Math. Soc. Ser. A, 44, 389, 10.1017/S144678870003216X Mann, 1942, The construction of orthogonal Latin squares, Ann. Math. Stat., 13, 418, 10.1214/aoms/1177731539 Mileva, 2014, Quasigroup representation of some lightweight block ciphers, Quasigr. Relat. Syst., 22, 267 Mittenthal, 1995, Block substitutions using orthomorphic mappings, Adv. Appl. Math., 16, 59, 10.1006/aama.1995.1003 Muratović-Ribić, 2014, A note on complete polynomials over finite fields and their applications in cryptography, Finite Fields Appl., 25, 306, 10.1016/j.ffa.2013.10.008 Murphy, 1994, A weak cipher that generates the symmetric group, J. Cryptol., 7, 61, 10.1007/BF00195210 Müyesser Niederreiter, 1982, Complete mappings of finite fields, J. Aust. Math. Soc. Ser. A, 33, 197, 10.1017/S1446788700018346 Ollis, 2002, Sequenceable groups and related topics, Electron. J. Comb., DS10, 34 Ollis, 2019, The spectrum of group-based complete Latin squares, Electron. J. Comb., 26 Paige, 1951, Complete mappings of finite groups, Pac. J. Math., 1, 111, 10.2140/pjm.1951.1.111 Paterson, 1999, Imprimitive permutation groups and trapdoors in iterated block ciphers, vol. 1636, 201 Praeger, 1980, On the orders of primitive permutation groups, Bull. Lond. Math. Soc., 12, 303, 10.1112/blms/12.4.303 Robbins, 1955, A remark on Stirling's formula, Am. Math. Mon., 62, 26 Robinson, 1996, A Course in the Theory of Groups, vol. 80 Schimanski, 2016 Schulz, 2000, On check digit systems using anti-symmetric mappings, 295 Shaheen, 2010, Permutations of finite fields for check digit systems, Des. Codes Cryptogr., 57, 361, 10.1007/s10623-010-9374-z Sparr, 2008, Group theoretic properties of Rijndael-like ciphers, Discrete Appl. Math., 156, 3139, 10.1016/j.dam.2007.12.011 Sparr, 2015, The round functions of KASUMI generate the alternating group, J. Math. Cryptol., 9, 23, 10.1515/jmc-2013-0028 Stafford, 1998, Groups of permutation polynomials over finite fields, Finite Fields Appl., 4, 450, 10.1006/ffta.1998.0224 Stănică, 2012, Investigations on bent and negabent functions via the nega-Hadamard transform, IEEE Trans. Inf. Theory, 58, 4064, 10.1109/TIT.2012.2186785 Sun, 2021, New constructions of complete permutations, IEEE Trans. Inf. Theory, 67, 7561, 10.1109/TIT.2021.3100756 Tu, 2014, Several classes of complete permutation polynomials, Finite Fields Appl., 25, 182, 10.1016/j.ffa.2013.09.007 Vaudenay, 1999, On the Lai-Massey scheme, vol. 1716, 8 Wang, 2000, More on sequences in groups, Australas. J. Comb., 21, 187 Wernsdorf, 1993, The one-round functions of the DES generate the alternating group, vol. 658, 99 Wilcox, 2009, Reduction of the Hall-Paige conjecture to sporadic simple groups, J. Algebra, 321, 1407, 10.1016/j.jalgebra.2008.11.033 Winterhof, 2014, Generalizations of complete mappings of finite fields and some applications, J. Symb. Comput., 64, 42, 10.1016/j.jsc.2013.12.006 Wu, 2014, Some classes of monomial complete permutation polynomials over finite fields of characteristic two, Finite Fields Appl., 28, 148, 10.1016/j.ffa.2014.01.011 Wu, 2006, Composite properties of orthomorphic permutations, Prog. Nat. Sci., 16, 1517 Xu, 2015, Complete permutation polynomials over finite fields of odd characteristic, Finite Fields Appl., 31, 228, 10.1016/j.ffa.2014.08.002 Zha, 2015, Constructing permutations and complete permutations over finite fields via subfield-valued polynomials, Finite Fields Appl., 31, 162, 10.1016/j.ffa.2014.10.002