Random quality measurements
Obviously, randomness is very important when doing cryptography.
Zenroom accepts a random seed when called or retrieves one automatically from the host system.
Zenroom is fully deterministic: if the same random seed is provided then all results of transformations will be exactly the same, except for the sorting order of elements in its output, which must be sorted by the caller with a constant algorithm.
In order to generate key material, it is often needed to have a random number generator (RNG). But generating good randomness (one which is unpredictable to attackers) is very challenging for a variety of reasons. An alternative to use RNG is to use Pseudo Random Generators (PRNG), which pseudo random data is generated from a seed by a deterministic algorithm. It is often the case as well that the seed for this PRNG is actual real random data.
In the context of a cryptographic system, this pseudo random data should not give information of any past nor future outputs from the PRNG. This is difficult to prevent as an attacker at some point might be able to acquire the internal state of a PRNG, which can lead to they being able to follow all of the outputs of the internal state of the generator. Once the PRNG internal state is compromised is difficult to recover it a secure state again.
Cryptographic strength is added to any random seed by Zenroom's pseudo-random generator (PRNG) which is an old RSA standard basically consisting of:
Unguessable seed -> SHA -> PRNG internal state -> SHA -> random numbers
This is a rather old PRNG and will soon be substituted with the Fortuna PRNG in forthcoming versions.
Fortuna was designed by Niels Ferguson and Bruce Schneier. There are three parts to Fortuna. The generator takes a fixed-size seed and generates arbitrary amounts of pseudorandom data. The accumulator that collects and pools entropy from various sources and occasionally reseeds the generator. The seed file control that ensures that the PRNG can generate random data even when the computer has just booted.
We will describe the three parts:
- The Generator: this is basically a block cipher in Counter Mode (CTR). It converts a fixed size state to arbitrary long outputs.
- Accumulator: collects real random data from various sources and uses it to reseed the generator.
- Seed file control: the PRNG keeps a separate file full of entropy, called the seed file, which is read and used as entropy to get into an unknown state.
Hamming distance frequency
As a reference indicator of results here we provide a graph that shows the Hamming distance measuring how many different bits are there between each new random 776 bit long octets. This benchmark was run on a PC gathering entropy from system events:
Here are represented four different random generation methods which are commonly used in cryptographic transformations. It is noticeable that the most common average distance is between 380 and 400 bits for all of them.
Measure your system
To have a value estimation on the system you are currently running Zenroom, run this simple lua script:
print( BENCH.random_hamming_freq() )
Then compare the number returned: if much lower than 350 then you should worry about the quality of random on your current system.