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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stability of degree-2 Rossby-Haurwitz waves
2度 罗斯比-豪维茨波 稳定性
2023/5/12
Rossby-Haurwitz waves are an important class of explicit solutions to the incompressible Euler equation on a rotating 2-sphere. We will introduce our recent work on the nonlinear stability of degree-2...
How to leverage hardness of constant degree expanding polynomials over R to build iO
public-key cryptography Obfuscation
2019/9/16
In this work, we introduce and construct DD-restricted Functional Encryption (FE) for any constant D≥3D≥3, based only on the SXDH assumption over bilinear groups. This generalizes the notion of 33-res...
On the Degree-Insensitive SI-GDH problem and assumption
public-key cryptography supersingular isogeny Diffie-Hellman
2019/8/19
Fujioka, Takashima, Terada and Yoneyama, in their 2018 work on an authenticated key exchange protocol using supersingular isogenies, use new assumptions in their security proof of the scheme. In parti...
Improved Interpolation Attacks on Cryptographic Primitives of Low Algebraic Degree
Block cipher Cryptanalysis Interpolation attack
2019/7/15
Symmetric cryptographic primitives with low multiplicative complexity have been proposed to improve the performance of emerging applications such as secure Multi-Party Computation. However, primitives...
Indistinguishability Obfuscation Without Multilinear Maps: New Paradigms via Low Degree Weak Pseudorandomness and Security Amplification
PFG iO
2019/6/4
The existence of secure indistinguishability obfuscators (iO) has far-reaching implications, significantly expanding the scope of problems amenable to cryptographic study. All known approaches to cons...
Optimal TNFS-secure pairings on elliptic curves with composite embedding degree
Optimal ate pairing twists of elliptic curves jacobian coordinates
2019/5/27
In this paper we present a comprehensive comparison between pairing-friendly elliptic curves, considering different curve forms and twists where possible. We define a measure of the efficiency of a pa...
Faster Initial Splitting for Small Characteristic Composite Extension Degree Fields
Discrete Log Finite fields Function Field Sieve Cryptography
2019/3/21
Let pp be a small prime and n=n1n2>1n=n1n2>1 be a composite integer. For the function field sieve algorithm applied to FpnFpn, Guillevic (2019) had proposed an algorithm for initial splitting of the t...
Degree 2 is Complete for the Round-Complexity of Malicious MPC
foundations Multi-Party Computation
2019/3/1
We show, via a non-interactive reduction, that the existence of a secure multi-party computation (MPC) protocol for degree-22 functions implies the existence of a protocol with the same round complexi...
Optimized Method for Computing Odd-Degree Isogenies on Edwards Curves
Isogeny Post-quantum cryptography Montgomery curves
2019/2/27
In this paper, we present an efficient method to compute arbitrary odd-degree isogenies on Edwards curves. By using the ww-coordinate, we optimized the isogeny formula on Edwards curves by Moody \text...
A set S⊆Fn2S⊆F2n is called degree-dd zero-sum if the sum ∑s∈Sf(s)∑s∈Sf(s) vanishes for all nn-bit Boolean functions of algebraic degree at most dd. Those sets correspond to the supports of...
Homomorphic Secret Sharing for Low Degree Polynomials
secret sharing Homomorphic secret sharing
2018/11/12
Homomorphic secret sharing (HSS) allows nn clients to secret-share data to mm servers, who can then homomorphically evaluate public functions over the shares. A natural application is outsourced compu...
Optimal TNFS-secure pairings on elliptic curves with even embedding degree
TNFS-secure optimal pairing twisted Ate pairing
2018/11/6
In this paper we give a comprehensive comparison between pairing-friendly elliptic curves in Jacobi Quartic and Edwards form with quadratic, quartic, and sextic twists. Our comparison looks at the bes...
How to leverage hardness of constant-degree expanding polynomials over $\mathbb{R}$ to build iO
FE Indistinguishability Obfuscation
2018/11/6
DD -restricted FE allows for useful evaluation of constant-degree polynomials, while only requiring the SXDH assumption over bilinear groups. As such, it is a powerful tool for leveraging hardness tha...
Efficient Evaluation of Low Degree Multivariate Polynomials in Ring-LWE Homomorphic Encryption Schemes
homomorphic encryption efficient polynomial evaluation ring lwe
2018/6/27
Homomorphic encryption schemes allow to perform computations over encrypted data. In schemes based on RLWE assumption the plaintext data is a ring polynomial. In many use cases of homomorphic encrypti...
A Simplified Approach to Rigorous Degree 2 Elimination in Discrete Logarithm Algorithms
Discrete Logarithm Algorithms discrete logarithm problem
2018/5/14
we revisit the ZigZag strategy of Granger, Kleinjung and Zumbrägel. In particular, we provide a new algorithm and proof for the so-called degree 2 elimination step. This allows us to provide a st...