Integrating post-quantum cryptography (NTRU) in the TLS protocol

Dissertação de mestrado em Computer ScienceWe aim to integrate new “suites”, using post-quantum authentication and encryption tech niques, in the TLS protocol. Namely, this project is dedicated to integrating algorithms belonging to the NTRU family of cryptossystems in the OpenSSL library and in the Python package “Cryptography”. Even though all the algorithms included in this project have already been imple mented as part of their submissions to the NIST Post-Quantum Standartization project, currently there doesn’t seem to exist a way to perform prototyping and testing of these cryp tossystems in real-life use cases, and it would be interesting to create such tools. We also aim to test if these algorithms could be further optimized for speed and efficiency by comparing the reference implementations (submited to NIST and publicly avail able) with our own implementations that perform some required mathematical operations in a very efficient manner (by using specialized number theory libraries).Pretende-se integrar novas “suites” no protocolo TLS que usem técnicas de autenticação e cifra na categoria de técnicas pós-quanticas. Nomeadamente, este projecto é dedicado à integração de algoritmos da família NTRU na biblioteca OPENSSL e na “package” Cryptography para o Python. Apesar de todos os algoritmos contemplados neste projeto já terem sido implementa dos no âmbito da sua submissão ao NIST Post-Quantum Standartization project, actualmente não parece existir forma de testar e prototipar estes criptossistemas em casos de uso realistas, e seria interessante desenvolver ferramentas que o permitam. Pretende-se também aferir se estes algoritmos podem ser optimizados em eficiência e velocidade de execução, comparando as implementações de referência (submetidas ao NIST e disponiveis publicamente) com as nossas implementações, que efectuam algumas operações matemáticas necessárias de forma muito eficiente (com recusro a bibliotecas de teoria de números especializadas)

Applying Grover's algorithm to AES: quantum resource estimates

We present quantum circuits to implement an exhaustive key search for the Advanced Encryption Standard (AES) and analyze the quantum resources required to carry out such an attack. We consider the overall circuit size, the number of qubits, and the circuit depth as measures for the cost of the presented quantum algorithms. Throughout, we focus on Clifford$+T$ gates as the underlying fault-tolerant logical quantum gate set. In particular, for all three variants of AES (key size 128, 192, and 256 bit) that are standardized in FIPS-PUB 197, we establish precise bounds for the number of qubits and the number of elementary logical quantum gates that are needed to implement Grover's quantum algorithm to extract the key from a small number of AES plaintext-ciphertext pairs.Comment: 13 pages, 3 figures, 5 tables; to appear in: Proceedings of the 7th International Conference on Post-Quantum Cryptography (PQCrypto 2016

Quantum Attacks on Modern Cryptography and Post-Quantum Cryptosystems

Cryptography is a critical technology in the modern computing industry, but the security of many cryptosystems relies on the difficulty of mathematical problems such as integer factorization and discrete logarithms. Large quantum computers can solve these problems efficiently, enabling the effective cryptanalysis of many common cryptosystems using such algorithms as Shor’s and Grover’s. If data integrity and security are to be preserved in the future, the algorithms that are vulnerable to quantum cryptanalytic techniques must be phased out in favor of quantum-proof cryptosystems. While quantum computer technology is still developing and is not yet capable of breaking commercial encryption, these steps can be taken immediately to ensure that the impending development of large quantum computers does not compromise sensitive data

Quantum algorithms for problems in number theory, algebraic geometry, and group theory

Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same problem appears to be intractable on classical computers. Understanding what other computational problems can be solved significantly faster using quantum algorithms is one of the major challenges in the theory of quantum computation, and such algorithms motivate the formidable task of building a large-scale quantum computer. This article will review the current state of quantum algorithms, focusing on algorithms for problems with an algebraic flavor that achieve an apparent superpolynomial speedup over classical computation.Comment: 20 pages, lecture notes for 2010 Summer School on Diversities in Quantum Computation/Information at Kinki Universit