Constructing Cryptographic Multilinear Maps Using Affine Automorphisms

使用 pro-p 群的密码学多线性映射

Cryptographic multilinear maps using pro-p groups

本文研究基于幂零群多线性换位子映射的非交互式密钥交换协议，分析其在有限 p-群上的安全性，并探索 pro-p 群作为替代平台。

Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves

We describe a framework for constructing an efficient non-interactive key exchange (NIKE) protocol for n parties for any n >= 2. Our approach is based on the problem of computing isogenies between isogenous elliptic curves, which is believed to be difficult. We do not obtain a working protocol because of a missing step that is currently an open mathematical problem. What we need to complete our protocol is an efficient algorithm that takes as input an abelian variety presented as a product of isogenous elliptic curves, and outputs an isomorphism invariant of the abelian variety. Our framework …

通过Suzuki函数域的自同构群对MST3密码系统的密码学增强

Cryptographic Strengthening of MST3 cryptosystem via Automorphism Group of Suzuki Function Fields

本文提出基于Suzuki函数域自同构群的MST3密码系统新实现，将对数签名扩展到群中心外坐标，提升了密码分析复杂度和消息容量平方，增强了系统可靠性。

Pairing for Greenhorn: Survey and Future Perspective

Pairing is the most powerful tool in cryptography that maps two points on the elliptic curve to the group over the finite field. Mostly cryptographers consider pairing as a black box and use it for implementing pairing-based cryptographic protocols. This paper aims to give the overview of pairing as simple as possible for greenhorn and those who are working and wish to work in the pairing. The paper gives the concrete background of pairing and recommends an appropriate pairing among different choices for constructing pairing-based cryptographic protocols. We also analyze the bandwidth and comp…

Efficient Multilinear Map from Graded Encoding Scheme

Though the multilinear maps have many cryptographic applications, secure and efficient construction of such maps is an open problem. Many multilinear maps like GGH, GGH15, CLT, and CLT15 have been and are being proposed, while none of them is both secure and efficient. The construction of some multilinear maps is based on the Graded Encoding Scheme (GES), where, the necessity of announcing zero-testing parameter and encoding of zero has destroyed the security of the multilinear map. Attempt is made to propose a new GES, where, instead of encoding an element, the users can obtain the encoding o…

The MOR cryptosystem and finite $p$-groups

The ElGamal cryptosystem is the most widely used public key cryptosystem. It uses the discrete logarithm problem as the cryptographic primitive. The MOR cryptosystem is a similar cryptosystem. It uses the discrete logarithm problem in the automorphism group as the cryptographic primitive. In this paper, we study the MOR cryptosystem for finite $p$-groups. The study is complete for $p^\prime$-automorphisms. For $p$-automorphisms there are some interesting open problems.