I am interested in generation of pseudo-random numbers for cryptography. Besides Chapter 5 of Menezes/Oorschot/Vanstone; Chapter 8 of Stinson; and Chapter 3 of Goldreich, where else could I find more? I'm interested in general principles for designing PRNGs (desirable properties, tests, etc).
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3$\begingroup$ Not on design per se, but you may be interested in Goldreich's newer book: books.google.com/books?id=9k6Lw2U2XCkC $\endgroup$– S HuntsmanDec 11, 2010 at 16:07
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$\begingroup$ @S Huntsman: thanks a lot for that! I didn't know Goldreich had a book on PRNGs. $\endgroup$– JayDec 11, 2010 at 16:10
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3 Answers
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You might want to check out
- Chapters 5 and 6 of Katz and Lindell
- Pseudorandomness by S. Vadhan
- Parwise Independence and Derandomization by Luby and Wigderson
- Pseudorandomness and Combinatorial Constructions by Trevisan
- Goldreich's webpage on pseudorandomness, where he has pointers to other sources.
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1$\begingroup$ Most of this is not very relevant to practical implementations of PRNGs for cryptography. This is not a good set of resources to give an implementor. $\endgroup$– D.W.May 11, 2011 at 9:01
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If you are thinking of implementing your ideas, there is a standard battery of tests that PRNG implementations are given. These tests (DIEHARD and successor DIEHARDER) may be downloaded from its archived webpage and http://www.phy.duke.edu/~rgb/General/dieharder.php respectively.
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4$\begingroup$ Important cautionary note: passing DIEHARD does not mean your PRNG is any good. This is not a resource I would give to an implementor who needs to implement a secure PRNG. $\endgroup$– D.W.May 11, 2011 at 9:02
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Are you interested in implementing a PRNG? If so, your best bet is not to design one yourself, but just use a standard one. /dev/urandom is the right answer on most platforms. If /dev/urandom doesn't exist, generating a random AES key with /dev/random and then running AES-CTR mode to generate lots of pseudorandom numbers is another reasonable approach.
I recommend that you read Cryptography Engineering, by Ferguson, Schneier, and Kohno. It is an excellent book. It will teach you a lot about how to design and build real cryptosystems.
If you actually have to build a system that will be deployed in practice, I recommend that you do not take your guidance from the theoretical CS community, but rather from the community of practitioners and practice-oriented researchers. Much of the theoretical CS work will not be very relevant, or potentially even misleading, to practical implementation of a secure PRNG. I also encourage you to look at the IT Security stack exchange for those kinds of questions.
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4$\begingroup$ The question explicitly says he is interested in general principles, and the question was asked on the Theoretical CS stack exchange... $\endgroup$ May 12, 2011 at 0:24