On the Cost of Factoring RSA-1024
msra(2003)
摘要
As many cryptographic schemes rely on the hardness of integer factorization, exploration of the concrete costs of factoring large integers is of considerable interest. Most research has focused on PC-based implementations of factoring algorithms; these have successfully factored 530-bit integers, but practically cannot scale much further. Recent works have placed the bottleneck at the sieving step of the Number Field Sieve algorithm. We present a new implementation of this step, based on a custom-built hardware device that achieves a very high level of parallelism ”for free”. The design combines algorithmic and technological aspects: by devising algorithms that take advantage of certain tradeoffs in chip manufacturing technology, efficiency is increased by many orders of magnitude compared to previous proposals. Using this hypothetical device (and ignoring the initial R&D costs), it appears possible to break a 1024-bit RSA key in one year using a device whose cost is about $10M (previous predictions were in the trillions of dollars).
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关键词
integer factorization
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