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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On cancellation laws in cardinal arithmetic without the axiom of choice
选择公理 基数算术 取消定律
2023/4/17
We survey known results concerning cancellation laws in cardinal arithmetic without the axiom of choice. These results include the cancellation law for Dedekind finite cardinals in cardinal addition a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Arithmetic purity of strong approximation for complete toric varieties
完整 复曲面品种 强近似 算术纯度
2023/4/18
In this talk, I will discuss arithmetic purity of strong approximation : motivations and related results. Finally, for complete toric varieties, I will briefly explain my work on this topic.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Density of orbits and arithmetic degrees of automorphisms of projective threefolds
射影三重 轨道密度 自同构 算术度
2023/4/18
The Zariski dense orbit conjecture of the arithmetic dynamic is to study the existence of a rational point P with a Zariski dense orbit of a dominant rational self-map f of a projective variety X. Whe...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Arithmetic mixed Siegel-Weil formulas and modular forms of arithmetic divisors
算术混合 西格尔-威尔公式 算术除数 模形式
2023/5/5
The classical Siegel–Weil formula relates theta series to Eisenstein series and its arithmetic version is central in Kudla's program. I will discuss arithmetic mixed Siegel-Weil formulas. I will focus...
Succinct Arguments for Bilinear Group Arithmetic: Practical Structure-Preserving Cryptography
NIZK short proofs
2019/8/30
In their celebrated work, Groth and Sahai [EUROCRYPT'08, SICOMP' 12] constructed non-interactive zero-knowledge (NIZK) proofs for general bilinear group arithmetic relations, which spawned the entire ...
Asymptotically-Good Arithmetic Secret Sharing over Z/(p^\ell Z) with Strong Multiplication and Its Applications to Efficient MPC
multiparty computation amortization information-theoretical security
2019/7/18
This paper deals with (1) asymptotics of ``strongly-multiplicative'' arithmetic secret sharing over an arbitrary fixed ring Rℓ:=Z/pℓZ (p>0 prime, ℓ>0 an integer) and supporting an un...
Commodity-Based 2PC for Arithmetic Circuits
Secure Two-Party Computation Information Theoretic Security Oblivious Linear Evaluation
2019/6/19
We revisit the framework of Commodity-based Cryptography presented by Beaver (STOC'97) with a focus on updating the framework to fit with modern multiparty computation (MPC) protocols. We study the po...
Concretely-Efficient Zero-Knowledge Arguments for Arithmetic Circuits and Their Application to Lattice-Based Cryptography
zero-knowledge lattice cryptography MPC
2019/5/23
In this work we present a new interactive Zero-Knowledge Argument of knowledge for general arithmetic circuits. Our protocol is based on the ``MPC-in-the-head''-paradigm of Ishai et al. (STOC 2009) an...
Fully Homomorphic Encryption with k-bit Arithmetic Operations
FHE lattices learning with errors (LWE)
2019/5/21
We present a fully homomorphic encryption scheme continuing the line of works of Ducas and Micciancio (2015, [DM15]), Chillotti et al. (2016, [CGGI16a]; 2017, [CGGI17]; 2018, [CGGI18a]), and Gao (2018...
Efficient Attribute-Based Signatures for Unbounded Arithmetic Branching Programs
attribute-based signatures arithmetic branching programs arithmetic span programs
2019/4/10
This paper presents the first attribute-based signature (ABS) scheme in which the correspondence between signers and signatures is captured in an arithmetic model of computation. Specifically, we desi...
MArBled Circuits: Mixing Arithmetic and Boolean Circuits with Active Security
MPC Garbled Circuits Secret Sharing
2019/3/1
There are two main ways of performing computation on private data: one method uses linear secret-sharing, in which additions require no communication and multiplications require two secrets to be broa...
We consider the problem of garbling arithmetic circuits and present a garbling scheme for inner-product predicates over exponentially large fields. Our construction stems from a generic transformation...
Multi-Party Oblivious RAM based on Function Secret Sharing and Replicated Secret Sharing Arithmetic
cryptographic protocols RAM
2019/1/2
In this work, we study the problem of constructing oblivious RAM for secure multi-party computation to obliviously access memory at private locations during secure computation. We build on recent two-...
Faster Modular Arithmetic For Isogeny Based Crypto on Embedded Devices
public-key cryptography Embedded Devices
2018/9/6
We show how to implement the Montgomery reduction algorithm for isogeny based cryptography such that it can utilize the "unsigned multiply accumulate accumulate long" instruction present on modern ARM...
Homomorphic Encryption for Approximate Matrix Arithmetic
Homomorphic encryption approximate arithmetic matrix multiplication
2018/6/5
Homomorphic Encryption for Arithmetic of Approximate Numbers (HEAAN) with its vector packing technique proved its potential in cryptographic applications. In this paper, we propose MHEAAN - a generali...