ISAAC (cipher)
Encyclopedia
ISAAC is a cryptographically secure pseudorandom number generator
and a stream cipher
designed by Robert J. Jenkins Jr.
in 1996.
has similarities with RC4
. It uses an array of 256 four-octet 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.
has been undertaken by Marina Pudovkina (2001). 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
instead of 
. This result has had no practical impact on the security of ISAAC.
In 2006 Jean-Philippe Aumasson discovered several sets of weak states. 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 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 is flawed, since the Paul
-Preneel
attack is based on an erroneous algorithm rather than the real ISAAC.
An improved version of ISAAC is proposed, called ISAAC+.
ISAAC is used in the Unix tool shred
to securely overwrite data.
Cryptographically secure pseudorandom number generator
A cryptographically secure pseudo-random number generator is a pseudo-random number generator with properties that make it suitable for use in cryptography.Many aspects of cryptography require random numbers, for example:...
and a stream cipher
Stream cipher
In cryptography, a stream cipher is a symmetric key cipher where plaintext digits are combined with a pseudorandom cipher digit stream . In a stream cipher the plaintext digits are encrypted one at a time, and the transformation of successive digits varies during the encryption...
designed by Robert J. Jenkins Jr.
Robert John Jenkins Junior
Robert John Jenkins Junior, also known as Bob Jenkins, is a computer professional and author of several fast pseudorandom number generators such as ISAAC and hash functions Bob Jenkins was born in Akron, Ohio, in 1966.-References:...
in 1996.
Operation
The ISAAC algorithmAlgorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
has similarities with RC4
RC4
In cryptography, RC4 is the most widely used software stream cipher and is used in popular protocols such as Secure Sockets Layer and WEP...
. It uses an array of 256 four-octet integers
Integer (computer science)
In computer science, an integer is a datum of integral data type, a data type which represents some finite subset of the mathematical integers. Integral data types may be of different sizes and may or may not be allowed to contain negative values....
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.
Cryptanalysis
CryptanalysisCryptanalysis
Cryptanalysis is the study of methods for obtaining the meaning of encrypted information, without access to the secret information that is normally required to do so. Typically, this involves knowing how the system works and finding a secret key...
has been undertaken by Marina Pudovkina (2001). 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
instead of . This result has had no practical impact on the security of ISAAC.In 2006 Jean-Philippe Aumasson discovered several sets of weak states. 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 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 is flawed, since the Paul
Souradyuti Paul
Souradyuti Paul is an Indian cryptologist . Formerly a member of COSIC, he is currently working as a Guest Researcher for the National Institute of Standards and Technology in the United States...
-Preneel
Bart Preneel
Bart Preneel is a Belgian cryptographer and cryptanalyst. He is a professor at Katholieke Universiteit Leuven, in the COSIC group, president of the International Association for Cryptologic Research, and project manager of ECRYPT....
attack is based on an erroneous algorithm rather than the real ISAAC.
An improved version of ISAAC is proposed, called ISAAC+.
Usage outside of cryptography
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.ISAAC is used in the Unix tool shred
Shred (Unix)
shred is a Unix command that can be used to securely delete files and devices so that they can be recovered only with great difficulty with specialised hardware, if at all. It is a part of GNU Core Utilities.-Background:...
to securely overwrite data.
External links
- Official ISAAC website
- Pascal/Delphi port
- Math::Random::ISAAC, a Perl module implementation of the algorithm