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Efficient Information-Theoretic Secure Multiparty Computation over Z/pkZ via Galois Rings
MPC Galois Rings
2019/7/30
At CRYPTO 2018, Cramer et al. introduced a secret-sharing based protocol called SPDZ2kZ2k that allows for secure multiparty computation (MPC) in the dishonest majority setting over the ring of integer...
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...
New Primitives for Actively-Secure MPC over Rings with Applications to Private Machine Learning
MPC Decision Trees SVM
2019/6/3
At CRYPTO 2018 Cramer et al. presented SPDZ2k, a new secret-sharing based protocol for actively secure multi-party computation against a dishonest majority, that works over rings instead of fields. Th...
Improved Multiplication Triple Generation over Rings via SHE
Secure Two-party Computation Beaver Multiplication Triples Somewhat Homomorphic Encryption
2019/5/29
An important characteristic of recent MPC protocols is an input independent preprocessing phase in which most computations are offloaded, which greatly reduces the execution overhead of the online pha...
ASTRA: High Throughput 3PC over Rings with Application to Secure Prediction
Secure Computation Machine Learning 3PC
2019/4/28
The concrete efficiency of secure computation has been the focus of many recent works. In this work, we present protocols for secure 33-party computation (3PC) tolerating one corruption in the offline...
Supersingular isogeny graphs and endomorphism rings: reductions and solutions
post-quantum cryptography isogeny-based cryptography cryptanalysis
2018/4/26
In this paper, we study several related computational problems for supersingular elliptic curves, their isogeny graphs, and their endomorphism rings. We prove reductions between the problem of path fi...
On the Hardness of Computing Endomorphism Rings of Supersingular Elliptic Curves
Supersingular isogeny based cryptography number theory
2017/10/10
Cryptosystems based on supersingular isogenies have been proposed recently for use in post-quantum cryptography. Three problems have emerged related to their hardness: computing an isogeny between two...
Yet Another Compiler for Active Security or: Efficient MPC Over Arbitrary Rings
MPC Blackbox Compiler
2017/9/25
We present a very simple yet very powerful idea for turning any semi-honestly secure MPC protocol into an actively secure one, at the price of reducing the threshold of tolerated corruptions.
Efficient reductions in cyclotomic rings - Application to R-LWE based FHE schemes
Polynomial Reduction Number Theoretic Transform Residue Number Systems
2017/8/9
With Fully Homomorphic Encryption (FHE), it is possible to process encrypted data without having an access to the private-key. This has a wide range of applications, most notably the offloading of sen...
Simple Amortized Proofs of Shortness for Linear Relations over Polynomial Rings
lattice cryptography zero-knowledge proofs
2017/8/8
For a public value yy and a linear function ff, giving a zero-knowledge proof of knowledge of a secret value xx that satisfies f(x)=yf(x)=y is a key ingredient in many cryptographic protocols. Lattice...
Partially Splitting Rings for Faster Lattice-Based Zero-Knowledge Proofs
Lattice cryptography Zero-Knowledge Proofs Ring-LWE
2017/6/6
In this work we show that one can use the optimal challenge sets CC and still have the polynomial Xn+1Xn+1 split into more than two factors. For the most common parameters that are used in such zero-k...
Provably Secure NTRUEncrypt over More General Cyclotomic Rings
Lattice-based cryptography NTRU Learning With Errors
2017/4/11
NTRUEncrypt is a fast and standardized lattice-based public key encryption scheme, but it lacks a solid security guarantee. In 2011, Stehlé and Steinfeld first proposed a provably secure variant of NT...
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 ...
LWE from Non-commutative Group Rings
Matrix-LWE Non-commutative group ring Dihedral group ring
2016/12/29
The Ring Learning-With-Errors (LWE) problem, whose security is based on hard ideal lattice problems, has proven to be a promising primitive with diverse applications in cryptography. There are however...
Digital Signatures Based on the Hardness of Ideal Lattice Problems in all Rings
lattice ideal lattice Ring-SIS
2016/12/10
In this work, we show that the above may actually be possible. We construct a digital signature scheme based (in the random oracle model) on a simple adaptation of the Ring-SIS problem which is as har...