A. K. Lenstra and H. W. Lenstra, Jr., eds., The Development of the Number Field Sieve, Lecture Notes in Mathematics No. 1554, Springer-Verlag (1993); this book contains reprints of the articles that were critical in the development of the fastest known factoring algorithm.  Home/Search   Document Not in Database   Summary   Related Articles

....were invented especially for this purpose, although Simon s problem does not appear contrived and could conceivably be useful. Discrete logarithms and integer factoring are two number theory problems which have been studied extensively but for which no polynomial time algorithms are known [16, 20, 21, 26]. In fact, these problems are so widely believed to be hard that cryptosystems based on their hardness have been proposed, and the RSA public key cryptosystem [27] based on the hardness of fac2 toring, is in use. We show that these problems can be solved in BQP. Currently, nobody knows how to ....

A. K. Lenstra and H. W. Lenstra, Jr., eds., The Development of the Number Field Sieve, Lecture Notes in Mathematics No. 1554, Springer-Verlag (1993); this book contains reprints of the articles that were critical in the development of the fastest known factoring algorithm.

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