Quantum Computing for Elliptic Curve Discrete Logarithms

2015 ◽  
pp. 173-228
Author(s):  
Song Y. Yan
Keyword(s):  
Quantum Computing ◽  
Elliptic Curve ◽  
Discrete Logarithms

scholarly journals Computing elliptic curve discrete logarithms with improved baby-step giant-step algorithm

2017 ◽  
Vol 11 (3) ◽  
pp. 453-469 ◽  
Author(s):  
Steven D. Galbraith ◽  
◽  
Ping Wang ◽  
Fangguo Zhang ◽  
◽  
...  
Keyword(s):  
Elliptic Curve ◽  
Discrete Logarithms ◽  
Giant Step ◽  
Step Algorithm

scholarly journals Quantum Resource Estimates for Computing Elliptic Curve Discrete Logarithms

2017 ◽  
pp. 241-270 ◽  
Author(s):  
Martin Roetteler ◽  
Michael Naehrig ◽  
Krysta M. Svore ◽  
Kristin Lauter
Keyword(s):  
Elliptic Curve ◽  
Discrete Logarithms

Attacks on Self-Certified Multi-Proxy Signature Schemes with Message Recovery

2011 ◽  
Vol 135-136 ◽  
pp. 316-320
Author(s):  
Qi Xie
Keyword(s):  
Finite Field ◽  
Elliptic Curve ◽  
Proxy Signature ◽  
Public Key ◽  
Signature Verification ◽  
Signature Schemes ◽  
Discrete Logarithms ◽  
The Public ◽  
Message Recovery ◽  
Public Keys

Signature schemes with message recovery based on self-certified public keys can reduce the amount of communications and computations, since the signature verification, the public key authentication and the message recovery are simultaneously carried out in a single logical step. Integrating self-certified public-key systems and the message recovery signature schemes, in 2009, Wu et al. proposed two multi-proxy signatures based on the discrete logarithms over a finite field and the elliptic curve discrete logarithms. The proxy warrant revision attacks are proposed, and it will show that Wu et al.’s schemes can not resist the proxy warrant revision attacks by either the proxy group or the original signer.

scholarly journals Fast Implementation of Elliptic Curve Cryptographic Algorithm on GF(3M) Based on FPGA

2021 ◽  
Author(s):  
Tan Yongliang ◽  
He Lesheng ◽  
Jin Haonan ◽  
Kong Qingyang
Keyword(s):  
Quantum Computing ◽  
Elliptic Curve ◽  
Elliptic Curves ◽  
Bilinear Pairings ◽  
Iot Security ◽  
Multiplication Algorithm ◽  
Security Environment ◽  
Cryptographic Algorithm ◽  
Hardware Encryption ◽  
Computation Speed

As quantum computing and the theory of bilinear pairings continue being studied in depth, elliptic curves on GF(3m ) are becoming of an increasing interest because they provide a higher security. What’s more, because hardware encryption is more efficient and secure than software encryption in today's IoT security environment, this article implements a scalar multiplication algorithm for the elliptic curve on GF(3m ) on the FPGA device platform. The arithmetic in finite fields is quickly implemented by bit-oriented operations, and then the computation speed of point doubling and point addition is improved by a modified Jacobia projection coordinate system. The final experimental results demonstrate that the structure consumes a total of 7518 slices, which is capable of computing approximately 3000 scalar multiplications per second at 124 Mhz. It has relative advantages in terms of performance and resource consumption, which can be applied to specific confidential communication scenarios as an IP core.

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