Reference Work Entry

Encyclopedia of Cryptography and Security

pp 767-768

McEliece Public Key Cryptosystem

  • Nicolas SendrierAffiliated withProject-Team SECRET, INRIA Paris-Rocquencourt

Related Concepts

Error Correcting Codes; Public-Key Encryption; Syndrome Decoding Problem


The McEliece PKC is a public-key encryption scheme based on error correcting codes. The cryptogram is a code word of a binary Goppa code to which errors are added. Only the legal user, who knows the hidden algebraic structure of the code, can remove those errors and recover the cleartext.


It was introduced by Robert J. McEliece in 1978 [1] and is among the oldest public-key encryption schemes. Its security is related to hard algorithmic problems of algebraic coding theory. Its main advantages are very efficient encryption and decryption procedures and a good practical and theoretical security. On the other hand, its main drawbacks are a public key of large size and a ciphertext which is larger than the cleartext.

General Idea

The cleartext of k binary digits is encoded into a code word of n > k binary digits by means of some encoder of a t-error correctin ...

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