We introduce the first candidate Lattice-based designated verifier (DV) zero knowledge sUccinct Non-interactive Argument (ZK-SNARG) protocol, named LUNA, with quasi-optimal proof length (quasi-linear in the security/privacy parameter). By simply relying on mildly stronger security assumptions, LUNA is also a candidate ZK-SNARK (i.e. argument of knowledge). LUNA achieves significant improvements in concrete proof sizes, reaching below 6 KB (compared to >32 KB in prior work) for 128-bit security/privacy level. To achieve our quasi-optimal succinct LUNA, we give a new regularity result for 'private' re-randomization of Module LWE (MLWE) samples using discrete Gaussian randomization vectors, also known as a lattice-based leftover hash lemma with leakage, which applies with a discrete Gaussian re-randomization parameter that is polynomial in the statistical privacy parameter (avoiding exponential smudging), and hides the coset of the re-randomization vector support set. Along the way, we derive bounds on the smoothing parameter of the intersection of short integer solution (SIS), gadget, and Gaussian perp module lattices over the power of 2 cyclotomic rings. We then introduce a new candidate linear-only homomorphic encryption scheme called Module Half-GSW (HGSW), and apply our regularity theorem to provide smudging-free circuit-private homomorphic linear operations for Module HGSW. Our implementation and experimental performance evaluation show that, for typical instance sizes, Module HGSW provides favourable performance for ZK-SNARG applications involving lightweight verifiers. It enables significantly (around 5x) shorter proof lengths while speeding up CRS generation and encryption time by 4-16x and speeding up decryption time by 4.3x, while incurring just 1.2-2x time overhead in linear homomorphic proof generation operations, compared to a Regev encryption used in prior work in the ZK-SNARG context. We believe our techniques are of independent interest and will find application in other privacy-preserving lattice-based protocols.

Quantum computers are believed to be capable of breaking the security of most classical public key cryptosystems. To mitigate future security risks, researchers have been working on a hybrid approach that uses both classical and post-quantum cryptographic techniques, with the aim of keeping the system secure as long as at least one of the cryptosystems remains secure. However, most existing hybrid cryptosystems require protocol revisions to accommodate post-quantum cryptographic algorithms, leading to extensive modifications of existing code-bases and increased complexity in the state machines. In this paper, we explore a novel generic hybrid model that requires only minimal changes to the codebase of a classical cryptosystem while maintaining the simplicity of the state machines. To illustrate the working principle and provide a benchmark for our generic hybrid model, we conduct a case study on the IKEv2 protocol using the strongS wan library. Our benchmark reveals that, in a hybrid configuration with two protocols, our generic model introduces minimal overhead compared to the combined key exchange time of both protocols. Moreover, our model design allows for the initiation of different protocols in parallel, resulting in an acceleration of the key exchange time, particularly in hybrid configurations Involving more than two protocols.

The United Kingdom (UK) government is considering advanced primitives such as identity-based encryption (IBE) for adoption as they transition their public-safety communications network from TETRA to an LTE-based service. However, the current LTE standard relies on elliptic-curve-based IBE, which will be vulnerable to quantum computing attacks, expected within the next 20–30 years. Lattices can provide quantum-safe alternatives for IBE. These schemes have shown promising results in terms of practicality. To date, several IBE schemes over lattices have been proposed, but there has been little in the way of practical evaluation. This paper provides the first complete optimised practical implementation and benchmarking of Latte, a promising Hierarchical IBE (HIBE) scheme proposed by the UK National Cyber Security Centre (NCSC) in 2017 and endorsed by European Telecommunications Standards Institute (ETSI). We propose optimisations for the KeyGen, Delegate, Extract and Gaussian sampling components of Latte, to increase attack costs, reduce decryption key lengths by 2x–3x, ciphertext sizes by up to 33%, and improve speed. In addition, we conduct a precision analysis, bounding the Rényi divergence of the distribution of the real Gaussian sampling procedures from the ideal distribution in corroboration of our claimed security levels. Our resulting implementation of the Delegate function takes 0.4 seconds at 80-bit security level on a desktop machine at 4.2GHz, significantly faster than the order of minutes estimated in the ETSI technical report. Furthermore, our optimised Latte Encrypt/Decrypt implementation reaches speeds up to 9.7x faster than the ETSI implementation.

