Communication Locality in Secure Multi-party Computation

Motivated by new applications such as secure Multi-Party Computation (MPC), Fully Homomorphic Encryption (FHE), and Zero-Knowledge proofs (ZK), many MPC-, FHE- and ZK-friendly symmetric-key primitives that minimize the< number of multiplications over Fp for a large prime p have been recently proposed in the literature. These symmetric primitives are usually defined via invertible functions, including (i) Feistel and Lai-Massey schemes and (ii) SPN constructions instantiated with invertible non-linear S-Boxes. However, the “invertibility” property is actually never required in any of the mentioned applications.In this paper, we discuss the possibility to set up MPC-/FHE-/ZK-friendly symmetric primitives instantiated with non-invertible bounded surjective functions. In contrast to one-to-one functions, each output of a l-bounded surjective function admits at most l pre-images. The simplest example is the square map x → x2 over Fp for a prime p ≥ 3, which is (obviously) 2-bounded surjective. When working over Fnp for n ≥ 2, we set up bounded surjective functions by re-considering the recent results proposed by Grassi, Onofri, Pedicini and Sozzi at FSE/ToSC 2022 as starting points. Given a quadratic local map F : Fmp → Fp for m ∈ {1, 2, 3}, they proved that the shift-invariant non-linear function over Fnp defined as SF (x0, x1, . . . , xn−1) = y0∥y1∥ . . . ∥yn−1 where yi := F(xi, xi+1) is never invertible for any n ≥ 2 · m − 1. Here, we prove that • the quadratic function F : Fmp → Fp for m ∈ {1, 2} that minimizes the probability of having a collision for SF over Fnp is of the form F(x0, x1) = x20 + x1 (or equivalent);• the function SF over Fnp defined as before via F(x0, x1) = x20 +x1 (or equivalent) is 2n-bounded surjective.As concrete applications, we propose modified versions of the MPC-friendly schemes MiMC, HadesMiMC, and (partially of) Hydra, and of the FHE-friendly schemes Masta, Pasta, and Rubato. By instantiating them with the bounded surjective quadratic functions proposed in this paper, we are able to improve the security and/or the performances in the target applications/protocols.

With the wide adoption of cloud computing paradigm, it is important to develop appropriate techniques to protect client data privacy in the cloud. Encryption is one of the major techniques that could be used to achieve this goal. However, data encryption at the rest alone is insufficient for secure cloud computation environments. There is also the need for efficient techniques to carry out computation over encrypted data. Fully homomorphic encryption (FHE) and garbled circuits are naturally used to process encrypted data without leaking any information about the data. However, existing FHE schemes are inefficient for processing large amount of data in cloud and garbled circuits are one time programs and cannot be reused. Based on quaternion/octonion algebra and Jordan algebra over finite rings \(\mathbb {Z}_q\), this paper designs efficient fully homomorphic symmetric key encryption (FHE) schemes without bootstrapping (that is, noise-free FHE schemes) that are secure in the weak ciphertext-only security model assuming the hardness of solving multivariate quadratic equation systems and solving univariate high degree polynomial equation systems in \(\mathbb {Z}_q\). The FHE scheme designed in this paper is sufficient for privacy preserving computation in cloud.

Multi‐key fully homomorphic encryption (MKFHE) allows computations on ciphertexts encrypted by different users, which can be applied to implement secure multi‐party computing (MPC). The current NTRU‐based MKFHE has the following two drawbacks: One is that the relinearisation process during homomorphic evaluation is so complicated that the corresponding computation time is costly. The other is that a class of subfield attacks are proposed and affects the security of NTRU schemes over power‐of‐2 cyclotomic rings for large moduli q, especially for the NTRU‐based fully homomorphic encryption (FHE) schemes. In this work, an efficient MKFHE scheme is proposed over prime cyclotomic rings with fewer relinearisations, which seems a good choice because of its potential to resist a subfield attack. More specifically, the time of the relinearisation process is reduced by half in homomorphic evaluations by separating the homomorphic multiplication and the relinearisation process (implementing two homomorphic multiplication operations together before relinearisation), while in current NTRU‐type MKFHE schemes, these two processes are usually performed together. The error bound of the basic function components is re‐analysed over prime cyclotomic rings in the average case, which can be used in the error analysis of our scheme. We construct an efficient NTRU‐based single‐key FHE scheme and an efficient MKFHE scheme over prime cyclotomic rings through relinearisation and modulus‐switching techniques. The MKFHE scheme proposed has the on‐the‐fly property and has a tight ciphertext size compared with the GSW‐type and BGV‐type MKFHE schemes. An experiment shows that the homomorphic evaluation of the optimised single‐key FHE scheme proposed is 1.9 times faster than an efficient NTRU‐type MKFHE DHS16 proposed at DCC 2016.

