| Summary: | 碩士 === 國立成功大學 === 電機工程研究所 === 82 === n recent years, Galios fields have received more attention due
o their important and practical applications in areas
ofommunications such as error-correcting codes, digital
signalrocessing, and cryptography. Although arithmetic in GF($2
^m$)oes not involve carries, the operations such as
multiplicationnd exponentiation are still a big challenge if we
want carryhem out efficiently . The elements of GF($2^m$) can
beepresented in several equivalent forms, i.e., standard basis,
ormal basis and dual basis. These basis representations
ofultipliers have their individual applications because each
hasts distinct features which can apply to different areas. In
thishesis, we propose a new scheme of standard basis multiplier
forerforming fast multiplication in GF($2^m$). The bit-
slicerchitecture of serial-in-serial-out standard basis
multipliers modified. Instead of multiplying the multiplicand
of multipliery one-bit by one-bit, the multiplicand of
multiplier can beerformed by two-bit by two-bit in one cycle.
So, the speed ofhe proposed multiplier is about one and half
times faster thanhe conventional bit-slice serial-in-serial-out
multiplier y Scott. Besides, the proposed architecture is
regular and uch that it is very suitable for VLSI
implementation. s the essential step in both Diffie-Hellman
and ElGamal systems.n this thesis, we also study a technique
for performing n GF($2^m$) based on the proposed multiplier
by using thequare -and-multiply algorithm.
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