Buchanan WJand Wang H, "Speed Enhancements
for the RSA Method", ACM Journal of Experimental
Algorithmics. Submitted.
Abstract:
This thesis
presents methods that can be used to improve the
operation of the RSA encryption method. It shows
the principles of encryption, and then expands this
to give the operation of public-key methods, which
includes the number value theorems applied onto
RSA system, Modular Multiplication and Modular Exponentiation,
and the basic theory and content of RSA system.
The thesis
then presents four methods which can be used to
improve the encryption/decryption process. In this,
Single Precision Multiplication and Listing Method
are used to speed up the modular calculation in
the modular multiplication, the M-ary Sliding window
is used to speed up exponentiation multiplication,
and Chinese Remainder Theory (CRT) is used to speed
up decryption.
Single
Precision Multiplication is a method of multiplying
and modulating to speed upmodular multiplication,
which after evaluation can increase about operations
by four to five times in speed. The Listing Method
pre-stores values from earlier calculations which
saves in the relocation of figures and calculation
time.
The M-ary
method can be used to complete the exponentiation
multiplication. Results show that an exponent of
1024 bits can give the calculation efficiency up
to 24%. The Chinese Remainder Theorem is used to
give an improvement of the decryption speed up by
up to four times.
Single
Precision Multiplication is a method of multiplying
and modulating to speed upmodular multiplication,
which after evaluation can increase about operations
by four to five times in speed. The Listing Method
pre-stores values from earlier calculations which
saves in the relocation of figures and calculation
time.