To tackle emerging security and privacy concerns in consortium blockchain applications, particularly in handling sensitive identity information and transaction data, a novel privacy-preserving framework is proposed. The scheme leverages advanced technologies such as post-quantum cryptography, multi-party computation (MPC), and fully homomorphic encryption (FHE) to enhance security and efficiency. Firstly, a quantum-resistant blind signature mechanism is designed using lattice-based cryptography to mitigate centralization issues and strengthen security against quantum attacks. Secondly, a regulatory-compliant hierarchical encryption model is developed using fully homomorphic encryption, enabling fine-grained access control and data integrity verification without decrypting sensitive data. Additionally, zero-knowledge succinct non-interactive arguments of knowledge (zk-SNARKs) are integrated to ensure privacy while allowing verifiable computation. Experimental evaluations demonstrate that the proposed scheme achieves high encryption efficiency, reduced computational overhead during encryption/decryption, and strong resistance to malicious activities such as tampering, eavesdropping, and replay attacks

Fully homomorphic encryption (FHE) is a "holy grail" of cryptography. However, it is not yet adopted in practice because no known scheme is efficient. In this paper, we mainly focus on how to reduce the public key sizes in FHE. Based on Dijk et al.'s FHE scheme (DGHV) and Gentry's fully homomorhpic technology, we propose two schemes with shorter public keys by encrypting with a combination of the public key elements to replace a linear form in DGHV scheme and a quadratic form in Coron et al.'s scheme. Compared with DGHV scheme and Coron et al.'s scheme, our schemes can greatly reduce the public key sizes, which make our schemes more efficient. Furthermore, we prove the security of our schemes based on difficulties of the approximate greatest common divisor (AGCD) problem and the sparse subset sum problem.

Fully Homomorphic Encryption (FHE) allows computations on encrypted data without decryption, providing strong security for sensitive information. However, computational and memory demands for FHE are significant challenges, particularly in the Number Theoretic Transform (NTT) phase. This paper presents three efficient Twiddle Factor Generators (TFGs) to address these challenges: the Half-Memory TFG, the On-the-fly Serial TFG, and the On-the-fly Parallel TFG. The Half-Memory TFG reduces memory usage by storing only half of the twiddle factors and calculating the rest as needed. The On-the-fly Serial TFG eliminates memory requirements by computing twiddle factors, while the On-the-fly Parallel TFG enhances computational speed through parallel processing. Implemented on the FPGA KCU105 board, these TFGs demonstrated significant improvements in hardware resource utilization and computational efficiency. The Half-Memory TFG effectively reduces memory footprint, the On-the-fly Serial TFG eliminates memory usage with acceptable computational overhead, and the On-the-fly Parallel TFG offers superior performance for high-throughput applications. These innovations make FHE more practical for real-world applications, contributing to the broader goal of enabling secure, privacy-preserving computations on encrypted data.

Fully Homomorphic Encryption (FHE) is pivotal for secure computation on encrypted data, crucial in privacy-preserving data analysis. However, efficiently processing high-dimensional data in FHE, especially for machine learning and statistical (ML/STAT) algorithms, poses a challenge. In this paper, we present an effective acceleration method using the kernel method for FHE schemes, enhancing time performance in ML/STAT algorithms within encrypted domains. This technique, independent of underlying FHE mechanisms and complementing existing optimizations, notably reduces costly FHE multiplications, offering near-constant time complexity relative to data dimension. Aimed at accessibility, this method is tailored for data scientists and developers with limited cryptography background, facilitating advanced data analysis in secure environments.

