Code-Based Cryptography

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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:

  1. Public-key encryption schemes [23]

  2. Digital signature scheme [4]

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

  3. Zero-knowledge authentification protocols [57]

  4. Pseudo-random number generator and stream cipher [89]

  5. Cryptographic hash function [10]