# Encyclopedia of Cryptography and Security

2011 Edition
| Editors: Henk C. A. van Tilborg, Sushil Jajodia

# Niederreiter Encryption Scheme

• Nicolas Sendrier
Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-5906-5_385

## Definition

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.

## Theory

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 $$H\in {F}^{r\times n}_{q}$$

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