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Many cryptographic schemes have been proposed from learning with errors problems over some rings (Ring-LWE). Polynomial time quantum reduction from the approximating Shortest Independent Vectors Probl...
Improved Secure Integer Comparison via Homomorphic Encryption
secure comparison homomorphic encryption
2019/4/28
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 enabl...
Secure Computation of the $k^\text{th}$-ranked Integer on Blockchains
applications secret sharing zero knowledge
2019/3/13
We focus on securely computing the kthkth-ranked integer in a sequence of integers distributed among nn parties, e.g., the largest or smallest integer or the median. Our specific objective is low inte...
Integer Matrices Homomorphic Encryption and Its application
integer matrices encryption implementation application
2018/11/2
We construct an integer matrices encryption scheme based on binary matrices encryption scheme proposed in [9], and support homomorphic addition and multiplication operations, we prove the correctness ...
LP Solutions of Vectorial Integer Subset Sums - Cryptanalysis of Galbraith's Binary Matrix LWE
Binary matrix LWE Linear Programming Cryptanalysis
2018/8/16
We consider Galbraith's space efficient LWE variant, where the (m×n)(m×n)-matrix AA is binary. In this binary case, solving a vectorial subset sum problem over the integers allows for decryption. We s...
Lattice-Based Zero-Knowledge Arguments for Integer Relations
Lattice-based cryptography zero-knowledge arguments integer relations
2018/8/2
We provide lattice-based protocols allowing to prove relations among committed integers. While the most general zero-knowledge proof techniques can handle arithmetic circuits in the lattice setting, a...
Threshold Properties of Prime Power Subgroups with Application to Secure Integer Comparisons
RSA homomorphic encryption homomorphic threshold
2018/3/5
In contrast to related work which encrypts and acts on each bit of the input separately, our protocol compares multiple input bits simultaneously within a single ciphertext. Compared to the related pr...
In [AJPS17], Aggarwal, Joux, Prakash & Santha described an elegant public-key cryptosystem (AJPS-1) mimicking NTRU over the integers. This algorithm relies on the properties of Mersenne primes instead...
A Certain Family of Subgroups of Zn⋆ Is Weakly Pseudo-Free under the General Integer Factoring Intractability Assumption
families of computational groups weak pseudo-freeness abelian groups
2017/11/28
A Certain Family of Subgroups of Zn⋆ Is Weakly Pseudo-Free under the General Integer Factoring Intractability Assumption.
This article appeared as Chapter 5 of the book "Topics in Computational Number Theory inspired by Peter L. Montgomery", edited by Joppe W. Bos and Arjen K. Lenstra and published by Cambridge Universit...
On Improving Integer Factorization and Discrete Logarithm Computation using Partial Triangulation
RSA factoring discrete logarithm problem
2017/8/8
The number field sieve is the best-known algorithm for factoring integers and solving the discrete logarithm problem in prime fields. In this paper, we present some new improvements to various steps o...
In this work, we describe an integer version of ring-LWE over the polynomial rings and prove that its hardness is equivalent to one of the polynomial ring-LWE. Moreover, we also present a public key c...
Detecting Large Integer Arithmetic for Defense Against Crypto Ransomware
Crypto Ransomware Malware Analysis Public Key Encryption
2017/6/9
The evolution of crypto ransomware has increasingly influenced real-life systems and lead to fatal threats to data security of individuals and enterprises. A crypto ransomware basically encrypts files...
Homomorphically Encrypted Arithmetic Operations over the Integer Ring
FHE HElib Encrypted integer arithmetic
2017/5/5
Fully homomorphic encryption allows cloud servers to evaluate any computable functions for clients without revealing any information. It attracts much attention from both of the scientific community a...
Computing generator in cyclotomic integer rings, A subfield algorithm for the Principal Ideal Problem in L(1/2) and application to cryptanalysis of a FHE scheme
Principal Ideal Problem cryptanalysis FHE
2017/2/21
The Principal Ideal Problem (resp. Short Principal Ideal Problem), shorten as PIP (resp. SPIP), consists in finding a generator (resp. short generator) of a principal ideal in the ring of integers of ...