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Compact and Scalable Arbitrary-centered Discrete Gaussian Sampling over Integers
Lattice-based crypto discrete Gaussian sampling implementation
2019/9/16
The arbitrary-centered discrete Gaussian sampler is a fundamental subroutine in implementing lattice trapdoor sampling algorithms. However, existing approaches typically rely on either a fast implemen...
Polar Sampler: Discrete Gaussian Sampling over the Integers Using Polar Codes
Discrete Gaussian sampling Polar codes Integer lattice
2019/6/10
Cryptographic constructions based on hard lattice problems have emerged as a front runner for the standardization of post quantum public key cryptography. As the standardization process takes place, o...
On the Distribution of Quadratic Residues and Non-residues Modulo Composite Integers and Applications to Cryptography
Jacobi symbol probability distribution statistical distance
2019/6/4
We develop exact formulas for the distribution of quadratic residues and non-residues in sets of the form a+X={(a+x)modn∣x∈X}a+X={(a+x)modn∣x∈X}, where nn is a prime or the product of two primes and X...
Faster Bootstrapping of FHE over the integers with large prime message space
Fully homomorphic encryption Bootstrapping Restricted depth-3 circuit
2019/5/27
Sampling the Integers with Low Relative Error
Sampling Discrete Gaussians Lattice-based Cryptography
2019/1/26
Randomness is an essential part of any secure cryptosystem, but many constructions rely on distributions that are not uniform. This is particularly true for lattice based cryptosystems, which more oft...
FACCT: FAst, Compact, and Constant-Time Discrete Gaussian Sampler over Integers
Lattice-based crypto Discrete Gaussian sampling Constant-time
2019/1/2
The discrete Gaussian sampler is one of the fundamental tools in implementing lattice-based cryptosystems. However, a naive discrete Gaussian sampling implementation suffers from side-channel vulnerab...
Fast Secure Comparison for Medium-Sized Integers and Its Application in Binarized Neural Networks
multiparty computation secret sharing secure comparison
2019/1/2
In 1994, Feige, Kilian, and Naor proposed a simple protocol for secure 33-way comparison of integers aa and bb from the range [0,2][0,2]. Their observation is that for p=7p=7, the Legendre symbol (x|p...
The FHE (fully homomorphic encryption) schemes [7, 13] based on the modified AGCD problem (noise-free AGCD problem) are vulnerable to quantum attacks, because its security relies partly on the hardnes...
On Rejection Sampling Algorithms for Centered Discrete Gaussian Distribution over Integers
lattice-based cryptography discrete Gaussian sampling rejection sampling
2017/10/12
Lattice-based cryptography has been accepted as a promising candidate for public key cryptography in the age of quantum computing. Discrete Gaussian sampling is one of fundamental operations in many l...
Gaussian Sampling over the Integers: Efficient, Generic, Constant-Time
Lattice-Based Cryptography Discrete Gaussian Sampling
2017/3/27
Sampling integers with Gaussian distribution is a fundamental problem that arises in almost every application of lattice cryptography, and it can be both time consuming and challenging to implement. M...
FHE Over the Integers: Decomposed and Batched in the Post-Quantum Regime
FHE homomorphic GSW
2017/2/20
Fully homomorphic encryption over the integers (FHE-OI) is currently the only alternative to lattice-based FHE. FHE-OI includes a family of schemes whose security is based on the hardness of different...
Faster Bootstrapping of FHE over the Integers
Bootstrapping Fully Homomorphic Encryption over the integers CLT scheme
2017/2/20
Bootstrapping in fully homomorphic encryption (FHE) over the integers is a homomorphic evaluation of the squashed decryption function suggested by van Dijk et al. The typical approach for the bootstra...
Two main computational problems serve as security foundations of current fully homomorphic encryption schemes: Regev's Learning With Errors problem (LWE) and Howgrave-Graham's Approximate Greatest Com...
Probability that the k-gcd of products of positive integers is B-smooth
gcd of products of positive integers B-smooth k-gcd
2016/4/7
In 1849, Dirichlet[5] proved that the probability that two positive integers are relatively prime is 1/zeta(2). Later, it was generalized into the case that positive integers has no nontrivial kth pow...
Removing the Strong RSA Assumption from Arguments over the Integers
Public-key cryptography Commitment schemes Interactive arguments of knowledge
2016/2/23
Committing integers and proving relations between them is an essential ingredient in many
cryptographic protocols. Among them, range proofs have shown to be fundamental. They consist of
proving that...