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A Note on Shor’s Quantum Algorithm for Prime Factorization
Authors: Zhengjun CaoAbstract:
It’s well known that Shor proposed a
polynomial time algorithm for prime factorization by using quantum
computers. For a given number n, he gave an algorithm for
finding the order r of an element x (mod n) instead of giving an algorithm for factoring n directly. The indirect
algorithm is feasible because factorization can be reduced to
finding the order of an element by using randomization. But a
point should be stressed that the order of the number must be
even. Actually, the restriction can be removed in a particular
case. In this paper, we show that factoring RSA modulus (a product
of two primes) only needs to find the order of 2, whether it is
even or not.
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