Enabling Faster Operations for Deeper Circuits in Full RNS Variants of FV-like Somewhat Homomorphic Encryption

Though Fully Homomorphic Encryption (FHE) has been realized, most practical implementations utilize leveled Somewhat Homomorphic Encryption (SHE) schemes, which have limits on the multiplicative depth of the circuits they can evaluate and avoid computationally intensive bootstrapping. Many SHE schemes exist, among which those based on Ring Learning With Error (RLWE) with operations on large polynomial rings are popular. Of these, variants allowing operations to occur fully in Residue Number Systems (RNS) have been constructed. This optimization allows homomorphic operations directly on RNS components without needing to reconstruct numbers from their RNS representation, making SHE implementations faster and highly parallel. In this paper, we present a set of optimizations to a popular RNS variant of the B/FV encryption scheme that allow for the use of significantly larger ciphertext moduli (e.g., thousands of bits) without increased overhead due to excessive numbers of RNS components or computational overhead, as well as computational optimizations. This allows for the use of larger ciphertext moduli, which leads to a higher multiplicative depth with the same computational overhead. Our experiments show that our optimizations yield runtime improvements of up to 4.48 for decryption and 14.68 for homomorphic multiplication for large ciphertext moduli

Homomorphic Encryption for Machine Learning in Medicine and Bioinformatics

Machine learning techniques are an excellent tool for the medical community to analyzing large amounts of medical and genomic data. On the other hand, ethical concerns and privacy regulations prevent the free sharing of this data. Encryption methods such as fully homomorphic encryption (FHE) provide a method evaluate over encrypted data. Using FHE, machine learning models such as deep learning, decision trees, and naive Bayes have been implemented for private prediction using medical data. FHE has also been shown to enable secure genomic algorithms, such as paternity testing, and secure application of genome-wide association studies. This survey provides an overview of fully homomorphic encryption and its applications in medicine and bioinformatics. The high-level concepts behind FHE and its history are introduced. Details on current open-source implementations are provided, as is the state of FHE for privacy-preserving techniques in machine learning and bioinformatics and future growth opportunities for FHE

SoK: New Insights into Fully Homomorphic Encryption Libraries via Standardized Benchmarks

Fully homomorphic encryption (FHE) enables arbitrary computation on encrypted data, allowing users to upload ciphertexts to cloud servers for computation while mitigating privacy risks. Many cryptographic schemes fall under the umbrella of FHE, and each scheme has several open-source implementations with its own strengths and weaknesses. Nevertheless, developers have no straightforward way to choose which FHE scheme and implementation is best suited for their application needs, especially considering that each scheme offers different security, performance, and usability guarantees. To allow programmers to effectively utilize the power of FHE, we employ a series of benchmarks called the Terminator 2 Benchmark Suite and present new insights gained from running these algorithms with a variety of FHE back-ends. Contrary to generic benchmarks that do not take into consideration the inherent challenges of encrypted computation, our methodology is tailored to the secure computational primitives of each target FHE implementation. To ensure fair comparisons, we developed a versatile compiler (called T2) that converts arbitrary benchmarks written in a domain-specific language into identical encrypted programs running on different popular FHE libraries as a backend. Our analysis exposes for the first time the advantages and disadvantages of each FHE library as well as the types of applications most suited for each computational domain (i.e., binary, integer, and floating-point)

Building an Efficient Lattice Gadget Toolkit: Subgaussian Sampling and More

Many advanced lattice cryptography applications require efficient algorithms for inverting the so-called gadget matrices, which are used to formally describe a digit decomposition problem that produces an output with specific (statistical) properties. The common gadget inversion problems are the classical (often binary) digit decomposition, subgaussian decomposition, Learning with Errors (LWE) decoding, and discrete Gaussian sampling. In this work, we build and implement an efficient lattice gadget toolkit that provides a general treatment of gadget matrices and algorithms for their inversion/sampling. The main contribution of our work is a set of new gadget matrices and algorithms for efficient subgaussian sampling that have a number of major theoretical and practical advantages over previously known algorithms. Another contribution deals with efficient algorithms for LWE decoding and discrete Gaussian sampling in the Residue Number System (RNS) representation. We implement the gadget toolkit in PALISADE and evaluate the performance of our algorithms both in terms of runtime and noise growth. We illustrate the improvements due to our algorithms by implementing a concrete complex application, key-policy attribute-based encryption (KP-ABE), which was previously considered impractical for CPU systems (except for a very small number of attributes). Our runtime improvements for the main bottleneck operation based on subgaussian sampling range from 18x (for 2 attributes) to 289x (for 16 attributes; the maximum number supported by a previous implementation). Our results are applicable to a wide range of other advanced applications in lattice cryptography, such as GSW-based homomorphic encryption schemes, leveled fully homomorphic signatures, key-hiding PRFs and other forms of ABE, some program obfuscation constructions, and more

High-Performance VLSI Architectures for Lattice-Based Cryptography

Lattice-based cryptography is a cryptographic primitive built upon the hard problems on point lattices. Cryptosystems relying on lattice-based cryptography have attracted huge attention in the last decade since they have post-quantum-resistant security and the remarkable construction of the algorithm. In particular, homomorphic encryption (HE) and post-quantum cryptography (PQC) are the two main applications of lattice-based cryptography. Meanwhile, the efficient hardware implementations for these advanced cryptography schemes are demanding to achieve a high-performance implementation. This dissertation aims to investigate the novel and high-performance very large-scale integration (VLSI) architectures for lattice-based cryptography, including the HE and PQC schemes. This dissertation first presents different architectures for the number-theoretic transform (NTT)-based polynomial multiplication, one of the crucial parts of the fundamental arithmetic for lattice-based HE and PQC schemes. Then a high-speed modular integer multiplier is proposed, particularly for lattice-based cryptography. In addition, a novel modular polynomial multiplier is presented to exploit the fast finite impulse response (FIR) filter architecture to reduce the computational complexity of the schoolbook modular polynomial multiplication for lattice-based PQC scheme. Afterward, an NTT and Chinese remainder theorem (CRT)-based high-speed modular polynomial multiplier is presented for HE schemes whose moduli are large integers

