# AES Counter-based RNG¶

class randomgen.aes.AESCounter(seed=None, *, counter=None, key=None, mode=None)

Container for the AES Counter pseudo-random number generator.

Parameters:
seed{None, int, SeedSequence}, optional

Random seed initializing the pseudo-random number generator. Can be an integer in [0, 2**128), a SeedSequence instance or None (the default). If seed is None, then data is read from /dev/urandom (or the Windows analog) if available. If unavailable, a hash of the time and process ID is used.

counter{None, int, array_like[uint64]}, optional

Counter to use in the AESCounter state. Can be either a Python int in [0, 2**128) or a 2-element uint64 array. If not provided, the counter is initialized at 0.

key{None, int, array_like[uint64]}, optional

Key to use in the AESCounter state. Unlike seed, which is run through another RNG before use, the value in key is directly set. Can be either a Python int in [0, 2**128) or a 2-element uint64 array. key and seed cannot both be used.

mode{None, “sequence”, “legacy”}, optional

The seeding mode to use. “legacy” uses the legacy SplitMix64-based initialization. “sequence” uses a SeedSequence to transforms the seed into an initial state. None defaults to “sequence”.

Notes

AESCounter is a 64-bit PRNG that uses a counter-based design based on the AES-128 cryptographic function [1]. Instances using different values of the key produce distinct sequences. AESCounter has a period of $$2^{128}$$ and supports arbitrary advancing and jumping the sequence in increments of $$2^{64}$$. These features allow multiple non-overlapping sequences to be generated.

AESCounter provides a capsule containing function pointers that produce doubles, and unsigned 32 and 64- bit integers. These are not directly consumable in Python and must be consumed by a Generator or similar object that supports low-level access.

See Philox and ThreeFry for a related counter-based PRNG.

State and Seeding

The AESCounter state vector consists of a 64-element array of uint8 that capture buffered draws from the distribution, a 22-element array of uint64s holding the seed (11 by 128bits), and an 8-element array of uint64 that holds the counters (4 by 129 bits). The first two elements of the seed are the value provided by the user (or from the entropy pool). The offset varies between 0 and 64 and shows the location in the buffer of the next 64 bits.

AESCounter is seeded using either a single 128-bit unsigned integer or a vector of 2 64-bit unsigned integers. In either case, the seed is used as an input for a second random number generator, SplitMix64, and the output of this PRNG function is used as the initial state. Using a single 64-bit value for the seed can only initialize a small range of the possible initial state values.

Parallel Features

AESCounter can be used in parallel applications by calling the jump method to advances the state as-if $$2^{64}$$ random numbers have been generated. Alternatively, advance can be used to advance the counter for any positive step in [0, 2**128). When using jump, all generators should be initialized with the same seed to ensure that the segments come from the same sequence.

>>> from numpy.random import Generator
>>> from randomgen import AESCounter
>>> rg = [Generator(AESCounter(1234)) for _ in range(10)]
# Advance each AESCounter instances by i jumps
>>> for i in range(10):
...     rg[i].bit_generator.jump(i)


Alternatively, AESCounter can be used in parallel applications by using a sequence of distinct keys where each instance uses different key.

>>> key = 2**93 + 2**65 + 2**33 + 2**17 + 2**9
>>> rg = [Generator(AESCounter(key=key+i)) for i in range(10)]


Compatibility Guarantee

AESCounter makes a guarantee that a fixed seed and will always produce the same random integer stream.

References

[1]

Advanced Encryption Standard. (n.d.). In Wikipedia. Retrieved June 1, 2019, from https://en.wikipedia.org/wiki/Advanced_Encryption_Standard

Examples

>>> from numpy.random import Generator
>>> from randomgen import AESCounter
>>> rg = Generator(AESCounter(1234))
>>> rg.standard_normal()
0.123  # random

Attributes:

Lock instance that is shared so that the same bit git generator can be used in multiple Generators without corrupting the state. Code that generates values from a bit generator should hold the bit generator’s lock.

seed_seq{None, SeedSequence}

The SeedSequence instance used to initialize the generator if mode is “sequence” or is seed is a SeedSequence. None if mode is “legacy”.

## Seeding and State¶

 seed([seed, counter, key]) Seed the generator state Get or set the PRNG state

## Parallel generation¶

 advance(delta) Advance the underlying RNG as-if delta draws have occurred. jump([iter]) Jumps the state as-if iter * 2**64 random numbers are generated jumped([iter]) Returns a new bit generator with the state jumped

## Extending¶

 cffi CFFI interface ctypes ctypes interface

## Testing¶

 random_raw([size, output]) Return randoms as generated by the underlying BitGenerator