Algorithms for inversion mod p(k)
Yükleniyor...
Dosyalar
Tarih
2020
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Ieee Computer Soc
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
This article describes and analyzes all existing algorithms for computing x = a(-1) omod pk THORN for a prime p, and also introduces a new algorithm based on the exact solution of linear equations using p-adic expansions. The algorithm starts with the initial value c = a(-1) omod pTHORN and iteratively computes the digits of the inverse x = a(-1) omod pk THORN in base p. The mod 2 version of the algorithm is more efficient than all existing algorithms for small values of k. Moreover, it stands out as being the only one that works for any p, any k, and digit-by-digit. While the new algorithm is asymptotically worse off, it requires the minimal number of arithmetic operations (just a single addition) per step, as compared to all existing algorithms.
Açıklama
Koç, Çetin Kaya (isu author)
Koç, Cetin/0000-0002-2572-9565
Koç, Cetin/0000-0002-2572-9565
Anahtar Kelimeler
Number-Theoretic Algorithms, Computer Arithmetic, Multiplicative Inverse
Kaynak
Ieee Transactions On Computers
WoS Q Değeri
Q2
Scopus Q Değeri
Q1
Cilt
69
Sayı
6
Künye
Koc, C. K. (2020). Algorithms for Inversion Mod p(k). IEEE TRANSACTIONS ON COMPUTERS, 69(6), 907–913. https://doi.org/10.1109/TC.2020.2970411
