A Study and Implementation of Exponentiation in GF(2^m)

• Main Authors: Wen-Ching Pong, 彭文清
• Other Authors: Chi-Sung Laih
• Format: Others
• Language: en_US
• Published: 1994
• Online Access: http://ndltd.ncl.edu.tw/handle/13980488351125333683

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.