How Shor's Algorithm Factors 314191

What is the main objective of Shor's Algorithm in the context of cryptography?

• To generate random numbers for encryption.

• To factor large composite numbers into their prime factors.

• To create unbreakable encryption keys.

• To perform complex quantum computations quickly.

How does a quantum computer primarily assist Shor's Algorithm in finding factors?

• By performing classical arithmetic operations faster than traditional computers.

• By generating random guesses for potential factors.

• By efficiently finding the period 'P' of a modular exponentiation function.

• By directly calculating the prime factors without intermediate steps.

Which quantum operation is applied to the superposition of possible powers to extract the frequency related to the period 'P'?

• Euclid's Algorithm

• Quantum Fourier Transform

• Modular Exponentiation

• Superposition Measurement

What critical property must the period 'P' possess for the g^(P/2) ± 1 step of Shor's Algorithm to be directly applicable in finding factors?

• 'P' must be a prime number.

• 'P' must be an odd number.

• 'P' must be an even number.

• 'P' must be greater than the number being factored.