Date of Award
Electrical and Computer Engineering
Crytpography, High-Speed, Mersenne Prime, Modular, Multiplication, Reduction
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
The work contained in this thesis is a representation of the successful attempt to speed-up the modular reduction as an independent step of modular multiplication, which is the central operation in public-key cryptosystems. Based on the properties of Mersenne and Quasi-Mersenne primes, four distinct sets of moduli have been described, which are responsible for converting the single-precision multiplication prevalent in many of today's techniques into an addition operation and a few simple shift operations. A novel algorithm has been proposed for modular folding. With the backing of the special moduli sets, the proposed algorithm is shown to outperform (speed-wise) the Modified Barrett algorithm by 80% for operands of length 700 bits, the least speed-up being around 70% for smaller operands, in the range of around 100 bits.
Sreehari, Suhas, "Fast Modular Reduction for Large-Integer Multiplication" (2012). Electronic Theses and Dissertations. 5360.