What is the Niederreiter cryptosystem?

Developed by Harald Niederreiter in 1986, the Niederreiter cryptosystem is a public-key cryptography variant of the McEliece cryptosystem. It utilizes the parity check matrix of a linear code rather than a generator matrix, treating the ciphertext as a syndrome and the message as an error pattern. While equivalent to McEliece in security, its encryption process is roughly ten times faster and can be utilized to construct digital signature schemes.

What we know

• The Niederreiter cryptosystem was developed in 1986 by Austrian mathematician Harald Niederreiter as a variation of the McEliece cryptosystem. [2, 3]
• The system applies public-key cryptographic principles to the parity check matrix of a linear code. [2]
• In the Niederreiter cryptosystem, the ciphertext is a syndrome and the message is represented as an error pattern. [2]
• Encryption in the Niederreiter scheme is approximately ten times faster than encryption in the McEliece cryptosystem. [2]
• The Niederreiter scheme can be used to construct a digital signature scheme. [2, 4]

Where to go next

• compared withHow does the McEliece cryptosystem work?
• whoWho is Harald Niederreiter?
• the bigger pictureWhat is public-key cryptography?
• how it workedHow are digital signature schemes constructed from error-correcting codes?
• how we knowWhat are parity check matrices in linear codes?
• an unexpected connectionHow does a cryptographic algorithm connect to quasi-Monte Carlo methods?Harald Niederreiter developed a prominent public-key cryptosystem while also specializing in completely different mathematical fields like quasi-Monte Carlo methods and discrepancy theory.

Sources

• [1]Niederreiter cryptosystem (Wikidata Q17083061) · CC0 1.0
• [2]Niederreiter cryptosystem · CC BY-SA 4.0
• [3]Harald Niederreiter · CC BY-SA 4.0
• [4]McEliece cryptosystem · CC BY-SA 4.0
• [5]Niederreiter · CC BY-SA 4.0