Cryptography Based on Error Correcting Codes

Abstract

Breaking contemporary cryptographic algorithms using any binary computer has at least sub-exponential complexity. However, if a quantum computer was used effectively, then our asymmetric cryptography would not be secure anymore. Since the code-based cryptography (cryptography based on error-correcting codes) relies on different problems, it is not as threatened as, for example, RSA or ECC. Recent years have been crucial in the progress of cryptography based on error-correcting codes. In contrast to the number-theoretic problems typically used in cryptography nowadays, certain instances of the underlying problems of code-based cryptography remain unbroken even employing quantum cryptanalysis. Thus, some code-based cryptography constructions belong to the post-quantum cryptography, especially cryptosystems based on binary irreducible Goppa codes. Many attempts to replace this underlying code in order to reduce the key size already have been proposed. Unfortunately, almost all of them have been broken. For instance, just a while ago, Reed Muller, Generalized Reed-Solomon Codes, and Convolutional codes were broken. Against some rank metric codes, a new attack was introduced. On the other hand, two prospective countermeasures in order to hide the exploitable code structure of the broken codes were fashioned. However, only the choice of binary irreducible Goppa codes remains secure in the post-quantum sense. This chapter surveys the more recent developments in code-based cryptography as well as implementations and side channel attacks. This work also recalls briefly the basic ideas, and provides a roadmap to readers.