Cloud-based homomorphic encryption for privacy-preserving machine learning in clinical decision support

While privacy and security concerns dominate public cloud services, Homomorphic Encryption (HE) is seen as an emerging solution that ensures secure processing of sensitive data via untrusted networks in the public cloud or by third-party cloud vendors. It relies on the fact that some encryption algorithms display the property of homomorphism, which allows them to manipulate data meaningfully while still in encrypted form; although there are major stumbling blocks to overcome before the technology is considered mature for production cloud environments. Such a framework would find particular relevance in Clinical Decision Support (CDS) applications deployed in the public cloud. CDS applications have an important computational and analytical role over confidential healthcare information with the aim of supporting decision-making in clinical practice. Machine Learning (ML) is employed in CDS applications that typically learn and can personalise actions based on individual behaviour. A relatively simple-to-implement, common and consistent framework is sought that can overcome most limitations of Fully Homomorphic Encryption (FHE) in order to offer an expanded and flexible set of HE capabilities. In the absence of a significant breakthrough in FHE efficiency and practical use, it would appear that a solution relying on client interactions is the best known entity for meeting the requirements of private CDS-based computation, so long as security is not significantly compromised. A hybrid solution is introduced, that intersperses limited two-party interactions amongst the main homomorphic computations, allowing exchange of both numerical and logical cryptographic contexts in addition to resolving other major FHE limitations. Interactions involve the use of client-based ciphertext decryptions blinded by data obfuscation techniques, to maintain privacy. This thesis explores the middle ground whereby HE schemes can provide improved and efficient arbitrary computational functionality over a significantly reduced two-party network interaction model involving data obfuscation techniques. This compromise allows for the powerful capabilities of HE to be leveraged, providing a more uniform, flexible and general approach to privacy-preserving system integration, which is suitable for cloud deployment. The proposed platform is uniquely designed to make HE more practical for mainstream clinical application use, equipped with a rich set of capabilities and potentially very complex depth of HE operations. Such a solution would be suitable for the long-term privacy preserving-processing requirements of a cloud-based CDS system, which would typically require complex combinatorial logic, workflow and ML capabilities

Gadgets and Gaussians in Lattice-Based Cryptography

This dissertation explores optimal algorithms employed in lattice-based cryptographic schemes. Chapter 2 focuses on optimizing discrete gaussian sampling on "gadget" and algebraic lattices. These gaussian sampling algorithms are used in lattice-cryptography's most efficient trapdoor mechanism for the SIS and LWE problems: "MP12" trapdoors. However, this trapdoor mechanism was previously not optimized and inefficient (or not proven to be statistically correct) for structured lattices (ring-SIS/LWE), lattice-cryptography's most efficient form, where the modulus is often a prime. The algorithms in this chapter achieve optimality in this regime and have (already) resulted in drastic efficiency improvement in independent implementations.Chapter 3 digs deeper into the gadget lattice's associated algorithms. Specifically, we explore efficiently sampling a simple subgaussian distribution on gadget lattices, and we optimize LWE decoding on gadget lattices. These subgaussian sampling algorithms correspond to a randomized bit-decomposition needed in lattice-based schemes with homomorphic properties like fully homomorphic encryption (FHE). Next, we introduce a general class of "Chinese Remainder Theorem" (CRT) gadgets. These gadgets allow advanced lattice-based schemes to avoid multi-precision arithmetic when the applications modulus is larger than 64 bits. The algorithms presented in the first two chapters improve the efficiency of many lattice-based cryptosystems: digital signature schemes, identity-based encryption schemes, as well as more advanced schemes like fully-homomorphic encryption and attribute-based encryption. In the final chapter, we take a closer look at the random matrices used in trapdoor lattices. First, we revisit the constants in the concentration bounds of subgaussian random matrices. Then, we provide experimental evidence for a simple heuristic regarding the singular values of matrices with entries drawn from commonly used distributions in cryptography. Though the proofs in this chapter are dense, cryptographers need a strong understanding of the singular values of these matrices since their maximum singular value determines the concrete security of the trapdoor scheme's underlying SIS problem

Lattice-based digital signature and discrete gaussian sampling

Lattice-based cryptography has generated considerable interest in the last two decades due toattractive features, including conjectured security against quantum attacks, strong securityguarantees from worst-case hardness assumptions and constructions of fully homomorphicencryption schemes. On the other hand, even though it is a crucial part of many lattice-basedschemes, Gaussian sampling is still lagging and continues to limit the effectiveness of this newcryptography. The first goal of this thesis is to improve the efficiency of Gaussian sampling forlattice-based hash-and-sign signature schemes. We propose a non-centered algorithm, with aflexible time-memory tradeoff, as fast as its centered variant for practicable size of precomputedtables. We also use the Rényi divergence to bound the precision requirement to the standarddouble precision. Our second objective is to construct Falcon, a new hash-and-sign signaturescheme, based on the theoretical framework of Gentry, Peikert and Vaikuntanathan for latticebasedsignatures. We instantiate that framework over NTRU lattices with a new trapdoor sampler

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum