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app_local/readme.txt

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+McEliece cryptosystem implementation
+
+Usage:
+0. pip install numpy and galois
+1. generate.py - generate and save public and private keys
+2. send pubkey.py and encode.py to your friend
+3. your friend runs encode.py, write secret string and send message.py to you
+4. decode.py - get secret string
+
+Hacker can get your private key if he will know a half of it (and pubkey.py, decode.py and Reed-Solomon algo).
+Check break.py to understand how hacker can do this.
+
+Notice: left part of G is E, because we use Reed-Solomon algo; so left part of S @ G is S and cutting right colomns works; my_fix(G) returns E and in break_S we needn't get inv(G), just S = my_fix(G_ @ inv(P)); try break_S with another (not Reed-Solomon) code (matrix G will be different; will my_fix(G) and my_fix(G_) return nonsingular matrices?; of course, rank(G) = rank(G_) = k and we can iterate through all possible combinations of column deletions and find one that does not lead to nonsingular matrices); another way to get S is calculating it row by row (solving k systems, each has  n equations with k variables, k < n, but we need to do it in Galois Field).

readme.txt

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-McEliece cryptosystem implementation
-
-Usage:
-0. pip install numpy and galois
-1. generate.py - generate and save public and private keys
-2. send pubkey.py and encode.py to your friend
-3. your friend runs encode.py, write secret string and send message.py to you
-4. decode.py - get secret string
-
-Hacker can get your private key if he will know a half of it (and pubkey.py, decode.py and Reed-Solomon algo).
-Check break.py to understand how hacker can do this.
-
-todo:
-1. left part of G is E, because we use Reed-Solomon algo; so left part of S @ G is S and cutting right colomns works; my_fix(G) returns E and in break_S we needn't get inv(G), just S = my_fix(G_ @ inv(P)), check it; try break_S with another (not Reed-Solomon) code (matrix G will be different; will my_fix(G) and my_fix(G_) return nonsingular matrices?; of course, rank(G) = rank(G_) = k and we can iterate through all possible combinations of column deletions and find one that does not lead to nonsingular matrices); another way to get S is calculating it row by row (solving k systems, each has  n equations with k variables, k < n, but we need to do it in Galois Field)
-2. DONE! check randomization during encode (add vector z, check https://en.wikipedia.org/wiki/McEliece_cryptosystem)
-3. DONE! make presentation that explains McEliece cryptosystem