Description
The purpose of this thesis is to examine if Quasi-Cyclic Moderate-Density Parity-Check (QC-MDPC) codes is a good family of error-correcting codes to replace the family of Goppa codes in the McEliece cryptosystem. This cryptosystem is one of a few cryptosystems which are thought to be secure against all-purpose quantum computers. Cryptographic techniques have been used to provide secure communication between users since classical times. However, advances in the field of quantum physics and quantum computing might give rise to all-purpose quantum computers within the next decade. These quantum computers are able to exploit properties from its core components, the quantum bits, to solve some of the hardest mathematical problems. However, these unsolvable problems grant current day encryptions its security. Some cryptosystems are found to be resistant against the power of quantum computers. One of which was proposed in 1978 by Robert McEliece. He proposed a cryptosystem based on techniques used in coding theory. Despite allowing for the rapid encryption and decryption of messages, storage of the users’ cryptographic key requires a large amount of memory, making its use impractical. Many professionals from the fields of mathematics, computer science and engineering have proposed changes to decrease the size of the key. So far, all these propositions have led to either a security breach or were found inefficient. The family of QC-MDPC codes has been coined to replace Goppa codes in the McEliece cryptosystem. These codes also allow for rapid encryption and decryption, but has the additional advantage that storage of its cryptographic key requires significantly less memory. This study shows that, like a lot of other families of codes, QC-MDPC codes is also vulnerable to a key-breaking cryptanalytic attack which excludes them from being a candidate to replace the originally proposed Goppa codes.