With the widespread adoption of Electronic Health Records (EHRs), ensuring data privacy while enabling efficient sharing and processing has emerged as a critical challenge in healthcare information systems. Existing approaches often struggle to balance stringent security requirements with practical performance needs. To address these challenges, this paper proposes a blockchain-based privacy protection scheme for EHRs that integrates Designated Verifier Aggregate Signatures (DVAS) and Fully Homomorphic Encryption (FHE). In the proposed scheme, healthcare institutions manage EHRs through smart contracts, while FHE is employed to encrypt and protect sensitive medical data used in research. By selectively applying FHE to critical data and minimizing encryption overhead for non-sensitive information, our design significantly enhances computational efficiency and storage performance. Furthermore, the DVAS algorithm minimizes redundant data transmission, ensures data integrity, and restricts signature verification to authorized parties only. Experimental evaluations based on computational time, storage cost, and security analysis demonstrate that the proposed scheme achieves robust security while meeting performance requirements, effectively balancing confidentiality and efficiency in healthcare information systems.

With the emerging techniques of wireless communication and cloud computing, large volumes of multimedia data are outsourced from resource constrained users to the cloud with abundant resource for both delegated storage and computation. Unfortunately, there is a risk of users’ image privacy leakage in the process of outsourcing to untrusted cloud. Most of the existing work achieved privacy-preserving image feature extraction and matching by using public key (fully) homomorphic encryption (FHE), but the heavy computational overhead and communication overhead cannot adapt to resource-constrained mobile devices. Other works disabled to realize image denoising in the encrypted domain or only focused on the scale-invariant feature transform (SIFT) descriptor that is inappropriate for position-sensitive feature extraction. To address these issues, in this paper, a privacy-preserving shape context based image denoising and matching protocol PPOIM with efficient outsourcing is proposed. Firstly, to improve the accuracy of image matching, a privacy-preserving image denoising scheme PPID is proposed without exploiting public key FHE. Then, based on PPID, a privacy-preserving image matching protocol PPOIM adopting shape context descriptor is devised, where two secure and efficient comparison and counting protocols in the encrypted domain are presented. All the original image privacy, query image privacy and image matching result privacy are well protected. Finally, formal security proof and extensive simulations on real-world data sets demonstrate the efficiency and practicability of our proposed PPOIM.

Adopting mobile healthcare network (MHN) services such as disease detection is fraught with concerns about the security and privacy of the entities involved and the resource restrictions at the Internet of Things (IoT) nodes. Hence, the essential requirements for disease detection services are to (i) produce accurate and fast disease detection without jeopardizing the privacy of health clouds and medical users and (ii) reduce the computational and transmission overhead (energy consumption) of the IoT devices while maintaining the privacy. For privacy preservation of widely used neural network– (NN) based disease detection, existing literature suggests either computationally heavy public key fully homomorphic encryption (FHE), or secure multiparty computation, with a large number of interactions. Hence, the existing privacy-preserving NN schemes are energy consuming and not suitable for resource-constrained IoT nodes in MHN. This work proposes a lightweight, fully homomorphic, symmetric key FHE scheme (SkFhe) to address the issues involved in implementing privacy-preserving NN. Based on SkFhe, widely used non-linear activation functions ReLU and Leaky ReLU are implemented over the encrypted domain. Furthermore, based on the proposed privacy-preserving linear transformation and non-linear activation functions, an energy-efficient, accurate, and privacy-preserving NN is proposed. The proposed scheme guarantees privacy preservation of the health cloud’s NN model and medical user’s data. The experimental analysis demonstrates that the proposed solution dramatically reduces the overhead in communication and computation at the user side compared to the existing schemes. Moreover, the improved energy efficiency at the user is accomplished with reduced diagnosis time without sacrificing classification accuracy.

Recommender systems facilitate personalized service provision through the statistical analysis and model training of user historical data (e.g., browsing behavior, travel history, etc). To address the underpinning privacy implications associated with such systems, a number of privacy-preserving recommendation approaches have been presented. There are, however, limitations in many of these approaches. For example, approaches that apply public key (fully) homomorphic encryption (FHE) on different users. historical ratings under a unique public key of a target recommendation user incur significant computational overheads on resource-constrained local users and may not be scalable. On the other hand, approaches without utilizing public key FHE can neither resist chosen ciphertext attack (CCA), nor be straightforwardly applied to the setting of distributed servers. In this paper, a lightweight privacy-preserving distributed recommender system is proposed. Specifically, we present a new cryptographic primitive (i.e., tag-based multikey fully homomorphic data encapsulation mechanism; TMFH-DEM) designed to achieve CCA security for both input privacy and result privacy. TMFH-DEM enables a set of distributed servers to collaboratively execute efficient privacy-preserving outsourced computation on multiple inputs encrypted under different secret keys from different data owners, without using public key FHE. Building on TMFH-DEM, we propose a lightweight privacy-preserving distributed recommender system, which flexibly returns all the recommended items with certain predicted ratings for all target users. Formal security proof shows that our proposal achieves both user historical rating data privacy and recommendation result privacy. Findings from our evaluations demonstrate its practicability in terms of scalability, recommendation accuracy, computational and communication efficiency.

