Top

Cryptography and Communications

Published in:

31-03-2022

The binary Gold function and its c-boomerang connectivity table

Authors: Sartaj Ul Hasan, Mohit Pal, Pantelimon Stănică

Published in: Cryptography and Communications | Issue 6/2022

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

Here, we give a complete description of the entire c-Boomerang Connectivity Table for the Gold function over finite fields of even characteristic, by using double Weil sums. As a by-product, we generalize a result of Boura and Canteaut (IACR Trans. Symmetric Cryptol. 2018(3) : 290–310, 2018) for the classical boomerang uniformity (see also the extended abstract by Eddahmani and Mesnager at the Boolean Functions and their Applications (BFA 2021) conference).

previous article Constructing new superclasses of bent functions from known ones

next article Encoding and decoding of several optimal rank metric codes

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Available only for authorised users

Bartoli, D., Calderini, M.: On construction and (non)existence of c-(almost) perfect nonlinear functions. Finite Fields Appl. 72, 101835 (2021)MathSciNetCrossRef

Boura, C., Canteaut, A.: On the boomerang uniformity of cryptographic Sboxes. IACR Trans. Symmetric Cryptol. 2018(3), 290–310 (2018)CrossRef

Carlet, C.: Boolean Functions for Cryptography and Coding Theory. Cambridge University Press, Cambridge, Cambridge (2021)MATH

Cid, C., Huang, T., Peyrin, T., Sasaki, Y., Song, L.: Boomerang connectivity table: a new cryptanalysis tool. In: Nielsen, J., Rijmen, V. (eds.) Advances in Cryptology-EUROCRYPT 2018, LNCS 10821, pp. 683–714. Springer, Cham (2018)CrossRef

Coulter, R.S.: On the evaluation of a class of Weil sums in characteristic 2. New Zealand J. Math. 28, 171–184 (1999)MathSciNetMATH

Cusick, T.W., Stănică, P.: Cryptographic boolean functions and applications (Ed. 2), Academic Press, San Diego, CA, (2017)

S. Eddahmani, S.: Mesnager, explicit values of the tables DDT, BCT, FBCT, and FBDT of the inverse, the Gold, and the Bracken-Leander functions, Boolean Functions and their Applications (BFA 2021) (2021)

Ellingsen, P., Felke, P., Riera, C., Stănică, P., Tkachenko, A.: C-differentials, multiplicative uniformity and (almost) perfect c-nonlinearity. IEEE Trans. Inform. Theory 66(9), 5781–5789 (2020)MathSciNetCrossRef

Hasan, S.U., Pal, M., Riera, C., Stănică, P.: On the c-differential uniformity of certain maps over finite fields. Des. Codes Cryptogr 89(2), 221–239 (2021)MathSciNetCrossRef

10.

Hasan, S.U., Pal, M., Stănică, P.: Boomerang uniformity of a class of power maps. Des. Codes Cryptogr. 89, 2627–2636 (2021)MathSciNetCrossRef

11.

Hasan, S.U., Pal, M., Stănică, P.: The c-differential uniformity and boomerang uniformity of two classes of permutation polynomials. IEEE Trans. Inform. Theory 68(1), 679–691 (2022)MathSciNetCrossRef

12.

Lidl, R., Niederreiter, H.: FiniteFields (Ed. 2), Encycl. Math. Appl., vol.20, Cambridge Univ. Press, Cambridge (1997)

13.

Li, K., Qu, L., Sun, B., Li, C.: New results about the boomerang uniformity of permutation polynomials. IEEE Trans. Inform. Theory 65(11), 7542–7553 (2019)MathSciNetCrossRef

14.

Mesnager, S., Riera, C., Stănică, P., Yan, H., Zhou, Z.: Investigations on c-(almost) perfect nonlinear functions. IEEE Trans. Inform. Theory 67(10), 6916–6925 (2021)MathSciNetCrossRef

15.

Nyberg, K.: Differentially uniform mappings for cryptography. In: Helleseth, T. (ed.) Advances in Cryptology-EUROCRYPT 1993, LNCS 765, pp. 55–64. Springer, Berlin, Heidelberg (1994)

16.

Stănică, P.: Investigations on c-boomerang uniformity and perfect nonlinearity. Discrete Appl. Math. 304, 297–314 (2021)MathSciNetCrossRef

17.

Stănică, P.: Low c-boomerang uniformity of the swapped inverse function. Discrete Math. 344(10), 112543 (2021)MathSciNetCrossRef

18.

Stănică, P.: Using double Weil sums in finding the c-boomerang connectivity table for monomial functions on finite fields. Appl. Algebra Eng. Commun. Comput (2021). https://doi.org/10.1007/s00200-021-00520-9CrossRef

19.

Stănică, P., Geary, A.: The c-differential behaviour of the inverse function under the c-equivalence. Cryptogr. Commun. 13, 295–306 (2021)MathSciNetCrossRef

20.

Stănică, P., Riera, C., Tkachenko, A.: Characters, Weil sums and c-differential uniformity with an application to the perturbed Gold function, Cryptogr. Commun. 6, 891–907 (2021)

21.

Wagner, D.: The boomerang attack, In: Knudsen, L.R. (ed.) Fast Software Encryption-FSE 1999. LNCS 1636, Springer, Berlin, Heidelberg, pp. 156–170 (1999)

22.

Zha, Z., Hu, L.: Some classes of power functions with low c-differential uniformity over finite fields. Des. Codes Cryptogr. 89, 1193–1210 (2021)MathSciNetCrossRef

Title: The binary Gold function and its c-boomerang connectivity table
Authors: Sartaj Ul Hasan
Mohit Pal
Pantelimon Stănică
Publication date: 31-03-2022
Publisher: Springer US
Published in: Cryptography and Communications / Issue 6/2022
Print ISSN: 1936-2447
Electronic ISSN: 1936-2455
DOI: https://doi.org/10.1007/s12095-022-00573-8

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Other articles of this Issue 6/2022

Encoding and decoding of several optimal rank metric codes

Constructing more quadratic APN functions with the QAM method

Construction of APN permutations via Walsh zero spaces

Editorial: Special issue on Boolean functions and their applications 2021

Explicit values of the DDT, the BCT, the FBCT, and the FBDT of the inverse, the gold, and the Bracken-Leander S-boxes

Constructing new superclasses of bent functions from known ones

Premium Partner