Clarification on multiplication from modular exponentiation precompiled contract

1. What is modular exponentiation method?
2. Which algorithm can be viewed as the reciprocal of modular exponentiation?
3. Which of these symbols is used for calculating exponentiation A * B C D?
4. What is the order of 2 modulo 11?
5. What is modulo inverse of a number?
6. What is the time complexity of modular exponentiation?
7. What is multiplicative inverse in modular arithmetic?
8. Which of the following method uses the concept that exponentiation is computationally inexpensive in the finite field?
9. Which of the following can be used for exponentiation in Python?
10. What is the order of 3 modulo 5?
11. What is the order of 9 modulo 13?

What is modular exponentiation method?

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.

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

A modular multiplicative inverse of a modulo m can be found by using the extended Euclidean algorithm. so, a modular multiplicative inverse of a has been calculated.

Which of these symbols is used for calculating exponentiation A * B C D?

The caret (^) is used as the exponentiation operator. Note: The exponent operator should not be confused with the base-10 exponent symbol.

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.

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 time complexity of modular exponentiation?

Modular exponentiation: [x^y mod N]. Directly calculate x^y with y-1 multiplications would take too long. The algorithm in Figure 1.4 does O(n) recursive calls, and each of them takes O(n²) time, so the complexity is O(n³).

What is multiplicative inverse in modular arithmetic?

The modular inverse of a number refers to the modular multiplicative inverse. For any integer a such that (a, p) = 1 there exists another integer b such that ab≡ 1 (mod p). The integer b is called the multiplicative inverse of a which is denoted as b = a⁻¹.

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.

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.

What is the order of 3 modulo 5?

As you can see, the answer to 3 mod 5 is 3.

What is the order of 9 modulo 13?

Modulus Method

We can see that multiples of 13 are 0, 13, 26, 39, etc. The highest multiple that is less than or equal to 9 is 0. As we can see, this is the same answer as the modulo method and the answer is 9.