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 cipher suites for the Transport Layer Security (TLS) protocol that provide key exchange based on the ring learning with errors (R-LWE) problem, we accompany these cipher suites 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's 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 cipher suites integrated into the Open SSL 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.
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 cipher suites for the Transport Layer Security (TLS) protocol that provide key exchange based on the ring learning with errors (R-LWE) problem, we accompany these cipher suites 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's 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 cipher suites integrated into the Open SSL 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.
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 cipher suites for the Transport Layer Security (TLS) protocol that provide key exchange based on the ring learning with errors (R-LWE) problem, we accompany these cipher suites 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's 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 cipher suites integrated into the Open SSL 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.
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 4.7x, 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 1.6x, and (even under heavy load) server throughput only decreases by factors of 1.5x and 1.2x 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.
The advancement of quantum computing poses a significant threat to classical cryptographic algorithms, particularly those based on factorization and discrete logarithm problems. In this paper, we propose a secure and quantum-resistant key exchange scheme leveraging the FrodoKEM algorithm, a lattice-based post-quantum key encapsulation mechanism designed to resist attacks from quantum adversaries. FrodoKEM, being based on the Learning with Errors (LWE) problem, offers a conservative and standard approach to post-quantum cryptography without relying on structured lattices. We compare the performance and security of the proposed scheme against traditional key exchange mechanisms such as RSA and Elliptic Curve Diffie-Hellman (ECDH), as well as other post-quantum algorithms like Kyber and NTRU. Our analysis demonstrates that FrodoKEM offers improved security assurances and competitive performance metrics, especially in environments where long-term confidentiality and forward secrecy are critical. The experimental results affirm FrodoKEM's suitability for real-world deployment in post-quantum secure communications.
With 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.
The necessity of a secure key exchange protocol arises from the critical need to establish encrypted communication over an untrusted network. Over time, a multitude of key exchange mechanisms have been developed to counteract adversarial threats. The Diffie-Hellman key exchange protocol (DHKE) is one of the most widely used protocols for symmetric key sharing. However, this protocol exhibits certain inherent limitations that attackers may exploit. It lacks authentication mechanism and is susceptible to Man-in-the-Middle (MITM) attacks and quantum attacks. To mitigate these vulnerabilities, we have designed a hybrid key exchange protocol combining DHKE with Learning With Errors (LWE), a lattice-based post-quantum primitive. This proposed protocol provides authentication via a Public Key Infrastructure (PKI) together with CRYSTALS-Dilithium digital signature, resilience against MITM attacks, and robustness against classical and quantum threats. We have done a security analysis using the Dolev-Yao threat model, extended to quantum-equipped attackers, and showed that the protocol achieves mutual authentication, session key secrecy, and forward secrecy under the hardness of LWE and DHKE. Lastly, we provided detailed parameter recommendations based on NIST standards and shed light on side-channel attacks.
The advent of quantum computing poses a significant existential threat to current public-key cryptographic systems, most notably RSA and Elliptic Curve Cryptography (ECC), which rely on the presumed hardness of integer factorization and discrete logarithm problems. Shor's algorithm, a quantum algorithm, can efficiently solve these problems, rendering classical asymmetric primitives insecure. This paper addresses the imperative need for post-quantum cryptography (PQC) by exploring lattice-based constructs as robust alternatives for asymmetric primitives. We provide a comprehensive overview of the fundamental mathematical problems underlying lattice-based cryptography, such as the Shortest Vector Problem (SVP), Closest Vector Problem (CVP), Learning With Errors (LWE), and Ring Learning With Errors (RLWE). The paper surveys prominent lattice-based schemes, including NTRU, CRYSTALS-Kyber, and CRYSTALS-Dilithium, analyzing their security foundations, performance characteristics, and the extent to which they offer a viable "post-quantum RSA." We delve into the methodology of constructing these primitives, discuss their resilience against both classical and quantum attacks, and evaluate their practical implications for key sizes, computational efficiency, and deployment challenges. Our analysis highlights that lattice-based cryptography, particularly the NIST-standardized schemes, presents a strong candidate for securing digital communications in the quantum era, offering provable security rooted in worst-case to average-case reductions for lattice problems.