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Lower Bounds for Monotone q-Multilinear Boolean Circuits
A monotone Boolean circuit is composed of OR gates, AND gates and input gates corresponding to the input variables and the Boolean constants. It is...
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Cloud-SMPC: two-round multilinear maps secure multiparty computation based on LWE assumption
Cloud computing has data leakage from all parties, security protection of private data, and existing solutions do not provide a trade-off between...
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On the Hardness of the Determinant: Sum of Regular Set-Multilinear Circuits
In this paper, we study the computational complexity of the commutative determinant polynomial computed by a class of set-multilinear circuits which...
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Fine-grained flexible access control: ciphertext policy attribute based encryption for arithmetic circuits
Applying access structure to encrypted sensitive data is one of the challenges in communication networks and cloud computing. Various methods have...
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Adaptively secure CP-ABE for circuits with fan-in n and fan-out 1
The attribute-based encryption (ABE) scheme is suitable for access control of ciphertext in cloud computing. Kowalczyk and Wee proposed an adaptively...
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On Constant-Depth Canonical Boolean Circuits for Computing Multilinear Functions
We consider new complexity measures for the model of multilinear circuits with general multilinear gates introduced by Goldreich and Wigderson (ECCC,...
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Lower Bounds for Arithmetic Circuits via the Hankel Matrix
We study the complexity of representing polynomials by arithmetic circuits in both the commutative and the non-commutative settings. Our approach...
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Efficiently Testable Circuits Without Conductivity
The notion of “efficiently testable circuits” (ETC) was recently put forward by Baig et al. (ITCS’23). Informally, an ETC compiler takes as input any...
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On the Size of Depth-Three Boolean Circuits for Computing Multilinear Functions
This paper introduces and initiates a study of a new model of arithmetic circuits coupled with new complexity measures. The new model consists of...
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Lower Bounds Against Sparse Symmetric Functions of ACC Circuits: Expanding the Reach of #SAT Algorithms
We continue the program of proving circuit lower bounds via circuit satisfiability algorithms. So far, this program has yielded several concrete...
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Obfuscating Circuits Via Composite-Order Graded Encoding
We present a candidate obfuscator based on composite-order graded encoding schemes (GES), which are a generalization of multilinear maps. Our...
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HyperPlonk: Plonk with Linear-Time Prover and High-Degree Custom Gates
Plonk is a widely used succinct non-interactive proof system that uses univariate polynomial commitments. Plonk is quite flexible: it supports...
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A #SAT Algorithm for Small Constant-Depth Circuits with PTF gates
We show that there is a better-than-brute-force algorithm that, when given a small constant-depth Boolean circuit C made up of gates that compute...
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Unlocking the Lookup Singularity with Lasso
This paper introduces Lasso, a new family of lookup arguments, which allow an untrusted prover to commit to a vector...
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Multilinear Maps from Obfuscation
We provide constructions of multilinear groups equipped with natural hard problems from indistinguishability obfuscation, homomorphic encryption, and...
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Succinct Attribute-Based Signatures for Bounded-Size Circuits by Combining Algebraic and Arithmetic Proofs
Attribute-based signatures allow fine-grained attribute-based authentication and at the same time keep a signer’s privacy as much as possible. While...
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Jolt: SNARKs for Virtual Machines via Lookups
Succinct Non-interactive Arguments of Knowledge (SNARKs) allow an untrusted prover to establish that it correctly ran some “witness-checking...
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Schur Polynomials Do Not Have Small Formulas If the Determinant does not
Schur Polynomials are families of symmetric polynomials that have been classically studied in Combinatorics and Algebra alike. They play a central...
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Improved bounds on the AN-complexity of \(O(1)\)-linear functions
We consider arithmetic circuits with arbitrary gates for computing Boolean functions that are represented by low-degree polynomials over GF(2). An...
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Extractable Witness Encryption for the Homogeneous Linear Equations Problem
Witness encryption is a cryptographic primitive which encrypts a message under an instance of an NP language and decrypts the ciphertext using a...