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| '''ISAAC''' ('''indirection, shift, accumulate, add, and count''') is a [[cryptographically secure pseudorandom number generator]] and a [[stream cipher]] designed by [[Robert John Jenkins Junior|Robert J. Jenkins Jr.]] in 1996.<ref>Robert J. Jenkins Jr., ISAAC. Fast Software Encryption 1996, pp41–49.</ref>
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| == Operation ==
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| The ISAAC [[algorithm]] has similarities with [[RC4]]. It uses an [[Array data structure|array]] of 256 four-octet [[Integer (computer science)|integers]] as the internal state, writing the results to another 256 four-octet integer array, from which they are read one at a time until empty, at which point they are recomputed. The computation consists of altering i-element with (i⊕128)-element, two elements of the state array found by indirection, an accumulator, and a counter, for all values of i from 0 to 255. Since it only takes about 19 32-bit operations for each 32-bit output word, it is very fast on 32-bit computers.
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| == Cryptanalysis ==
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| [[Cryptanalysis]] has been undertaken by Marina Pudovkina (2001).<ref>Marina Pudovkina, A known plaintext attack on the ISAAC keystream generator, 2001, Cryptology ePrint Archive: Report 2001/049, [http://eprint.iacr.org/2001/049/].</ref> Her attack can recover the initial state with a complexity that is approximated to be less than the time needed for searching through the square root of all possible initial states. In practice this means that the attack needs <math>4.67 \times 10^{1240}</math> instead of <math>10^{2466}</math>. This result has had no practical impact on the security of ISAAC.
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| In 2006 Jean-Philippe Aumasson discovered several sets of weak states.<ref>Jean-Philippe Aumasson, [http://eprint.iacr.org/2006/438 On the pseudo-random generator ISAAC]. Cryptology ePrint archive, report 2006/438, 2006.</ref> The fourth presented (and smallest) set of weak states leads to a highly biased output for the first round of ISAAC and allows the derivation of the internal state, similar to a [[Fluhrer, Mantin and Shamir attack|weakness in RC4]]. It is not clear if an attacker can tell from just the output whether the generator is in one of these weak states or not. He also shows that a previous attack<ref>Souradyuti Paul, Bart Preneel, On the (In)security of Stream Ciphers Based on Arrays and Modular Addition.Asiacrypt 2006.</ref> is flawed, since the [[Souradyuti Paul|Paul]]-[[Bart Preneel|Preneel]] attack is based on an erroneous algorithm rather than the real ISAAC.
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| An improved version of ISAAC is proposed, called ISAAC+.
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| == Usage outside of cryptography ==
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| Many implementations of ISAAC are so fast that they can compete with other high speed PRNGs, even with those designed primarily for speed not for security. Only a few other generators of such high quality and speed exist in usage.
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| ISAAC is used in the Unix tool [[shred (Unix)|shred]] to securely overwrite data.
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| == References ==
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| {{reflist|30em}}
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| == External links ==
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| * [http://www.burtleburtle.net/bob/rand/isaacafa.html Official ISAAC website]
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| * [http://www.wolfgang-ehrhardt.de/misc_en.html#prng Pascal/Delphi port]
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| * [http://search.cpan.org/dist/Math-Random-ISAAC Math::Random::ISAAC], a Perl module implementation of the algorithm
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| * [https://github.com/rubycon/isaac.js isaac.js], a JavaScript implementation
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| {{Cryptography navbox | stream}}
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| {{DEFAULTSORT:Isaac (Cipher)}}
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| [[Category:Cryptographically secure pseudorandom number generators]]
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| [[Category:Stream ciphers]]
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