Şanal, Pakize

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https://gcris.yasar.edu.tr/handle/123456789/12711
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Araş.Gör.
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01.01.09.01. Bilgisayar Mühendisliği Bölümü
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    Master Thesis
    Çok basamaklı sayılar için hızlandırılmış modüler ters alma algoritması
    (2019) Şanal, Pakize; Hışıl, Hüseyin
    In this thesis, a multi-digit modular multiplicative inverse algorithm has been aimed to SIMD parallelized by utilizing AVX2 instructions which are commonly encountered on new generation Intel processors. Euclid's extended GCD approach is an well known method which also computes modular inverse and GCD together. Binary XGCD algorithms based upon this technique are quite fast in computer architecture since they only use shifting operations instead of multiplication. Generalized version of binary XGCD algorithm was firstly introduced by Lehmer. It reduces the numbers in digit level instead of bits, from left to right which makes the algorithm fast for large numbers. The accelerated GCD algorithm proposed by Jebelean and Weber also realized the same operation in reverse direction; from right to left. Their method has been improved by some other researchers, and eventually became more efficient. In all of these algorithms process Euclid's invariant equations the distinct data in similar way and by same operation, naturally convenient for SIMD parallelization. In this thesis, the modular multiplicative inverse version of this algorithm is developed. The fundamental part of this algorithm has been SIMD parallelized successfully and the sub-functions have been parallelized partially.