Now in a new study, physicists have set a new record for quantum factorization by developing the first quantum algorithm that can factor a three-digit integer, 143, into its prime factors, 11 and 13.

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Keeping the private key private only matters if integer factorization (or discrete logarithms, for the other major family of asymmetric encryption algorithms) remains a hard problem.

This algorithm enables the solving of integer factorization and discrete logarithm problems, which are the basis of most (not to say all) widely used public-key cryptography algorithms.

Therefore, if an 'algorithm that enables prime factorization of a huge number of digits' is developed, its safety will be shaken.

The need to evaluate the security of factor-based cryptosystems, has led to advancements in integer factorization algorithms.