Modular exponentiation

Modular exponentiation is exponentiation performed over a modulus. ... Modular exponentiation is the remainder when an integer b (the base) is raised to the power e (the exponent), and divided by a positive integer m (the modulus); that is, c = b^e mod m. From the definition of division, it follows that 0 ≤ c < m.

1. What is considered in the modular arithmetic?
2. Which algorithm can be viewed as the reciprocal of modular exponentiation?
3. What does mod mean in math?
4. What is the order of 2 modulo 11?
5. How can we calculate a B mod C quickly for any B?
6. What is modulo inverse of a number?
7. What is the function of modular arithmetic?
8. Why do we use modular arithmetic?
9. Why do we use modular exponentiation?
10. Which of the following can be used for exponentiation in Python?
11. Which of the following method uses the concept that exponentiation is computationally inexpensive in the finite field?

What is considered in the modular arithmetic?

Modular arithmetic is a system of arithmetic for integers, which considers the remainder. In modular arithmetic, numbers "wrap around" upon reaching a given fixed quantity (this given quantity is known as the modulus) to leave a remainder.

Which algorithm can be viewed as the reciprocal of modular exponentiation?

In the extended Euclidean algorithm, x is the modular multiplicative inverse of A under modulo M. Therefore, the answer is x. You can use the extended Euclidean algorithm to find the multiplicative inverse. For example, if A=5 and M=12, then G C D ( A , B ) = 1 .

What does mod mean in math?

Given two positive numbers a and n, a modulo n (abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor. The modulo operation is to be distinguished from the symbol mod, which refers to the modulus (or divisor) one is operating from.

What is the order of 2 modulo 11?

10, so it can be 1, 2,5 OR 10. we know 20= 1 mod Il by Euler's Theorem Cor Permat's since it is prime), so the Order of 2 modulo 11 is 10.

How can we calculate a B mod C quickly for any B?

Computing (a*b) mod c quickly for c=2^N +-1.

What is modulo inverse of a number?

A modular inverse of an integer (modulo ) is the integer such that. A modular inverse can be computed in the Wolfram Language using PowerMod[b, -1, m]. Every nonzero integer has an inverse (modulo ) for a prime and not a multiple of. . For example, the modular inverses of 1, 2, 3, and 4 (mod 5) are 1, 3, 2, and 4.

What is the function of modular arithmetic?

In computer algebra, modular arithmetic is commonly used to limit the size of integer coefficients in intermediate calculations and data. It is used in polynomial factorization, a problem for which all known efficient algorithms use modular arithmetic.

Why do we use modular arithmetic?

Modular arithmetic is used extensively in pure mathematics, where it is a cornerstone of number theory. But it also has many practical applications. It is used to calculate checksums for international standard book numbers (ISBNs) and bank identifiers (Iban numbers) and to spot errors in them.

Why do we use modular exponentiation?

Modular exponentiation is efficient to compute, even for very large integers. On the other hand, computing the modular discrete logarithm – that is, finding the exponent e when given b, c, and m – is believed to be difficult.

Which of the following can be used for exponentiation in Python?

The Python ** operator is used to raise a number in Python to the power of an exponent. In other words, ** is the power operator in Python. Our program returns the following result: 25.

Which of the following method uses the concept that exponentiation is computationally inexpensive in the finite field?

Now, the Diffie–Hellman key exchange can have the concept that exponentiation is computationally inexpensive in the finite fields and the discrete logarithm which is the inverse of exponentiation, can be computationally expensive.