We describe novel methods for obtaining fast software implementations of the
arithmetic operations in the finite field GF(p) and GF(p[superscript k]). In GF(p) we realize
an extensive speedup in modular addition and subtraction routines and some small
speedup in the modular multiplication routine with an arbitrary prime modulus p
which is of arbitrary length. The most important feature of the method is that it
avoids bit-level operations which are slow on microprocessors and performs word-level
operations which are significantly faster. The proposed method has applications in
public-key cryptographic algorithms defined over the finite field GF(p), most notably
the elliptic curve digital signature algorithm. The new method provides up to 13% speedup in the execution of the ECDSA algorithm over the field GF(p) for the
length of p in the range 161���k���256.
In the finite extension field GF(p[superscript k]) we describe two new methods for obtaining
fast software implementations of the modular multiplication operation with an
arbitrary prime modulus p, which has less bit-length than the word-length of a microprocessor
and an arbitrary generator polynomial. The second algorithm is a significant
improvement over the first algorithm by using the same concepts introduced
in GF(p) arithmetic. / Graduation date: 2002
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/32447 |
| Date | 21 November 2001 |
| Creators | Yanik, Tu��rul |
| Contributors | Koc, Cetin K. |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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