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classic mceliece intro classic mceliece intro comparison implementation specification nist iso papers talks people credits classic mceliece intro dedicated to the memory of robert j mceliece 1942 2019 the first code based public key cryptosystem was introduced by mceliece in 1978 the public key specifies a random binary goppa code a ciphertext is a codeword plus random errors the private key allows efficient decoding extracting the codeword from the ciphertext identifying and removing the errors the mceliece system was designed to be one way ow cpa meaning that an attacker cannot efficiently find the codeword from a ciphertext and public key when the codeword is chosen randomly the security level of the mceliece system has remained remarkably stable despite half a century of attack papers the system easily scales up to overkill sizes that provide ample security margin against advances in computer technology including quantum computers the mceliece system has prompted a tremendous amount of follow up work some of this work improves efficiency while clearly preserving security this includes a dual pke proposed by niederreiter software speedups and hardware speedups furthermore there is a straightforward conversion of an ow cpa pke into a kem that is ind cca2 secure against all rom attacks this conversion is tight preserving the security level under two assumptions that are satisfied by the mceliece pke first the pke is deterministic i e decryption recovers all randomness that was used second the pke has no decryption failures for valid ciphertexts even better the same conversion provides similar tightness for a broader class of attacks namely qrom attacks the risk that a hash function specific attack could be faster than a rom or qrom attack is addressed by the standard practice of selecting a well studied high security unstructured hash function classic mceliece brings all of this together it is a kem designed for ind cca2 security at a very high security level even against quantum computers the kem is built conservatively from a pke designed for ow cpa security namely niederreiter s dual version of mceliece s pke using binary goppa codes every level of the construction is designed so that future cryptographic auditors can be confident in the long term security of post quantum public key encryption version this is version 2026 06 19 of the intro web page