Paper 2017/077
Quantum algorithms for computing short discrete logarithms and factoring RSA integers
Martin Ekerå and Johan Håstad
Abstract
In this paper we generalize the quantum algorithm for computing short discrete logarithms previously introduced by Ekerå so as to allow for various tradeoffs between the number of times that the algorithm need be executed on the one hand, and the complexity of the algorithm and the requirements it imposes on the quantum computer on the other hand. Furthermore, we describe applications of algorithms for computing short discrete logarithms. In particular, we show how other important problems such as those of factoring RSA integers and of finding the order of groups under side information may be recast as short discrete logarithm problems. This immediately gives rise to an algorithm for factoring RSA integers that is less complex than Shor’s general factoring algorithm in the sense that it imposes smaller requirements on the quantum computer. In both our algorithm and Shor’s algorithm, the main hurdle is to compute a modular exponentiation in superposition. When factoring an n bit integer, the exponent is of length 2n bits in Shor’s algorithm, compared to slightly more than n/2 bits in our algorithm.
Metadata
 Available format(s)
 Category
 Publickey cryptography
 Publication info
 Preprint.
 Keywords
 discrete logarithm problemfactoringRSAShor's algorithm
 Contact author(s)
 ekera @ kth se
 History
 20170206: received
 Short URL
 https://ia.cr/2017/077
 License

CC BY
BibTeX
@misc{cryptoeprint:2017/077, author = {Martin Ekerå and Johan Håstad}, title = {Quantum algorithms for computing short discrete logarithms and factoring {RSA} integers}, howpublished = {Cryptology ePrint Archive, Paper 2017/077}, year = {2017}, note = {\url{https://eprint.iacr.org/2017/077}}, url = {https://eprint.iacr.org/2017/077} }