tii_crypto_challenges

This repository contains the scripts accompanying the McEliece Challenges from TII

Contributers

• Elena Kirshanova
• Andre Esser

Requirements

• SageMath 9.3+

Description of files

Short description of the content:

• McElieceKeyGen.sage contains the main function to generate McEliece secret/public keys and a random syndrome
• McEliece_challenge_track2.sage generates McEliece public/secret for McEliece parameters given in key_rec_instances
• McEliece_challenge_track3.sage generates McEliece keys and a random syndrome for toy McEliece parameters, parameters for secuirty level 70-75, 80-90
• key_rec_instances contains list of dictionaries with parameters for Track 2 (McEliece key recovery)
• params.sage contains a script that find concrete Goppa code parameters for Track 2 (McEliece key recovery) and Track 3 (McElice message recovery)
• check_solution_track2.sage checks solution for Track 2
• check_solution_track3.sage checks solution for Track 3

These are the solutions to McEliece challenges Track 2.

• public_keyRec/ contains files 'pk_McEliece_'+bit_security+'.txt' with:

  • public matrix H in the systematic form (the identity matrix is also stored),
  • coefficients of unitary irreducbile polynomial f s.t. F_{2^m} = F_2[x]/f(x). This is public data for McEliece challenges Track 2.

• public/ contains files 'pk_McEliece_'+bit_security+'.txt' with:

  • public matrix H in the systematic form (the identity matrix is also stored)
  • syndrome vector
  • coefficients of unitary irreducbile polynomial f s.t. F_{2^m} = F_2[x]/f(x).
  • parameter n
  • parameter k
  • parameter t
  • parameter m This is public data for McEliece challenges Track 3.

How to verify your solution

Track 2: Key Recovery

To check a solution, create a file that contains

• coefficient-vector of the secret Goppa polynomial g in variable 'a' (from low degree to high degree) of your solution
• a vector that contains L elements of the field F_{2^m} in variable 'a'. Then execute the script check_solution_track2.sage providing the sec. level of the solved challenge as the first argument and the file name as the second. For example, run

sage check_solution_track2.sage 22 priv_keyRec/sk_McEliece_22.txt

If the provided solution is correct, the script returns 1. Otherwise it returns 0.

Track 3: Message Recovery

To check a solution execute the script check_solution_track3.sage providing the sec. level of the solved challenge as the first argument and the error vector as a binary string with no space. For example,

sage check_solution_track3.sage 22 0000000000000000010000000000000000000000100000100000000000000000000000000000000000000000000000

If the provided solution is correct, the script returns 1. Otherwise it returns 0.

How to generate your own challenges

Track 2: Key Recovery

To generate all challenges for Track 2 run

sage McEliece_challenge_track2.sage

This will re-generate all the files with non-toy security levels in folders priv_keyRec/ and public_keyRec/. The generation might take a few minutes. See the script McEliece_challenge_track2.sage to know how to generate only toy-challenges.

Track 3: Message Recovery

To generate all challenges for Track 3 run

sage McEliece_challenge_track3.sage

This will re-generate all the files with the desired security levels in folders priv/ and public/. See the script McEliece_challenge_track3.sage to know how to generate the other challenges.

The scripts to generate challenges (both Track 2 and Track 3) merely exemplify how the TII decoding challenges were created. If you wish to check your solution for the TII challenge, the content of the public folders should not be modified.