# modular arithmetic

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## modular arithmetic

(mathematics)
(Or "clock arithmetic") A kind of integer arithmetic that reduces all numbers to one of a fixed set [0..N-1] (this would be "modulo N arithmetic") by effectively repeatedly adding or subtracting N (the "modulus") until the result is within this range.

The original mathematical usage considers only __equivalence__ modulo N. The numbers being compared can take any values, what matters is whether they differ by a multiple of N. Computing usage however, considers modulo to be an operator that returns the remainder after integer division of its first argument by its second.

Ordinary "clock arithmetic" is like modular arithmetic except that the range is [1..12] whereas modulo 12 would be [0..11].
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After that, if the corresponding bit of the exponent is '1' then we put in that register the modular multiplication of the base by the register C.
Secondly, we used the Interleaved Algorithm as the modular multiplication.
Rather than using relatively straightforward modular multiplication or exponentiation to relate the values within a cyclic group, elliptic curve cryptography (ECC) is based on the group of modulo n points that lie on a curve typically described as [Y.
l]) bit operations, then a modular multiplication in (2) takes (1024/160) (2) 41 times longer than a field multiplication in (1).
Compared with the hash computation, the point addition computation and the scalar multiplication computation based on the elliptic curve E, the inverse computation, the exponent computation and the modular multiplication computation over the finite field [Z.
t exponent computations when executing the Joint-Shamir-ZSS algorithm to share 0, and execute 1 inverse computation and 1 modular multiplication computation when computing [k.
So we can sum up the computational amounts (the number of modular multiplication and modular square) in all of the above procedures below.
From the first step to the fifth step, the proposed Wilson's primality test method requires 7, 4, 2, 1 modular multiplication and one modular square, respectively.
A broad-based approach to solving the modular multiplication problem defined in the previous section is to analyze all components of the problem separately, and then check if there is a fast algorithm to speed up each component.
Verbauwhede, "Faster Interleaved Modular Multiplication Based on Barrett and Montgomery Reduction Methods," IEEE Transactions on Computers, Vol.
Keywords: cryptography, encryption, modular multiplication, modular reduction.
Table 1 shows that our scheme Exp makes 2calls to Rand plus 5 modular multiplications (MM) and 2 modular inverses (MInv) in order to compute [u.

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