Creation of a class for McEliece cryptosystem

[979f6f8a-3a13-4974-bc2f-8b26846177fc]

This class can encrypt and decrypt messages using McEliece cryptosystem.

Depends on #20970

CC: @sagetrac-dlucas @ralfarogit @johanrosenkilde @miguelmarco @sagetrac-danielaugot @TaniaRichmond @jlavauzelle @emes4

Component: cryptography

Keywords: sd75

Author: Fangan Dosso, Marketa Slukova

Branch/Commit: u/gh-emes4/crypto/mceliece @ ea3c326

Issue created by migration from https://trac.sagemath.org/ticket/21352

[979f6f8a-3a13-4974-bc2f-8b26846177fc]

Description changed:

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+++ 
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-This class can encrypt and decrypt messages using McEliece cryptosystem.
+This class can encrypt and decrypt messages using `McEliece` cryptosystem.

[979f6f8a-3a13-4974-bc2f-8b26846177fc]

Branch: u/fdosso48/mc_eliece_cryptosystem

[979f6f8a-3a13-4974-bc2f-8b26846177fc]

Commit: 6ecc978

[979f6f8a-3a13-4974-bc2f-8b26846177fc]

comment:3

First commit done as backup.

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New commits:

6ecc978

adds a first commit as backup

[1861b8a9-77f0-4f35-8431-8514a75b40d1]

comment:4

Hello,

A framework which supports cryptosystems already exists in Sage (see sage/crypto/cryptosystem.py), but it does not contain a lot of code, and is designed in a way which does not support our needs.

We're about to discuss the redesign of this crypto framework.

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 6ecc978 to b819ada

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Branch pushed to git repo; I updated commit sha1. New commits:

b819ada

Adds the decoding radius as parameter because 'decoder.decoding_radius()' method gives incorrect results. Adds also an example of test.

[emes4]

Changed branch from u/fdosso48/mc_eliece_cryptosystem to u/gh-emes4/crypto/mceliece

[emes4]

Dependencies: #20970

[emes4]

Changed author from Fangan Dosso to Fangan Dosso, Marketa Slukova

[emes4]

Changed commit from b819ada to none

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

3917048	Merge branch 'develop' of git://trac.sagemath.org/sage into rank_metric
01d9a3d	Merge branch 'develop' of git://trac.sagemath.org/sage into t/28350/abstract_linear_code_no_metric_class
226ffbf	Added no metric to coding documentation index. Moved zero method from AbstractLinearCode. Changed base_field check.
bd31704	Merge branch 'u/gh-emes4/coding/no_metric' of git://trac.sagemath.org/sage into rank_metric
0a115d0	Removed zero method. Added field extension method.
9d74474	Merge branch 'u/gh-emes4/coding/linear_rank_metric' of git://trac.sagemath.org/sage into gabidulin
55128af	Initial completed, working version. No Metric changes. Documentation and doctests.
d736c4a	Merge branch 'develop' of git://trac.sagemath.org/sage into gabidulin
d9776d7	Rank static error channel.
ea3c326	Rough working version of rank metric Gabidulin McEliece

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Commit: ea3c326

[emes4]

comment:10

As part of my GSoC 2019 project, I added support for rank metric and Gabidulin codes - partially to use these to create a rank metric McEliece cryptosystem class.

This is a rough, working version. I used the original definition for the key generation, SG + P. It is probably better to later change this to one of the newer column scrambler definitions. It might be nice to have a choice of which one to use.

[johanrosenkilde]

comment:11

This implementation is nice and barebone, but it's specialised to rank distance. The McEliece cryptosystem is originally, and usually, for Hamming-metric.

It seems that the only place this makes a difference in the current implementation is where the error is added. If this channel was simply given at construction time, then the class could be invoked with both a Hamming metric code or a rank metric code.

It would be nice to see a doctest with both instantiations.

The methods of the class are missing doc-strings and -tests, and the file should have a module doc-string that explains what the McEliece cryptosystem is.