Features of digital signal processing algorithms using Galois fields GF(2n+1)
An alternating representation of integers in binary form is proposed, in which the numbers -1 and +1 are used instead of zeros and ones. It is shown that such a representation creates considerable convenience for multiplication numbers modulo p = 2 n +1. For such numbers, it is possible to implement...
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| Veröffentlicht in: | PloS one Jg. 18; H. 10; S. e0293294 |
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| Abstract | An alternating representation of integers in binary form is proposed, in which the numbers -1 and +1 are used instead of zeros and ones. It is shown that such a representation creates considerable convenience for multiplication numbers modulo p = 2
n
+1. For such numbers, it is possible to implement a multiplication algorithm modulo p, similar to the multiplication algorithm modulo the Mersenne number. It is shown that for such numbers a simple algorithm for digital logarithm calculations may be proposed. This algorithm allows, among other things, to reduce the multiplication operation modulo a prime number p = 2
n
+1 to an addition operation. |
|---|---|
| AbstractList | An alternating representation of integers in binary form is proposed, in which the numbers -1 and +1 are used instead of zeros and ones. It is shown that such a representation creates considerable convenience for multiplication numbers modulo p = 2
n
+1. For such numbers, it is possible to implement a multiplication algorithm modulo p, similar to the multiplication algorithm modulo the Mersenne number. It is shown that for such numbers a simple algorithm for digital logarithm calculations may be proposed. This algorithm allows, among other things, to reduce the multiplication operation modulo a prime number p = 2
n
+1 to an addition operation. An alternating representation of integers in binary form is proposed, in which the numbers -1 and +1 are used instead of zeros and ones. It is shown that such a representation creates considerable convenience for multiplication numbers modulo p = 2n+1. For such numbers, it is possible to implement a multiplication algorithm modulo p, similar to the multiplication algorithm modulo the Mersenne number. It is shown that for such numbers a simple algorithm for digital logarithm calculations may be proposed. This algorithm allows, among other things, to reduce the multiplication operation modulo a prime number p = 2n+1 to an addition operation. An alternating representation of integers in binary form is proposed, in which the numbers -1 and +1 are used instead of zeros and ones. It is shown that such a representation creates considerable convenience for multiplication numbers modulo p = 2n+1. For such numbers, it is possible to implement a multiplication algorithm modulo p, similar to the multiplication algorithm modulo the Mersenne number. It is shown that for such numbers a simple algorithm for digital logarithm calculations may be proposed. This algorithm allows, among other things, to reduce the multiplication operation modulo a prime number p = 2n+1 to an addition operation.An alternating representation of integers in binary form is proposed, in which the numbers -1 and +1 are used instead of zeros and ones. It is shown that such a representation creates considerable convenience for multiplication numbers modulo p = 2n+1. For such numbers, it is possible to implement a multiplication algorithm modulo p, similar to the multiplication algorithm modulo the Mersenne number. It is shown that for such numbers a simple algorithm for digital logarithm calculations may be proposed. This algorithm allows, among other things, to reduce the multiplication operation modulo a prime number p = 2n+1 to an addition operation. |
| Author | Matrassulova, Dinara K. Suleimenov, Ibragim E. Vitulyova, Yelizaveta S. |
| AuthorAffiliation | 2 Almaty University of Power Engineering and Telecommunications Named After Gumarbek Daukeyev, Almaty, Republic of Kazakhstan Roma Tre University: Universita degli Studi Roma Tre, ITALY 1 National Engineering Academy of the Republic of Kazakhstan, Almaty, Kazakhstan |
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| Cites_doi | 10.1109/ISTC.2010.5613874 10.1142/S0218126620300081 10.11591/ijeecs.v23.i2.pp871-878 10.1038/s41598-023-28272-1 10.1007/s10958-022-05688-0 10.11591/ijeecs.v23.i3.pp1718-1726 10.24234/wisdom.v21i1.721 10.24297/ijct.v3i2c.2896 10.1145/272991.272995 10.1080/11663081.2019.1656393 10.11591/eei.v11i1.3463 10.1049/cmu2.12443 10.1016/j.entcs.2020.10.006 |
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| Title | Features of digital signal processing algorithms using Galois fields GF(2n+1) |
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