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

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

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 Improved Quantum Circuits for Elliptic Curve Discrete Logarithms

2020 ◽  
pp. 425-444
Author(s):  
Thomas Häner ◽  
Samuel Jaques ◽  
Michael Naehrig ◽  
Martin Roetteler ◽  
Mathias Soeken
Keyword(s):  
Elliptic Curve ◽  
Quantum Circuits ◽  
Discrete Logarithms

Shor's discrete logarithm quantum algorithm for elliptic curves

2003 ◽  
Vol 3 (4) ◽  
pp. 317-344
Author(s):  
J. Proos ◽  
Ch. Zalka
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Finite Fields ◽  
Quantum Computer ◽  
Discrete Logarithm ◽  
Quantum Algorithm ◽  
Technical Difficulty ◽  
Discrete Logarithms ◽  
Modulo P ◽  
Cryptographic Key

We show in some detail how to implement Shor's efficient quantum algorithm for discrete logarithms for the particular case of elliptic curve groups. It turns out that for this problem a smaller quantum computer can solve problems further beyond current computing than for integer factorisation. A 160 bit elliptic curve cryptographic key could be broken on a quantum computer using around 1000 qubits while factoring the security-wise equivalent 1024 bit RSA modulus would require about 2000 qubits. In this paper we only consider elliptic curves over GF(p) and not yet the equally important ones over GF(2^n) or other finite fields. The main technical difficulty is to implement Euclid's gcd algorithm to compute multiplicative inverses modulo p. As the runtime of Euclid's algorithm depends on the input, one difficulty encountered is the ``quantum halting problem''.

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