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Unformatted text preview: years from now, we may be able to factor anything. I think that is unlikely, though. Not everyone will agree with my recommendations. The NSA has mandated 512-bit to 1024-bit keys for their Digital Signature Standard (see Section 20.1)—far less than I recommend for long-term security. Pretty Good Privacy (see Section 24.12) has a maximum RSA key length of 2047 bits. Arjen Lenstra, the world’s most successful factorer, refuses to make predictions past 10 years . Table 7.8 gives Ron Rivest’s key-length recommendations, originally made in 1990, which I consider much too optimistic . While his analysis looks fine on paper, recent history illustrates that surprises regularly happen. It makes sense to choose your keys to be resilient against future surprises. Table 7.7 Long-range Factoring Predictions Year Key Length (in bits) 1995 2005 2015 2025 2035 2045 1024 2048 4096 8192 16,384 32,768 Low estimates assume a budget of $25,000, the quadratic sieve algorithm, and a technology advance of 20 percent per year. Average estimates assume a budget of $25 million, the general number field sieve algorithm, and a technology advance of 33 percent per year. High estimates assume a budget of $25 billion, a general quadratic sieve algorithm running at the speed of the special number field sieve, and a technology advance of 45 percent per year. There is always the possibility that an advance in factoring will surprise me as well, but I factored that into my calculations. But why trust me? I just proved my own foolishness by making predictions. DNA Computing
Now it gets weird. In 1994 Leonard M. Adleman actually demonstrated a method for solving an NP-complete problem (see Section 11.2) in a biochemistry laboratory, using DNA molecules to represent guesses at solutions to the problem . (That’s “solutions” meaning “answers,” not meaning “liquids containing solutes.” Terminology in this field is going to be awkward.) The problem that Adleman solved was an instance of the Directed Hamiltonian Path problem: Given a map of cities connected...
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- Fall '10