| 1. | Also in 1994, Peter Shor devised his quantum factorization algorithm.
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| 2. | The unique factorization of Euclidean domains is useful in many applications.
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| 3. | They exploited a weakness unique to cryptosystems based on integer factorization.
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| 4. | Integer factorization for large integers appears to be a difficult problem.
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| 5. | For instance using the factorization of the sum of two cubes:
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| 6. | This asserts that every integer has a unique factorization into primes.
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| 7. | This is roughly the basis of Fermat's factorization method.
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| 8. | To finish this factorization example, continue reading Congruence of squares.
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| 9. | This factorization is unique up to the sign of the content.
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| 10. | Resulting list of strings is standard factorization of a given string.
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