McEliece
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In cryptography, McEliece is an asymmetric key algorithm developed in 1978 by Robert McEliece. It has never gained much acceptance in the cryptographic community, although the mathematical theory behind it makes it an interesting algorithm to study.
The algorithm uses Goppa codes, which are a type of error-correcting code (see coding theory). The algorithm disguises a Goppa code made from the plaintext as a general linear code. Goppa codes are easy to decode, but distinguishing them from a general linear code is hard. This is McEliece's hard problem.
The private and public keys are large matrices, which is one of the main disadvantages of the algorithm. The public key is very large: 219 bits long.
Attempts have been made to cryptanalyze McEliece, but none have been successful. However, the algorithm is never used in practice because of the massive keys and because the ciphertext is twice as large as the plaintext. The similarity between this algorithm and the knapsack problem (which has been proven insecure) also worries some.