Pairing-friendly curves and elliptic curves with a trapdoor for the discrete
logarithm problem are versatile tools in the design of cryptographic protocols. We
show that curves having both properties enable a deterministic identity-based signing
with “short” signatures in the random oracle model. At PKC 2003, Choon and Cheon
proposed an identity-based signature scheme along with a provable security reduction.
We propose a modification of their scheme with several performance benefits. In
addition to faster signing, for batch signing the signature size can be reduced, and if
multiple signatures for the same identity need to be verified, the verification can be
accelerated. Neither the signing nor the verification algorithm rely on the availability
of a (pseudo)random generator, and we give a provable security reduction in the
random oracle model to the (`-)Strong Diffie-Hellman problem. Implementing the group arithmetic is a cost-critical task when designing quantum circuits for Shor’s algorithm to solve the discrete logarithm problem. We introduce a tool for the automatic generation of addition circuits for ordinary binary elliptic curves, a prominent platform group for digital signatures. Our Python software generates circuit descriptions that, without increasing the number of qubits or T-depth, involve less than 39% of the number of T-gates in the best previous construction. The software also optimizes the (CNOT) depth for F2-linear operations by means of suitable graph colorings. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2014. / FAU Electronic Theses and Dissertations Collection
| Identifer | oai:union.ndltd.org:fau.edu/oai:fau.digital.flvc.org:fau_13652 |
| Contributors | Budhathoki, Parshuram (author), Steinwandt, Rainer (Thesis advisor), Eisenbarth, Thomas (Thesis advisor), Florida Atlantic University (Degree grantor), Charles E. Schmidt College of Science, Department of Mathematical Sciences |
| Publisher | Florida Atlantic University |
| Source Sets | Florida Atlantic University |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation, Text |
| Format | 74 p., application/pdf |
| Rights | Copyright © is held by the author, with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder., http://rightsstatements.org/vocab/InC/1.0/ |
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