Back
 OJDM  Vol.10 No.4 , October 2020
Full-Rank Factoring of Elementary 2-Groups with Equal Size Factors
Abstract: In order to answer a question motivated by constructing substitution boxes in block ciphers we will exhibit an infinite family of full-rank factorizations of elementary 2-groups into two factors having equal sizes.
Cite this paper: Szabó, S. (2020) Full-Rank Factoring of Elementary 2-Groups with Equal Size Factors. Open Journal of Discrete Mathematics, 10, 89-95. doi: 10.4236/ojdm.2020.104009.
References

[1]   Dinitz, M. (2006) Full Rank Tilings of Finite Abelian Groups. SIAM Journal on Discrete Mathematics, 20, 160-170.
https://doi.org/10.1137/S0895480104445794

[2]   Etzion, T. and Vardy, A. (1998) On Perfect Codes and Tilings: Problems and Solutions. SIAM Journal on Discrete Mathematics, 11, 205-223.
https://doi.org/10.1137/S0895480196309171

[3]   Qu, M.H. and Venstone, S.A. (1994) Factorizations in the Elementary Abelian p-Groups and Their Cryptographic Significance. Journal of Cryptography, 7, 201-212.
https://doi.org/10.1007/BF00203963

[4]   Szabó, S. (2006) Completing Codes and the Rédei Property of Groups. Theoretical Computer Science, 359, 449-454.
https://doi.org/10.1016/j.tcs.2006.02.002

[5]   Carlet, C. and Youssef, A. Building S-Boxes from Full-Rank Factorization of an Elementary 2-Group. Private Communication.

[6]   Carlet, C. (2010) Vectorial Boolean Functions for Cryptography. In: Crama, Y., Ed., Boolean Models and Methods in Mathematics, Computer Science, and Engineering, Cambridge University Press, Cambridge, 398-470.
https://doi.org/10.1017/CBO9780511780448.012

 
 
Top