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Transparent Polynomial Commitment Scheme with Polylogarithmic Communication Complexity
polynomial commitments zero-knowledge proofs proximity testing
2019/9/16
We introduce novel efficient and transparent construction of the polynomial commitment scheme. A polynomial commitment scheme allows one side (the prover) to commit to a polynomial of predefined degre...
Optimal-Round Preprocessing-MPC via Polynomial Representation and Distributed Random Matrix (extended abstract)
MPC with preprocessing correlated randomness optimal round complexity
2019/9/16
We present preprocessing-MPC schemes of arithmetic functions with optimal round complexity, function-independent correlated randomness, and communication and space complexities that grow linearly with...
Low Weight Discrete Logarithms and Subset Sum in 20.65n with Polynomial Memory
Low weight dlog subset sum representations Nested Rho
2019/8/19
We propose two polynomial memory collision finding algorithms for the low Hamming weight discrete logarithm problem in any abelian group GG. The first one is a direct adaptation of the Becker-Coron-Jo...
We give the first construction of statistical Zaps. Our construction satisfies computational soundness and relies on the quasi-polynomial hardness of learning with errors assumpteprint.iacr.orgion.
Discrete logarithms in quasi-polynomial time in finite fields of fixed characteristic
discrete logarithm problem finite field
2019/6/26
We prove that the discrete logarithm problem can be solved in quasi-polynomial expected time in the multiplicative group of finite fields of fixed characteristic. More generally, we prove that it can ...
A Note on Lower Digits Extraction Polynomial for Bootstrapping
Fully Homomorphic Encryption Bootstrapping
2019/6/12
Bootstrapping is a crucial but computationally expensive step for realizing Fully Homomorphic Encryption (FHE). Recently, Chen and Han (Eurocrypt 2018) introduced a family of low-degree polynomials to...
A Candidate Access Structure for Super-polynomial Lower Bound on Information Ratio
secret sharing general access structures information ratio
2019/6/3
The contribution vector (convec) of a secret sharing scheme is the vector of all share sizes divided by the secret size. A measure on the convec (e.g., its maximum or average) is considered as a crite...
Nearly all secret sharing schemes studied so far are linear or multi-linear schemes. Although these schemes allow to implement any monotone access structure, the share complexity may be suboptimal -- ...
Obfuscation from Polynomial Hardness: Beyond Decomposable Obfuscation
indistinguishability obfuscation functional encryption
2019/3/21
Every known construction of general indistinguishability obfuscation (iOiO) is either based on a family of exponentially many assumptions, or is based on a single assumption -- e.g.~functional encrypt...
Design and Implementation of a Fast and Scalable NTT-Based Polynomial Multiplier Architecture
Number Theoretic Transform Large-Degree Polynomial Multiplication Fan-Vercauteren
2019/2/27
In this paper, we present an optimized FPGA implementation of a novel, fast and highly parallelized NTT-based polynomial multiplier architecture, which proves to be effective as an accelerator for lat...
On the Existence of Non-Linear Invariants and Algebraic Polynomial Constructive Approach to Backdoors in Block Ciphers
block ciphers Boolean functions Algebraic Normal Form
2018/11/19
In this paper we study cryptanalysis with non-linear polynomials cf. Eurocrypt’95 (adapted to Feistel ciphers at Crypto 2004). Previously researchers had serious difficulties in making such attacks wo...
Non-Malleable Codes Against Bounded Polynomial Time Tampering
non-malleable code non-malleable commitment derandomization
2018/11/2
We construct efficient non-malleable codes (NMC) that are (computationally) secure against tampering by functions computable in any fixed polynomial time. Our construction is in the plain (no-CRS) mod...
In this paper we focus on Polynomial Learning with Errors(PLWE). This problem is parametrized by a polynomial and we are interested in relating the hardness of the PLWEf and PLWEh problems for differe...
Polynomial Functional Encryption Scheme with Linear Ciphertext Size
Functional Encryption Hybrid Scheme
2018/6/13
Our main idea is to generically combine two abstract encryption schemes that satisfies some special properties. We also gives an instantiation of our scheme by combining ElGamal scheme and Ring-LWE ba...
Reducing Complexity of Pairing Comparisons using Polynomial Evaluation
elliptic curve cryptosystem implementation polynomials bilinear maps
2018/6/5
We propose a new method for reducing complexity of the pairing comparisons based on polynomials. Thought the construction introduces uncertainty into (usually deterministic) checks, it is easily quant...