Post-quantum cryptography: an efficient differential fault analysis attack and a new one-time signature scheme - Grados Vásquez, Juan del Carmen (2018)
yptography is present in many fields in our daily life such as bank transac tions, e-commerce, military communications, among others. Cryptography scien tists have dedicated enormous effort to develop efficient and secure cryptographic schemes. The most common and successful ones are based on problems of num ber theory, for example, RSA and elliptic-curve cryptography. However, in 1994 Peter Shor of Bell laboratories managed to develop a quantum algorithm that can break RSA and other public-key cryptosystems based on number theory by using quantum computers. Symmetric primitives are also threatened by the arrival of quantum computers. Nonetheless, they are more resistant than the asymmetric primitives. In fact, the best-known quantum algorithm for attacking symmetric primitives is the Grover algorithm, which has a quadratic improvement over the best classical algorithm. So, according to the literature, it is enough to double the size of the keys to resist attacks of this algorithm. Efforts are concentrated in de veloping public and private key cryptographic schemes that resist the quantum at tacks. These schemes are usually classified as 1) hash-based schemes, 2) code-based schemes, 3) lattice-based schemes, 4) multivariate-quadratic-equation schemes, and 5) secret-key schemes. We study schemes of the classes 1), 2), and 5); and we divide the thesis into vii three parts. In the first part, we introduce coding theory and provide an overview of code-based cryptography focusing mainly on the digital signature of Courtois, Finiasz, and Sendrier. In the second part, we study one-time signature schemes that resist quantum attacks. These schemes belong to the hash-based and code based classes. Our contribution in this part is a new code-based one-time signature scheme. In the third part, we give an overview of differential fault analysis, and we study one scheme proposed by NSA in 2013 — Simon. Our contribution in this part is an efficient differential fault analysis on Simon.