SBox class for Sage

[malb]

The attached patch adds a class SBox to the module sage.crypto.mq which offers basic functionality to work with cryptographic substitution boxes like:

• substitution (obviously)
• difference distribution and linear approximation matrices
• multivariate polynomial system generation
• univariate polynomial interpolation

It might be a bit controversial if this functionality should go in (it is not math but applied math), so here are some points in favour:

• Sage has a sage.crypto module with LFSRs and such.
• SBox supports (algebraic) cryptanalysis by simplifying experiments with ciphers and algebraic aspects of cryptography is an application of Sage (Sage was advertised for this application in the past)
• Some people have expressed (some) interest in such a class.

Component: commutative algebra

Issue created by migration from https://trac.sagemath.org/ticket/2501

[malb]

Attachment: sbox.patch.gz

[williamstein]

comment:1

It might be a bit controversial if this functionality should go in (it is not math but applied math)

It's not controversial at all, in my opinion -- this should definitely go in.

"Applied math" belongs squarely within the mission of Sage, and S-Box's most certainly do.

[mwhansen]

comment:2

Applies to 2.10.4.alpha0 and passes tests after #2444 is applied.

[85eec1a4-3d04-4b4d-b711-d4db03337c41]

comment:3

Merged in Sage 2.10.4.rc0