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Shorter Linear SLPs for MDS Matrices

SLPs for our ToSC Volume 2017 Issue 4 paper 'Shorter Linear Straight-Line Programs for MDS Matrices'

  • The makefile compiles the slp_heuristic C++ program.

  • The makefile compiles for each matrix header in the 'paar_header' folder two executables: one for Paar1 algorithm and one for Paar2. Each executable prints the XOR count for this matrix and the corresponding SLP for implementing the matrix with the said XOR count.

  • For each matrix there is a second file in the 'bp_format' folder that contains the correct format for the slp_heuristic executable. You can call the programs on, e.g. the M_4_4 matrix, as follows: $ ./slp_heuristic < bp_format/M_4_4.txt It will then output the corresponding XOR count and the SLP.

  • All matrices and functions for converting them etc. are additionally in the code.sage file. This was also used to construct the above headers and text files. The SageMath code can be loaded into a SageMath REPL and then used to compute Paar1 or slp_heuristic XOR counts (for the latter the program need to be available as a compiled executable).

  • The code in the slp_heuristic.cpp is based on the implementation of Boyar and Peralta, available at http://www.imada.sdu.dk/~joan/xor/. We adjusted the program such that it prints the corresponding SLP program.

  • Three SLPs where provided by Andrea Visconti through personal communication. The code used to generate these SLPs is not available to us.

  • Twenty-five SLPs were generated with code kindly provided by René Peralta, based on recent work of Joan Boyar, Magnus Gausdal Find, and him. This program is called LinOpt in this repository. Its source code is not yet public.

  • For every matrix listed in the paper there is a corresponding file in the 'slp_implementations' directory. These files contain a comment with what program the SLP was computed, the XOR count and the SLP itself.

  • All SLPs are also contained in the 'check_implementations.sage' file, which can be loaded in the SageMath REPL and all SLPs can be verified with the 'run_tests()' function.

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SLPs for the ToSC Volume 2017 Issue 4 paper 'Shorter Linear Straight-Line Programs for MDS Matrices'

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