Code-Based Cryptography

Related Concepts

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

Definition

Code-based cryptography includes all cryptosystems, symetric or asymetric, whose security relies, partially or totally, on the hardness of decoding in a linear error correcting code, possibly chosen with some particular structure or in a specific family (for instance, quasi-cyclic codes, or Goppa codes).

Applications

In the case of asymmetric primitives, the security relies, in addition to the hardness of decoding [1], on how well the trapdoor is concealed (typically the difficulty of obtaining a Goppa code distinguisher). The main primitives are:

• – Public-key encryption schemes [2,  3]

• – Digital signature scheme [4]

  For other primitives, the security only depends on the hardness of decoding:

• – Zero-knowledge authentification protocols [5–7]

• – Pseudo-random number generator and stream cipher [8,  9]

• – Cryptographic hash function [10]