Post-quantum key exchange for the TLS protocol from the ring learning with errors problem

Lattice-based cryptographic primitives are believed to offer resilience against attacks by quantum computers. We demonstrate the practicality of post-quantum key exchange by constructing ciphersuites for the Transport Layer Security (TLS) protocol that provide key exchange based on the ring learning with errors (R-LWE) problem; we accompany these ciphersuites with a rigorous proof of security. Our approach ties lattice-based key exchange together with traditional authentication using RSA or elliptic curve digital signatures: the post-quantum key exchange provides forward secrecy against future quantum attackers, while authentication can be provided using RSA keys that are issued by today\u27s commercial certificate authorities, smoothing the path to adoption. Our cryptographically secure implementation, aimed at the 128-bit security level, reveals that the performance price when switching from non-quantum-safe key exchange is not too high. With our R-LWE ciphersuites integrated into the OpenSSL library and using the Apache web server on a 2-core desktop computer, we could serve 506 RLWE-ECDSA-AES128-GCM-SHA256 HTTPS connections per second for a 10 KiB payload. Compared to elliptic curve Diffie--Hellman, this means an 8 KiB increased handshake size and a reduction in throughput of only 21%. This demonstrates that provably secure post-quantum key-exchange can already be considered practical

Frodo: Take off the ring! Practical, quantum-secure key exchange from LWE

Lattice-based cryptography offers some of the most attractive primitives believed to be resistant to quantum computers. Following increasing interest from both companies and government agencies in building quantum computers, a number of works have proposed instantiations of practical post-quantum key exchange protocols based on hard problems in ideal lattices, mainly based on the Ring Learning With Errors (R-LWE) problem. While ideal lattices facilitate major efficiency and storage benefits over their nonideal counterparts, the additional ring structure that enables these advantages also raises concerns about the assumed difficulty of the underlying problems. Thus, a question of significant interest to cryptographers, and especially to those currently placing bets on primitives that will withstand quantum adversaries, is how much of an advantage the additional ring structure actually gives in practice. Despite conventional wisdom that generic lattices might be too slow and unwieldy, we demonstrate that LWE-based key exchange is quite practical: our constant time implementation requires around 1.3ms computation time for each party; compared to the recent NewHope R-LWE scheme, communication sizes increase by a factor of 4.7×, but remain under 12 KiB in each direction. Our protocol is competitive when used for serving web pages over TLS; when partnered with ECDSA signatures, latencies increase by less than a factor of 1.6×, and (even under heavy load) server throughput only decreases by factors of 1.5× and 1.2× when serving typical 1 KiB and 100 KiB pages, respectively. To achieve these practical results, our protocol takes advantage of several innovations. These include techniques to optimize communication bandwidth, dynamic generation of public parameters (which also offers additional security against backdoors), carefully chosen error distributions, and tight security parameters

Integration of post-quantum cryptography in the TLS protocol (LWE Option)

Dissertação de mestrado em Computer ScienceWith the possibility of quantum computers making an appearance, possibly capable of breaking several well established and widespread crytposystems (especially those that implement public key cryptography), necessity has arisen to create new cryptographic algorithms which remain safe even against adversaries using quantum computers. Several algorithms based on different mathematical problems have been proposed which are considered to be hard to solve with quantum computers. In recent years, a new lattice-based mathematical problem called Learning With Errors (and its variant Ring - Learning With Errors) was introduced, and several cryptosystems based on this problem were introduced, some of which are becoming practical enough to compete with traditional schemes that have been used for decades. The primary focus in this work is the implementation of two Ring - Learning With Errors based schemes (one key exchange mechanism and one digital signature scheme) on the TLS protocol via the OpenSSL library as a way of checking their overall viability in real-world scenarios, by comparing them to classical schemes implementing the same functionalities.Com a possibilidade do surgimento dos primeiros computadores quânticos, possivelmente capazes de quebrar muitos dos cripto-sistemas bem difundidos e considerados seguros, tornou-se necessário tomar precauções com a criação de novas técnicas criptográficas que visam manter as suas propriedades de segurança mesmo contra adversários que usem computadores quânticos. Existem já muitas propostas de algoritmos baseados em problemas matemáticos distintos que são considerados difíceis de resolver recorrendo a computadores quânticos. Recentemente, foi introduzido um novo problema baseado em reticulados denominado de Learning With Errors (e a sua variante Ring - Learning With Errors), e consequentemente foram propostos vários cripto-sistemas baseados nesse problema, alguns dos quais começam já a ser utilizáveis ao ponto de poderem ser comparados com os esquemas clássicos usados há décadas. O foco principal neste trabalho é a implementação de dois esquemas baseados no problema Ring - Learning With Errors (mais precisamente, um esquema de troca de chaves e uma assinatura digital) no protocolo TLS através da sua integração no OpenSSL como forma de verificar a sua viabilidade em contextos reais, comparando-os com esquemas clássicos que implementem as mesmas funcionalidades

