A Number-Theoretic Error-Correcting Code

In this paper we describe a new error-correcting code (ECC) inspired by the Naccache-Stern cryptosystem. While by far less efficient than Turbo codes, the proposed ECC happens to be more efficient than some established ECCs for certain sets of parameters. The new ECC adds an appendix to the message. The appendix is the modular product of small primes representing the message bits. The receiver recomputes the product and detects transmission errors using modular division and lattice reduction

Privacy-Preserving Ridge Regression Without Garbled Circuits

Ridge regression is an algorithm that takes as input a large number of data points and finds the best-fit linear curve through these points. It is a building block for many machine-learning operations. This report presents a system for privacy-preserving ridge regression. The system outputs the best-fit curve in the clear, but exposes no other information about the input data. This problem was elegantly addressed by Nikolaenko et al. (S\&P 2013). They suggest an approach that combines homomorphic encryption and Yao garbled circuits. The solution presented in this report only involves homomorphic encryption. This improves the performance as Yao circuits were the main bottleneck in the previous solution

Floating Point Arithmetic Protocols for Constructing Secure Data Analysis Application

AbstractA large variety of data mining and machine learning techniques are applied to a wide range of applications today. There- fore, there is a real need to develop technologies that allows data analysis while preserving the confidentiality of the data. Secure multi-party computation (SMC) protocols allows participants to cooperate on various computations while retaining the privacy of their own input data, which is an ideal solution to this issue. Although there is a number of frameworks developed in SMC to meet this challenge, but they are either tailored to perform only on specific tasks or provide very limited precision. In this paper, we have developed protocols for floating point arithmetic based on secure scalar product protocols, which is re- quired in many real world applications. Our protocols follow most of the IEEE-754 standard, supporting the four fundamental arithmetic operations, namely addition, subtraction, multiplication, and division. We will demonstrate the practicality of these protocols through performing various statistical calculations that is widely used in most data analysis tasks. Our experiments show the performance of our framework is both practical and promising

On the Implementation of Spread Spectrum Fingerprinting in Asymmetric Cryptographic Protocol

<p/> <p>Digital fingerprinting of multimedia contents involves the generation of a fingerprint, the embedding operation, and the realization of traceability from redistributed contents. Considering a buyer's right, the asymmetric property in the transaction between a buyer and a seller must be achieved using a cryptographic protocol. In the conventional schemes, the implementation of a watermarking algorithm into the cryptographic protocol is not deeply discussed. In this paper, we propose the method for implementing the spread spectrum watermarking technique in the fingerprinting protocol based on the homomorphic encryption scheme. We first develop a rounding operation which converts real values into integer and its compensation, and then explore the tradeoff between the robustness and communication overhead. Experimental results show that our system can simulate Cox's spread spectrum watermarking method into asymmetric fingerprinting protocol.</p

Rational Modular Encoding in the DCR Setting: Non-Interactive Range Proofs and Paillier-Based Naor-Yung in the Standard Model

International audienceRange proofs allow a sender to convince a verifier that committed integers belong to an interval without revealing anything else. So far, all known non-interactive range proofs in the standard model rely on groups endowed with a bilinear map. Moreover, they either require the group order to be larger than the range of any proven statement or they suffer from a wasteful rate. Recently (Eurocrypt'21), Couteau et al. introduced a new approach to efficiently prove range membership by encoding integers as a modular ratio between small integers. We show that their technique can be transposed in the standard model under the Composite Residuosity (DCR) assumption. Interestingly, with this modification, the size of ranges is not a priori restricted by the common reference string. It also gives a constant ratio between the size of ranges and proofs. Moreover, we show that their technique of encoding messages as bounded rationals provides a secure standard model instantiation of the Naor-Yung CCA2 encryption paradigm under the DCR assumption

Efficient Fully Homomorphic Encryption from (Standard) LWE

A fully homomorphic encryption (FHE) scheme allows anyone to transform an encryption of a message, m, into an encryption of any (efficient) function of that message, f(m), without knowing the secret key. We present a leveled FHE scheme that is based solely on the (standard) learning with errors (LWE) assumption. (Leveled FHE schemes are initialized with a bound on the maximal evaluation depth. However, this restriction can be removed by assuming “weak circular security.”) Applying known results on LWE, the security of our scheme is based on the worst-case hardness of “short vector problems” on arbitrary lattices. Our construction improves on previous works in two aspects: 1. We show that “somewhat homomorphic” encryption can be based on LWE, using a new relinearization technique. In contrast, all previous schemes relied on complexity assumptions related to ideals in various rings. 2. We deviate from the “squashing paradigm” used in all previous works. We introduce a new dimension-modulus reduction technique, which shortens the ciphertexts and reduces the decryption complexity of our scheme, without introducing additional assumptions. Our scheme has very short ciphertexts, and we therefore use it to construct an asymptotically efficient LWE-based single-server private information retrieval (PIR) protocol. The communication complexity of our protocol (in the public-key model) is k·polylog(k)+log |DB| bits per single-bit query, in order to achieve security against 2k-time adversaries (based on the best known attacks against our underlying assumptions). Key words. cryptology, public-key encryption, fully homomorphic encryption, learning with errors, private information retrieva

Privacy preservation in peer-to-peer gossiping networks in presence of a passive adversary

In the Web 2.0, more and more personal data are released by users (queries, social networks, geo-located data, ...), which create a huge pool of useful information to leverage in the context of search or recommendation for instance. In fully decentralized systems, tapping on the power of this information usually involves a clustering process that relies on an exchange of personal data (such as user proles) to compute the similarity between users. In this internship, we address the problem of computing similarity between users while preserving their privacy and without relying on a central entity, with regards to a passive adversary