An Efficient Solution to The Millionaires\u27 Problem Based on Homomorphic Encryption

We proposed a two-round protocol for solving the Millionaires\u27 Problem in the setting of semi-honest parties. Our protocol uses either multiplicative or additive homomorphic encryptions. Previously proposed protocols used additive or XOR homomorphic encryption schemes only. The computation and communication costs of our protocol are in the same asymptotic order as those of the other efficient protocols. Nevertheless, since multiplicative homomorphic encryption scheme is more efficient than an additive one practically, our construction saves computation time and communication bandwidth in practicality

Improved Secure Integer Comparison via Homomorphic Encryption

Secure integer comparison has been one of the first problems introduced in cryptography, both for its simplicity to describe and for its applications. The first formulation of the problem was to enable two parties to compare their inputs without revealing the exact value of those inputs, also called the Millionaires\u27 problem. The recent rise of fully homomorphic encryption has given a new formulation to this problem. In this new setting, one party blindly computes an encryption of the boolean $(a<b)$ given only ciphertexts encrypting $a$ and $b$. In this paper, we present new solutions for the problem of secure integer comparison in both of these settings. The underlying idea for both schemes is to avoid decomposing the integers in binary in order to improve the performances. Our fully homomorphic based solution is inspired by Bourse et al, and makes use of the fast bootstrapping techniques recently developpedto obtain scalability for large integers while preserving high efficiency. On the other hand, our solution to the original Millionaires\u27 problem is inspired by the protocol of Carlton et al, based on partially homomorphic encryption. We tweak their protocol in order to minimize the number of interactions required, while preserving the advantage of comparing non-binary integers. Both our techniques provide efficient solutions to the problem of secure integer comparison for large (even a-priori unbounded in our first scenario) integers with minimum interaction

Some Efficient Solutions to Yao's Millionaire Problem

We present three simple and efficient protocol constructions to solve Yao's Millionaire Problem when the parties involved are non-colluding and semi-honest. The first construction uses a partially homomorphic Encryption Scheme and is a 4-round scheme using 2 encryptions, 2 homomorphic circuit evaluations (subtraction and XOR) and a single decryption. The second construction uses an untrusted third party and achieves a communication overhead linear in input bit-size with the help of an order preserving function.Moreover, the second construction does not require an apriori input bound and can work on inputs of different bit-sizes. The third construction does not use a third party and, even though, it has a quadratic communication overhead, it is a fairly simple construction.Comment: 17 page

Secret charing vs. encryption-based techniques for privacy preserving data mining

Privacy preserving querying and data publishing has been studied in the context of statistical databases and statistical disclosure control. Recently, large-scale data collection and integration efforts increased privacy concerns which motivated data mining researchers to investigate privacy implications of data mining and how data mining can be performed without violating privacy. In this paper, we first provide an overview of privacy preserving data mining focusing on distributed data sources, then we compare two technologies used in privacy preserving data mining. The first technology is encryption based, and it is used in earlier approaches. The second technology is secret-sharing which is recently being considered as a more efficient approach

Data Mining Applications in Banking Sector While Preserving Customer Privacy

In real-life data mining applications, organizations cooperate by using each other’s data on the same data mining task for more accurate results, although they may have different security and privacy concerns. Privacy-preserving data mining (PPDM) practices involve rules and techniques that allow parties to collaborate on data mining applications while keeping their data private. The objective of this paper is to present a number of PPDM protocols and show how PPDM can be used in data mining applications in the banking sector. For this purpose, the paper discusses homomorphic cryptosystems and secure multiparty computing. Supported by experimental analysis, the paper demonstrates that data mining tasks such as clustering and Bayesian networks (association rules) that are commonly used in the banking sector can be efficiently and securely performed. This is the first study that combines PPDM protocols with applications for banking data mining. Doi: 10.28991/ESJ-2022-06-06-014 Full Text: PD

TFHE-rs: A library for safe and secure remote computing using fully homomorphic encryption and trusted execution environments

Fully Homomorphic Encryption (FHE) and Trusted Execution Environ-ments (TEEs) are complementing approaches that can both secure computa-tions running remotely on a public cloud. Existing FHE schemes are, however, malleable by design and lack integrity protection, making them susceptible to integrity breaches where an adversary could modify the data and corrupt the output. This paper describes how both confidentiality and integrity of remote compu-tations can be assured by combining FHE with hardware based secure enclave technologies. We provide a software library for performing FHE within the Intel SGX TEE, written in the memory-safe programming language Rust to strengthen the internal safety of software and reduce its attack surface. We evaluate a sample application written with our library. We demonstrate that we can feasibly combine these concepts and provide stronger security guar-antees with a minimal development effort

Secure Integer Comparisons Using the Homomorphic Properties of Prime Power Subgroups

Secure multi party computation allows two or more parties to jointly compute a function under encryption without leaking information about their private inputs. These secure computations are vital in many fields including law enforcement, secure voting and bioinformatics because the privacy of the information is of paramount importance. One common reference problem for secure multi party computation is the Millionaires\u27 problem which was first introduced by Turing Award winner Yao in his paper Protocols for secure computation . The Millionaires\u27 problem considers two millionaires who want to know who is richer without disclosing their actual worth. There are public-key cryptosystems that currently solve this problem, however they use bitwise decomposition and Boolean algebra on encrypted bits. This type of solution is costly as it requires each bit requires its own encryption and decryption. Our solution to the Millionaires\u27 problem and secure integer comparison looks at a new approach which doesn\u27t use the decomposition method and instead encrypts the full length of the message in one encryption (within scope). This method also extends in a linear fashion, so larger integers remain efficient to compare. In this thesis, we present a new cryptosystem with a novel homomorphic property used for secure integer comparison, as well as a protocol implementing the cryptosystem and a simulation security proof for the protocol. Finally, we implemented the system and compared it to systems that are being used today

Reuse It Or Lose It: More Efficient Secure Computation Through Reuse of Encrypted Values

Two-party secure function evaluation (SFE) has become significantly more feasible, even on resource-constrained devices, because of advances in server-aided computation systems. However, there are still bottlenecks, particularly in the input validation stage of a computation. Moreover, SFE research has not yet devoted sufficient attention to the important problem of retaining state after a computation has been performed so that expensive processing does not have to be repeated if a similar computation is done again. This paper presents PartialGC, an SFE system that allows the reuse of encrypted values generated during a garbled-circuit computation. We show that using PartialGC can reduce computation time by as much as 96% and bandwidth by as much as 98% in comparison with previous outsourcing schemes for secure computation. We demonstrate the feasibility of our approach with two sets of experiments, one in which the garbled circuit is evaluated on a mobile device and one in which it is evaluated on a server. We also use PartialGC to build a privacy-preserving "friend finder" application for Android. The reuse of previous inputs to allow stateful evaluation represents a new way of looking at SFE and further reduces computational barriers.Comment: 20 pages, shorter conference version published in Proceedings of the 2014 ACM SIGSAC Conference on Computer and Communications Security, Pages 582-596, ACM New York, NY, US