Reference Work Entry

Encyclopedia of Cryptography and Security

pp 842-843

Niederreiter Encryption Scheme

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

Related Concepts

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


The Niederreiter PKC is a public-key encryption scheme based on error correcting codes. The cryptogram is a syndrome of an error pattern relatively to a parity check matrix of some linear code. Only the legal user, who knows the hidden algebraic structure of this code, can recover the error pattern, the cleartext, from the syndrome.


The system was introduced by Harald Niederreiter in 1986 [1]. Its security is, as for the McEliece public-key cryptosystem, related to difficult algorithmic problems of algebraic coding theory. It has the same advantages (efficient encryption and decryption) and drawbacks (public-key size, information rate) as the McEliece system. The block size, however, is smaller.

General idea

The cryptogram is a linear combination of t columns of a parity check matrix ...

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