National Engineering Academy of the Republic of Kazakhstan, Almaty, Kazakhstan.
Almaty University of Power Engineering and Telecommunications Named After Gumarbek Daukeyev, Almaty, Republic of Kazakhstan.
PLoS One. 2023 Oct 25;18(10):e0293294. doi: 10.1371/journal.pone.0293294. eCollection 2023.
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.
提出了一种二进制形式整数的交替表示法，其中使用-1 和 +1 代替 0 和 1。结果表明，这种表示法对于模 p = 2n+1 的乘法运算非常方便。对于这样的数字，可以实现类似于模 Mersenne 数的乘法算法。结果表明，可以为这样的数字提出一种简单的数字对数计算算法。该算法除其他外，允许将模素数 p = 2n+1 的乘法运算减少为加法运算。