The US National Institute of Standards and Technology initiated a standardization process for post-quantum cryptography in 2017, with the aim of selecting key encapsulation mechanisms and signature schemes that can withstand the threat from emerging quantum computers. In 2022, Falcon was selected as one of the standard signature schemes, eventually attracting effort to optimize the implementation of Falcon on various hardware architectures for practical applications. Recently, Mitaka was proposed as an alternative to Falcon, allowing parallel execution of most of its operations. These recent advancements motivate us to develop high throughput implementations of Falcon and Mitaka signature schemes on Graphics Processing Units (GPUs), a massively parallel architecture widely available on cloud service platforms. In this paper, we propose the first parallel implementation of Falcon on various GPUs. An iterative version of the sampling process in Falcon, which is also the most time-consuming Falcon operation, was developed. This allows us to implement Falcon signature generation without relying on expensive recursive function calls on GPUs. In addition, we propose a parallel random samples generation approach to accelerate the performance of Mitaka on GPUs. We evaluate our implementation techniques on state-of-the-art GPU architectures (RTX 3080, A100, T4 and V100). Experimental results show that our Falcon-512 implementation achieves 58,595 signatures/second and 2,721,562 verifications/second on an A100 GPU, which is$20.03\times$and$29.51\times$faster than the highly optimized AVX2 implementation on CPU. Our Mitaka implementation achieves 161,985 signatures/second and 1,421,046 verifications/second on the same GPU. Due to the adoption of a parallelizable sampling process, Mitaka signature generation enjoys$\approx 2$–$20 \times$higher throughput than Falcon on various GPUs. The high throughput signature generation and verification achieved by this work can be very useful in various emerging applications, including the Internet of Things.

In this work, we study the blockchain leader election problem. The purpose of such protocols is to elect a leader who decides on the next block to be appended to the blockchain, for each block proposal round. Solutions to this problem are vital for the security of blockchain systems. We introduce an efficient blockchain leader election method with security based solely on standard assumptions for cryptographic hash functions (rather than public-key cryptographic assumptions) and that does not involve a racing condition as in Proof-of-Work based approaches. Thanks to the former feature, our solution provides the highest confidence in security, even in the post-quantum era. A particularly scalable application of our solution is in the Proof-of-Stake setting, and we investigate our solution in the Algorand blockchain system. We believe our leader election approach can be easily adapted to a range of other blockchain settings.

Post-Quantum cryptography (PQC), in the past few years, constitutes the main driving force of the quantum resistance transition for security primitives, protocols and tools. TLS is one of the widely used security protocols that needs to be made quantum safe. However, PQC algorithms integration into TLS introduce various implementation overheads compared to traditional TLS that in battery powered embedded devices with constrained resources, cannot be overlooked. While there exist several works, evaluating the PQ TLS execution time overhead in embedded systems there are only a few that explore the PQ TLS energy consumption cost. In this paper, a thorough power/energy consumption evaluation and analysis of PQ TLS 1.3 on embedded systems has been made. A WolfSSL PQ TLS 1.3 custom implementation is used that integrates all the NIST PQC algorithms selected for standardisation as well as 2 out of 3 of those evaluated in NIST Round 4. Also 1 out of 2 of the BSI recommendations have been included. The PQ TLS 1.3 with the various PQC algorithms is deployed in a STM Nucleo evaluation board under a mutual and a unilateral client-server authentication scenario. The power and energy consumption collected results are analyzed in detail. The performed comparisons and overall analysis provide very interesting results indicating that the choice of the PQC algorithms in TLS 1.3 to be deployed on an embedded system may be very different depending on the device use as an authenticated or not authenticated, client or server. Also, the results indicate that in some cases, PQ TLS 1.3 implementations can be equally or more energy consumption efficient compared to traditional TLS 1.3.

