Commercial applications, including Blockchain, require large numbers of cryptographic
signing and verification operations, increasingly using Elliptic Curve Cryptography. This uses a
group operation (called point addition) in the set of points on an elliptic curve over a prime field. Scalar multiplication of the repeated addition of a fixed point, P , in the curve. Along with the infinity point, which serves as the identity of addition and the zero of scalar multiplication, this forms a vector space over the prime field. The scalar multiplication can be accelerated by decomposing the number of additions into nibbles or other digits, and using a pre-computed table of values P , 2P , 3P, . . . This is called a windowed method. To avoid side-channel attacks, implementations must ensure that the time and power used do not depend on the scalar. Avoiding conditional execution ensures constant-time and constant-power execution.
This thesis presents a theoretical reduction in latency for the windowed method by introducing parallelism. Using three cores can achieve an improvement of 42% in the latency versus a single-threaded computation. / Thesis / Master of Science (MSc)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/26191 |
| Date | January 2021 |
| Creators | Bouman, Tanya |
| Contributors | Anand, Christopher, Kahl, Wolfram, Computing and Software |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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