1. A cryptographically secure pseudorandom number generator for Julia
JuliCha (ChaCha.jl):
A cryptographically secure pseudorandom number generator for Julia
Adam Sealfon

2. Random numbers in computing
Modeling and simulation
Optimization
Randomized algorithms
Approximation algorithms
Primality testing
Games, e.g. poker
Cryptography

3. Pseudorandom number generators (PRNGs)
True randomness is expensive or limited
PRNGs take a short random seed and expand it to produce a long sequence of bits that “look random”
Programs can use this instead of true randomness
The sequence should have the same statistical properties as a random sequence, e.g.:
Roughly equal number of 0s and 1s
Short substrings are repeated with the expected probability
Ascending and descending sequences should occur in the right pattern
Random binary matrices should have high rank
etc.

4. The need for better pseudorandomness
For some applications it’s not enough for PRNG output to have the same statistical properties as a random string
We want it to be impossible to distinguish from true randomness
E.g. Poker, cryptography
Poor design or buggy implementations of PRNGs has led to cryptographic breaks

5. Cryptographically secure PRNGs (CS-PRNGs)
No efficient program should be able to tell whether it is given PRNG output or truly random bits
Equivalently, having seen many bits of the output, no efficient program should be able to guess the next bit more than 50% of the time
Indistinguishable from true randomness, so safe to use for cryptography
More complicated than ordinary PRNGs, so they tend to be slower

6. PRNGs in Julia AbstractRNG MersenneTwister ChaCha CS-PRNG
LCG is the old standard. Imperfect, but good enough for many practical purposes.
MersenneTwister predictable after 624 iterations
Linear Congruential Generator

7. PRNGs in Julia AbstractRNG MersenneTwister JuliCha
LCG is the old standard. Imperfect, but good enough for many practical purposes.
Linear Congruential Generator

8. The ChaCha CS-PRNG State consists of 16 32-bit words
Constants
State consists of bit words
From initial configuration, apply transformation via a sequence of additions, bit shifts, and xors
For each counter value, extract 512 pseudorandom bits.
Then increment counter.
Key
Counter
Nonce

9. The ChaCha CS-PRNG Relatively fast Easy to parallelize
Constants
Relatively fast
Easy to parallelize
Can be used as a stream cipher for encryption
Adopted by Google as the basis for MACs in OpenSSL
Key
Counter
Nonce

10. The U01 Test suite Runs a series of statistical tests on PRNG output
Implemented in Julia package RNGTest.jl
JuliCha and MersenneTwister passed all smallCrush tests
LCG behaved variably depending on parameters

11. Runtime of ChaCha vs. MersenneTwister

12. Runtime of ChaCha vs. C libcrypto wrapper
Not shown: wrapper for system call to /dev/urandom

13. Runtime of ChaCha vs. C libcrypto wrapper

14. Median time to produce 1000 UInt32s
Mersenne
Twister
ChaCha
C libcrypto wrapper
OS /dev/
urandom
3.19 μs μs
1.4 ms
6.8 s
85x faster -
5x slower
25,000x slower

16. Encryption using JuliCha