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What is the security implication of non-full-rank systematic matrix in McEliece cryptosystem?

The Classic McEliece cryptosystem has the following key generation procedure: Choose a field $\mathbb{F}_{2^m}$, an irreducible polynomial $g(x)$ of degree $t$, and $n$ field elements $\alpha_1, \...
user2249675's user avatar
2 votes
2 answers
415 views

Code used for McEliece cryptosystem

In the McEliece cryptosystem, is choice of the code known to the attacker? And if a structural attack succeeded and the attacker found the generator matrix of the code, how did the attacker decode the ...
Mathsa's user avatar
  • 113
1 vote
1 answer
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McEliece cryptosystem

There is something intriguing me about this cryptosystem. That is : Let $(S, G, P)$ be the secret key: $S$ : invertible matrix $G$ : generator matrix for some linear code $C$ $P$ : permutation ...
Younes's user avatar
  • 111
0 votes
1 answer
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How can we prove that the scrambled G matrix in McEliece cryptosystem preserves the minimum distance properties of G matrix?

In McEliece cryptosystem, G matrix is scrambled using S and P so that scrambled G matrix is G' = SGP. Here G is the generator matrix of a linear code and after scrambling it is converted into another ...
Surya's user avatar
  • 91
4 votes
2 answers
508 views

Basic attacks on McEliece; finding S and P

Take a McEliece cryptosystem with public generator matrix $G' = S G P$ where $G$ is a generator of a secret code with known fast decoding (not necessarily a Goppa code over $\mathbb{F}_2$), $S$ is ...
QuadrExAtt's user avatar
11 votes
1 answer
257 views

Is the Couvreur et al. polynomial time attack on McEliece practical?

There's a new e-print out on arXiv titled "A Polynomial Time Attack against Algebraic Geometry Code Based Public Key Cryptosystems" by Alain Couvreur, Irene Márquez-Corbella and Ruud Pellikaan: "We ...
fractal's user avatar
  • 121
2 votes
1 answer
462 views

McEliece Public Key Encryption

The definition of Public Key Encryption(PKE) say that: A PKE scheme is a triple of probabilistic polynomial time algorithm (PPT) (Gen,Enc,Dec). The definition of PPT say: In complexity theory, ...
juaninf's user avatar
  • 2,761
3 votes
1 answer
233 views

McEliece for streaming data

Under the assumption that there exists a real-world implementation of the McEliece scheme, could it be applied to streaming data as is? By that I mean in 'block cipher mode'? I've read that McEliece ...
publixo's user avatar
  • 31
12 votes
4 answers
2k views

Is key size the only barrier to the adoption of the McEliece cryptosystem, or is it considered broken/potentially vulnerable?

A recent paper showed that the McEliece cryptosystem is not, unlike RSA and other cryptosystems, weakened as drastically by quantum computing because strong Fourier sampling cannot solve the hidden ...
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