Author Type

Graduate Student

Date of Award

2014

Document Type

Dissertation

Publication Status

Version of Record

Submission Date

October 2026

Thesis/Dissertation Advisor [Chair]

Steinwandt, Rainer

Thesis/Dissertation Co-Chair

Eisenbarth, Thomas

Abstract

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.

Extent

74 p.

Comments

Includes bibliography.|Dissertation (Ph.D.)--Florida Atlantic University, 2014.|FAU Electronic Theses and Dissertations Collection|Includes bibliography.

Identifier

FA00004182

Format

pdf

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