:dancers: Discohash

2-5GB/s, passed SMHasher

Discohash (also known as BEBB4185) is a super simple and super fast hash that passes all of SMHasher, and runs at 2-5GB/s (depending on hardware) in this naive, portable, serial implementation.

Link to the SUPERCOP ECRYPT benchmark for bebb4185

The ECRYPT benchmark is 4x faster than BLAKE3

Cryptanalysis

Cryptanalysis Open

Inviting all budding hashbreakers to attack the 128-bit version. Should be easy, right?

If you'd like something a little more challenging, try breaking beamsplitter-128

Submit your results as PR requests updating the README to a link to your analysis, or contact Cris directly.

Important Note The 128-bit variants must be modified from the existing source C/C++ files. Find the commented out lines at the end of the main hash function, and return 128-bits, instead of 64.

CLI app included

Quick Facts

• A super-fast 64-bit hash.
• one of the fastest hashes ever benchmarked at ecrypt
• ECRYPT benchmark is 4x faster than BLAKE3
• Mix is super simple.
• Tested at ~ 5GB/s @ 3Gz, (Google Cloud Platform, N1 CPU)
• Passes all SMHasher tests.
• Also known as: BEBB4185
• Implemented in C++, and also a port to JS
• This repo includes a simple CLI app for hashing files or stdin from the command line.

Simplicity

The main 128-bit-to-128-bit mixing function is just this:

  mix(const int A)
    {
      const int B = A+1;
      
      ds[A] *= P;
      ds[A] = rot(ds[A], 23);
      ds[A] *= Q;
      
      ds[B] ^= ds[A];

      ds[B] *= P;
      ds[B] = rot(ds[B], 23);
      ds[B] *= Q;
    }

which is just multiplications by two 64-bit primes, P and Q, bit rotation, and xor.

P, and Q are:

• P = 0xFFFFFFFFFFFFFFFF - 58 (largest 64-bit prime)
• Q = 13166748625691186689 (random prime, 2^9×3×19×73×773×35149×227467 + 1)

More about P and Q

Binary

• 1111111111111111111111111111111111111111111111111111111111000101
• 1011011010111001101100000001110101011001001011111001011000000001

The difference is particularly interesting:

• P - Q + 1 = 5279995448018364869 = 16445111 × 321067790179
• P - Q = 2^2 × 31 × 107 × 397949611698701
• P - Q - 1 = 3 × 17 × 289086659 × 358125563
• P - Q == P ^ Q (difference equals xor, not true for most pairs)

The count of numbers less than some n whose difference equals their xor is also known as Gould's sequence, and is equal to the number of odd entries in row n of Pascal's triangle, while the binary exponents of this give the number of non-zero bits in n, and taking the mod 2 remainders of those values, gives the Thue-Morse sequence. See A001316 for more.

Standard Version

The standard internal state is 256-bits and the mixing function windows across that.

The standard digest is 64-bits, but you can modify it to yield 128-bits or more if you want a cryptographically secure hash.

Using

Use the C code from this repository, either in your project or as a CL-app (included):

cd src
./build.sh
./bin/bebbsum < 0xa2a647993898a3df.txt
> 0xa2a647993898a3df
./bin/bebbsum 0xa2a647993898a3df.txt
> 0xa2a647993898a3df

or, for a JS implementation:

npm i --save bebb4185
// or
npm i --save @dosy/discohash

Use in Node.JS:

import {discohash} from 'bebb4185'

Or using Snowpack as a webmodule:

import {discohash} from './web_modules/bebb4185.js';

Then call it:

const hash = discohash(string_or_typed_array_key, optional_seed);

JS Implementation

• The JS Implementation produces the same value hashes as the C++ implementation.
• The JS implementation is ~ 500x slower than the C++ implementation.
• This is probably because of the use of BigInts to stand in for uint64_t
• It's possible to implement a 64-bit mult using 32-bit view which would remove the need for BigInt. I have no plan to do this.

SMHasher verification value

The value is: BEBB4185

Possible future work

• Make a parallel version using Merkle tree
• Make a note about how internal state can be extended
• Implement a variable-output variant using a sponge construction