Frodo: Take off the ring! Practical, Quantum-Secure Key Exchange from LWE

Lattice-based cryptography offers some of the most attractive primitives believed to be resistant to quantum computers. Following increasing interest from both companies and government agencies in building quantum computers, a number of works have proposed instantiations of practical post-quantum key exchange protocols based on hard problems in ideal lattices, mainly based on the Ring Learning With Errors (R-LWE) problem. While ideal lattices facilitate major efficiency and storage benefits over their non-ideal counterparts, the additional ring structure that enables these advantages also raises concerns about the assumed difficulty of the underlying problems. Thus, a question of significant interest to cryptographers, and especially to those currently placing bets on primitives that will withstand quantum adversaries, is how much of an advantage the additional ring structure actually gives in practice. Despite conventional wisdom that generic lattices might be too slow and unwieldy, we demonstrate that LWE-based key exchange is quite practical: our constant time implementation requires around 1.3ms computation time for each party; compared to the recent NewHope R-LWE scheme, communication sizes increase by a factor of 4.7$\times$, but remain under 12 KiB in each direction. Our protocol is competitive when used for serving web pages over TLS; when partnered with ECDSA signatures, latencies increase by less than a factor of 1.6$\times$, and (even under heavy load) server throughput only decreases by factors of 1.5$\times$ and 1.2$\times$ when serving typical 1 KiB and 100 KiB pages, respectively. To achieve these practical results, our protocol takes advantage of several innovations. These include techniques to optimize communication bandwidth, dynamic generation of public parameters (which also offers additional security against backdoors), carefully chosen error distributions, and tight security parameters

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)

Ring Learning With Errors: A crossroads between postquantum cryptography, machine learning and number theory

The present survey reports on the state of the art of the different cryptographic functionalities built upon the ring learning with errors problem and its interplay with several classical problems in algebraic number theory. The survey is based to a certain extent on an invited course given by the author at the Basque Center for Applied Mathematics in September 2018.Comment: arXiv admin note: text overlap with arXiv:1508.01375 by other authors/ comment of the author: quotation has been added to Theorem 5.

CRYSTALS - Kyber: A CCA-secure Module-Lattice-Based KEM

Rapid advances in quantum computing, together with the announcement by the National Institute of Standards and Technology (NIST) to define new standards for digital-signature, encryption, and key-establishment protocols, have created significant interest in post-quantum cryptographic schemes. This paper introduces Kyber (part of CRYSTALS - Cryptographic Suite for Algebraic Lattices - a package submitted to NIST post-quantum standardization effort in November 2017), a portfolio of post-quantum cryptographic primitives built around a key-encapsulation mechanism (KEM), based on hardness assumptions over module lattices. Our KEM is most naturally seen as a successor to the NEWHOPE KEM (Usenix 2016). In particular, the key and ciphertext sizes of our new construction are about half the size, the KEM offers CCA instead of only passive security, the security is based on a more general (and flexible) lattice problem, and our optimized implementation results in essentially the same running time as the aforementioned scheme. We first introduce a CPA-secure public-key encryption scheme, apply a variant of the Fujisaki-Okamoto transform to create a CCA-secure KEM, and eventually construct, in a black-box manner, CCA-secure encryption, key exchange, and authenticated-key-exchange schemes. The security of our primitives is based on the hardness of Module-LWE in the classical and quantum random oracle models, and our concrete parameters conservatively target more than 128 bits of post-quantum security

CRYSTALS - Kyber: A CCA-secure Module-Lattice-Based KEM

Rapid advances in quantum computing, together with the announcement by the National Institute of Standards and Technology (NIST) to define new standards for digitalsignature, encryption, and key-establishment protocols, have created significant interest in post-quantum cryptographic schemes. This paper introduces Kyber (part of CRYSTALS - Cryptographic Suite for Algebraic Lattices - a package submitted to NIST post-quantum standardization effort in November 2017), a portfolio of post-quantum cryptographic primitives built around a key-encapsulation mechanism (KEM), based on hardness assumptions over module lattices. Our KEM is most naturally seen as a successor to the NEWHOPE KEM (Usenix 2016). In particular, the key and ciphertext sizes of our new construction are about half the size, the KEM offers CCA instead of only passive security, the security is based on a more general (and flexible) lattice problem, and our optimized implementation results in essentially the same running time as the aforementioned scheme. We first introduce a CPA-secure public-key encryption scheme, apply a variant of the Fujisaki-Okamoto transform to create a CCA-secure KEM, and eventually construct, in a black-box manner, CCA-secure encryption, key exchange, and authenticated-key-exchange schemes. The security of our primitives is based on the hardness of Module-LWE in the classical and quantum random oracle models, and our concrete parameters conservatively target more than 128 bits of postquantum security

Post-Quantum Key Exchange for the Internet and the Open Quantum Safe Project

Designing public key cryptosystems that resist attacks by quantum computers is an important area of current cryptographic research and standardization. To retain confidentiality of today\u27s communications against future quantum computers, applications and protocols must begin exploring the use of quantum-resistant key exchange and encryption. In this paper, we explore post-quantum cryptography in general and key exchange specifically. We review two protocols for quantum-resistant key exchange based on lattice problems: BCNS15, based on the ring learning with errors problem, and Frodo, based on the learning with errors problem. We discuss their security and performance characteristics, both on their own and in the context of the Transport Layer Security (TLS) protocol. We introduce the Open Quantum Safe project, an open-source software project for prototyping quantum-resistant cryptography, which includes liboqs, a C library of quantum-resistant algorithms, and our integrations of liboqs into popular open-source applications and protocols, including the widely used OpenSSL library