Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Quantum computation and quantum information
Quantum computation and quantum information
Sharp probability estimates for Shor's order-finding algorithm
Quantum Information & Computation
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The quantum factorization effectiveness is limited both by inherent randomness of the quantum measurement and requirement of special selection of parameters controlling behavior of classic algorithms supporting quantum device operation. However, only coarse bounds on probability of successful parameters selection have been published so far. The proof of an exact expression on factorization efficiency constitutes the main contribution of the paper. The proved expression simply relates Shor's algorithm efficiency to properties of the factors forming the composite number.