We introduce MatRiCT+, a practical private blockchain payment protocol based on “post-quantum” lattice assumptions. MatRiCT+builds on MatRiCT due to Esgin et al. (ACM CCS’19) and, in general, follows the Ring Confidential Transactions (RingCT) approach used in Monero, the largest privacy-preserving cryptocurrency. In terms of the practical aspects, MatRiCT+has 2-18× shorter proofs (depending on the number of input accounts, M) and runs 3-11× faster (for a typical transaction) in comparison to MatRiCT. A significant advantage of MatRiCT+is that the proof length’s dependence on M is very minimal (only O(logM)), while MatRiCT has a proof length linear in M. To support its efficiency, we devise several novel techniques in our design of MatRiCT+to achieve compact lattice-based zeroknowledge proof systems, exploiting the algebraic properties of power-of-2 cyclotomic rings commonly used in practical latticebased cryptography. Along the way, we design a family of “optimal” challenge spaces, using a technique we call partition-and-sample, with minimal $\ell_{1}$-norm and invertible challenge differences (with overwhelming probability), while supporting highly-splitting power-of-2 cyclotomic rings. We believe all these results to be widely applicable and of independent interest.

The discrete Gaussian sampler is one of the fundamental tools in implementing lattice-based cryptosystems. However, a naive discrete Gaussian sampling implementation suffers from side-channel vulnerabilities, and the existing countermeasures usually introduce significant overhead in either the running speed or the memory consumption. In this paper, we propose a fast, compact, and constant-time implementation of the binary sampling algorithm, originally introduced in the BLISS signature scheme. Our implementation adapts the Rényi divergence and the transcendental function polynomial approximation techniques. The efficiency of our scheme is independent of the standard deviation, and we show evidence that our implementations are either faster or more compact than several existing constant-time samplers. In addition, we show the performance of our implementation techniques applied to and integrated with two existing signature schemes: qTesla and Falcon. On the other hand, the convolution theorems are typically adapted to sample from larger standard deviations, by combining samples with much smaller standard deviations. As an additional contribution, we show better parameters for the convolution theorems.

We introduce MatRiCT, an efficient RingCT protocol for blockchain confidential transactions, whose security is based on "post-quantum'' (module) lattice assumptions. The proof length of the protocol is around two orders of magnitude shorter than the existing post-quantum proposal, and scales efficiently to large anonymity sets, unlike the existing proposal. Further, we provide the first full implementation of a post-quantum RingCT, demonstrating the practicality of our scheme. In particular, a typical transaction can be generated in a fraction of a second and verified in about 23 ms on a standard PC. Moreover, we show how our scheme can be extended to provide auditability, where a user can select a particular authority from a set of authorities to reveal her identity. The user also has the ability to select no auditing and all these auditing options may co-exist in the same environment. The key ingredients, introduced in this work, of MatRiCT are 1) the shortest to date scalable ring signature from standard lattice assumptions with no Gaussian sampling required, 2) a novel balance zero-knowledge proof and 3) a novel extractable commitment scheme from (module) lattices. We believe these ingredients to be of independent interest for other privacy-preserving applications such as secure e-voting. Despite allowing 64-bit precision for transaction amounts, our new balance proof, and thus our protocol, does not require a range proof on a wide range (such as 32- or 64-bit ranges), which has been a major obstacle against efficient lattice-based solutions. Further, we provide new formal definitions for RingCT-like protocols, where the real-world blockchain setting is captured more closely. The definitions are applicable in a generic setting, and thus are believed to contribute to the development of future confidential transaction protocols in general (not only in the lattice setting).