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Numerical Methods for Comparison on Homomorphically Encrypted Numbers
Homomorphic Encryption Comparison Min/Max
2019/4/25
We propose a new method to compare numbers which are encrypted by Homomorphic Encryption (HE). Previously, comparison and min/max functions were evaluated using Boolean functions where input numbers a...
Fully homomorphic encryption modulo Fermat numbers
public-key cryptography Fully Homomorphic Encryption
2019/3/1
In this paper, we recast state-of-the-art constructions for fully homomorphic encryption in the simple language of arithmetic modulo large Fermat numbers. The techniques used to construct our scheme a...
Safety in Numbers: On the Need for Robust Diffie-Hellman Parameter Validation
Primality testing Miller-Rabin test Diffie-Hellman
2019/1/18
We consider the problem of constructing Diffie-Hellman (DH) parameters which pass standard approaches to parameter validation but for which the Discrete Logarithm Problem (DLP) is relatively easy to s...
Efficient Parallel Binary Operations on Homomorphic Encrypted Real Numbers
implementation homomorphic encryption
2018/3/5
A number of homomorphic encryption application areas, such as privacy-preserving machine learning analysis in the cloud, could be better enabled if there existed a general solution for combining suffi...
(Finite) Field Work: Choosing the Best Encoding of Numbers for FHE Computation
Fully Homomorphic Encryption FHE Encoding
2017/6/22
Fully Homomorphic Encryption (FHE) schemes are a powerful tool that allows arbitrary computations on encrypted data. This makes them a promising tool for a variety of use cases that require outsourcin...
A New Public-Key Cryptosystem via Mersenne Numbers
public-key cryptosystem Public-Key Cryptosystem via Mersenne Numbers
2017/5/31
In this work, we propose a new public-key cryptosystem whose security is based on the computational intractability of the following problem: Given a Mersenne number p = 2^n - 1, where n is a prime, a ...
Condition on composite numbers easily factored with elliptic curve method
factoring number theory RSA
2017/5/12
For a composite integer NN that we would like to factor, we consider a condition for the elliptic curve method using NN as a scalar value to succeed and show that if NN has a prime factor pp such that...
Alternative Implementations of Secure Real Numbers
Secure fixed- and floating-point arithmetic privacy-preserving data analysis secure computations
2016/12/10
This paper extends the choice available for secure real number implementations with two new contributions. We will consider the numbers represented in form a−φba−φb where φφ is the golden ...
Accelerating Homomorphic Computations on Rational Numbers
Fully Homomorphic Encryption Encoding Confidential Machine Learning
2016/7/7
Fully Homomorphic Encryption (FHE) schemes are conceptually very powerful tools for outsourcing computations on confidential data. However, experience shows that FHE-based solutions are not sufficient...
Chaos Machine: Different Approach to the Application and Significance of Numbers
number theory pseudo-randomness one-way functions
2016/5/18
In this paper we describe a theoretical model of \underline{chaos machine}, which combines the benefits of hash function and pseudo-random function, forming flexible \textit{one-way} \underline{push-p...
Fully Homomorphic Encryption for Point Numbers
Fully homomorphic encryption FV scheme Fixed point number
2016/4/26
In this paper, based on the FV scheme, we construct a first fully homomorphic encryption scheme FHE4FX that can homomorphically compute addition and/or multiplication of encrypted fixed point numbers ...
Canary Numbers: Design for Light-weight Online Testability of True Random Number Generators
TRNG FPGA Online Test
2016/4/18
We introduce the concept of canary numbers, to be used in
health tests for true random number generators. Health tests are essential
components of true random number generators because they are used...
Encoding Rational Numbers for FHE-based Applications
Continued fractions Gosper algorithm Rational numbers
2016/4/6
This work addresses a basic problem of security systems that operate on very sensitive
information, such as healthcare data. Specifically, we are interested in the problem of privately
handling medi...
Hybrid Model of Fixed and Floating Point Numbers in Secure Multiparty Computations
cryptographic protocols secret sharing multi-party computations
2016/1/25
This paper develops a new hybrid model of floating point numbers suitable for operations
in secure multi-party computations. The basic idea is to consider the significand of the floating
point numbe...
SHADOW NUMBERS PUBLIC KEY ENCRYPTION
public key encryption algorithm public key private key
2016/1/9
The present public key encryption in this paper involves the use
of two values and they are the shadow’s values of a base value, and
the base value is derived from the two shadows’ values. Whenever ...