Fast and flexible hardware support for elliptic curve cryptography over multiple standard prime finite fields

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dc.contributor.author Alrimeih, Hamad
dc.date.accessioned 2012-03-29T18:47:53Z
dc.date.available 2012-03-29T18:47:53Z
dc.date.copyright 2012 en_US
dc.date.issued 2012-03-29
dc.identifier.uri http://hdl.handle.net/1828/3861
dc.description.abstract Exchange of private information over a public medium must incorporate a method for data protection against unauthorized access. Elliptic curve cryptography (ECC) has become widely accepted as an efficient mechanism to secure private data using public-key protocols. Scalar multiplication (which translates into a sequence of point operations each involving several modular arithmetic operations) is the main ECC computation, where the scalar value is secret and must be secured. In this dissertation, we consider ECC over five standard prime finite fields recommended by the National Institute of Standard and Technology (NIST), with the corresponding prime sizes of 192, 224, 256, 384, and 521 bits. This dissertation presents our general hardware-software approach and technical details of our novel hardware processor design, aimed at accelerating scalar multiplications with flexible security-performance tradeoffs. To enhance performance, our processor exploits parallelism by pipelining modular arithmetic computations and associated input/output data transfers. To enhance security, modular arithmetic computations and associated data transfers are grouped into atomically executed computational blocks, in order to make curve point operations indistinguishable and thus mask the scalar value. The flexibility of our processor is achieved through the software-controlled hardware programmability, which allows for different scenarios of computing atomic block sequences. Each scenario is characterized by a certain trade-off between the processor’s security and performance. As the best trade-off scenario is specific to the user and/or application requirements, our approach allows for such a scenario to be chosen dynamically by the system software, thus facilitating system adaptation to dynamically changing requirements. Since modular multiplications are the most critical low-level operation in ECC computations, we also propose a novel modular multiplier specifically optimized to take full advantage of the fast reduction algorithms associated with the five NIST primes. The proposed architecture has been prototyped on a Xilinx Virtex-6 FPGA and takes between 0.30 ms and 3.91 ms to perform a typical scalar multiplication. Such performance figures demonstrate both flexibility and efficiency of our proposed design and compares favourably against other systems reported in the literature. en_US
dc.language English eng
dc.language.iso en en_US
dc.subject Elliptic Curve Cryptography en_US
dc.subject Programmable Hardware en_US
dc.subject Parallel Atomic Computations en_US
dc.subject Security-Performance Tradeoffs en_US
dc.title Fast and flexible hardware support for elliptic curve cryptography over multiple standard prime finite fields en_US
dc.type Thesis en_US
dc.contributor.supervisor Rakhmatov, Daler N.
dc.degree.department Dept. of Electrical and Computer Engineering en_US
dc.degree.level Doctor of Philosophy Ph.D. en_US
dc.rights.temp Available to the World Wide Web en_US
dc.description.scholarlevel Graduate en_US

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