generateInitialization: Generates a random integer vector of a specified length using...

View source: R/functions.R

generateInitializationR Documentation

Generates a random integer vector of a specified length using AES

Description

In a typical application of the package, this function is not called directly by the user and the function is called from setVectorSeed(). The function is made available in order to simplify testing correctness of the package and the documentation of this function explains the exact algorithm used by setVectorSeed().

Usage

  generateInitialization(vseed, m)

Arguments

vseed

Numeric vector of an arbitrary nonzero length, whose components have integer values from [0, 2^32 - 1].

m

Numeric, the length of the required output integer vector.

Details

The function transforms an input vector vseed of an arbitrary length to a random integer vector of length m using Advanced Encryption Standard (AES) block cipher. The function setVectorSeed() calls generateInitialization(vseed, 624) and uses its output as an initial state of the R base Mersenne-Twister random number generator.

The vector vseed is first replaced by c(vseed, length(vseed)) in order to guarantee that if vseed1 is a prefix of vseed2, but they have a different length, then the outputs are unrelated. If the length of the resulting vector is not divisible by 8, the vector is padded by zeros to the nearest larger length divisible by 8 in order to meet the requirements of the AES algorithm. The resulting vector is splitted into blocks of length 8 and these blocks are used as 256-bit keys in AES. Each of these keys is used to encrypt a counter sequence of length ceiling(m/4). The encrypted values of these sequences are combined by XOR to a single sequence of ceiling(m/4) values, each of which is a sequence of 16 bytes. These sequences are splitted into subsequences of 4 bytes, each of which encodes a 32-bit integer in an endianness independent way. The first m of the obtained integers form the output.

If length(vseed) <= 7, then the above algorithm uses AES in counter mode suggested in Fortuna random number generator as described at https://en.wikipedia.org/wiki/Fortuna_(PRNG) with a key specified by the user. If length(vseed) >= 8, the algorithm uses XOR of the outputs of several Fortuna generators with keys formed from disjoint parts of the input vector and disjoint counter sequences.

Value

Vector of length m of integer type suitable for substituting into the components of .Random.seed. This means that the components are integers from the interval [-2^31 + 1, 2^31 - 1] or NA, which represents -2^31. If m == 624, the output vector is suitable as the initial state of Mersenne-Twister to be copied into .Random.seed[3:626].

If m1 < m2, then generateInitialization(vseed, m1) is equal to the first m1 components of generateInitialization(vseed, m2).

References

https://en.wikipedia.org/wiki/Advanced_Encryption_Standard, https://en.wikipedia.org/wiki/Fortuna_(PRNG).

See Also

setVectorSeed

Examples

  s1 <- generateInitialization(1, 3)
  s2 <- generateInitialization(c(1, 0), 3)
  s3 <- generateInitialization(c(1, 0, 0), 3)
  stopifnot(s1 == c(2054882070, -83320660, -37036705))
  stopifnot(s2 == c(-1435341980, 1760892082, 970206446))
  stopifnot(s3 == c(1941187208, 915534877, -365000103))

rngSetSeed documentation built on Sept. 19, 2023, 9:06 a.m.