Progress in the areas of multi-party computation (MPC) and fully homomorphic encryption (FHE) caused the demand of new design strategies, that minimize the number of multiplications in symmetric primitives. Rasta is an approach for a family of stream ciphers with an exceptional low AND depth, which equals the number of ANDs per encrypted bit. This is achieved in particular by randomizing parts of the computation with the help of a PRNG, implying that the security arguments rely on the provided randomness and the encryption/ decryption is potentially slowed down by this generation.In this paper we propose a variant of Rasta that achieves the same performance with respect to the AND depth and the number of ANDs per encrypted bit, but does not rely on a PRNG, i.e. is based on fixed linear layers.

The chapter outlines a range of advanced techniques in cryptography that build on basic primitives like encryption and digital signatures that have been explained in earlier chapters. These advanced techniques may at present be solely in the realm of academic cryptography, but possible real-world applications and deployments are also highlighted. Topics considered include the idea of a trusted third party, leading to the presentation of identity-based and attribute-based encryption. Privacy-enhancing technologies (PETs) including fully homomorphic encryption (FHE), secure multi-party computation (MPC), and differential privacy are discussed. Advanced signature schemes including blind signatures and ring signatures are also mentioned.

Problem statement: A cryptosystem is a way for a sender and a receiver to communicate digitally by which the sender can send receiver any confidential or private message by first encrypting it using the receiver’s public key. Upon receiving the encrypted message, the receiver can confirm the originality of the message’s contents using his own secret key. Up to now, most of the existing cryptosystems were developed based on a single cryptographic assumption like factoring, discrete logarithms, quadratic residue or elliptic curve discrete logarithm. Although these schemes remain secure today, one day in a near future they may be broken if one finds a polynomial algorithm that can efficiently solve the underlying cryptographic assumption. Approach: By this motivation, we designed a new cryptosystem based on two cryptographic assumptions; quadratic residue and discrete logarithms. We integrated these two assumptions in our encrypting and decrypting equations so that the former depends on one public key whereas the latter depends on one corresponding secret key and two secret numbers. Each of public and secret keys in our scheme determines the assumptions we use. Results: The newly developed cryptosystem is shown secure against the three common considering algebraic attacks using a heuristic security technique. The efficiency performance of our scheme requires 2Texp+2Tmul +Thash time complexity for encryption and Texp+2Tmul +Tsrt time complexity for decryption and this magnitude of complexity is considered minimal for multiple cryptographic assumptions-like cryptosystems. Conclusion: The new cryptosystem based on multiple cryptographic assumptions offers a greater security level than that schemes based on a single cryptographic assumption. The adversary has to solve the two assumptions simultaneously to recover the original message from the received corresponding encrypted message but this is very unlikely to happen.

Ciminion is a symmetric cryptographic algorithm proposed by Dobraunig et al. in EUROCRYPT 2021, which is based on Toffoli-Gates over \(\mathbb {F}_{2^n}\) or \(\mathbb {F}_p\). This cipher is a multiparty computation (MPC), fully-homomorphic encryption (FHE) and zero-knowledge (ZK) friendly symmetric-key primitive due to its low multiplicative complexity. There is currently no published third-party cryptanalysis of this algorithm. In this paper, we give the first analysis on Ciminion based on higher order differential cryptanalysis and integral cryptanalysis. We consider the three sets of instances, i.e., “standard” set, “conservative” set and the instances used in MPC application, and construct the corresponding reduced-round distinguishers over \(\mathbb {F}_{2^n}\) and \(\mathbb {F}_p\), respectively. On the other hand, we observe a linear relation between the input and output of the round function and conclude a new set of weak random numbers based on this observation. For an aggressive evolution of Ciminion called Aiminion, we recover the subkeys under these weak random numbers. Although we cannot recover the master key, the information disclosure of the subkeys also poses certain potential threats to the cryptographic algorithm. Our results can provide guidance for designers to choose round random numbers.KeywordsCiminionAiminionHigher order differential cryptanalysisIntegral cryptanalysisDistinguisherWeak random numbers