Hash algorithm analysis

== Discussion of Candidates

I've implemented and tested the following algorithms, all of which are 256-bit (in alphabetical order):

* BLAKE2b (libb2)
* BLAKE2bp (libb2)
* KangarooTwelve (imported from the Keccak Code Package)
* SHA-256 (OpenSSL)
* SHA-512/256 (OpenSSL)
* SHA3-256 (OpenSSL)
* SHAKE128 (OpenSSL)

I also rejected some other candidates. I couldn't find any reference or implementation of SHA256×16, so I didn't implement it. I didn't consider SHAKE256 because it is nearly identical to SHA3-256 in almost all characteristics (including performance).

I imported the optimized 64-bit implementation of KangarooTwelve. The AVX2 implementation was not considered for licensing reasons (it's partially generated from external code, which falls foul of the GPL's "preferred form for modifications" rule).

=== BLAKE2b and BLAKE2bp

These are the non-parallelized and parallelized 64-bit variants of BLAKE2.

Benefits:
* Both algorithms provide 256-bit preimage resistance.

Downsides:
* Some people are uncomfortable that the security margin has been
  decreased from the original SHA-3 submission, although it is still
  considered secure.
* BLAKE2bp, as implemented in libb2, uses OpenMP (and therefore
  multithreading) by default.  It was no longer possible to run the
  testsuite with -j3 on my laptop in this configuration.

=== Keccak-based Algorithms

SHA3-256 is the 256-bit Keccak algorithm with 24 rounds, processing 136 bytes at a time. SHAKE128 is an extendable output function with 24 rounds, processing 168 bytes at a time. KangarooTwelve is an extendable output function with 12 rounds, processing 136 bytes at a time.

Benefits:
* SHA3-256 provides 256-bit preimage resistance.
* SHA3-256 has been heavily studied and is believed to have a large
  security margin.

I noted the following downsides:
* There's a lack of a availability of KangarooTwelve in other
  implementations.  It may be the least available option in terms of
  implementations.
* Some people are uncomfortable that the security margin of
  KangarooTwelve has been decreased, although it is still considered
  secure.
* SHAKE128 and KangarooTwelve provide only 128-bit preimage resistance.

=== SHA-256 and SHA-512/256

These are the 32-bit and 64-bit SHA-2 algorithms that are 256 bits in size.

I noted the following benefits:
* Both algorithms are well known and heavily analyzed.
* Both algorithms provide 256-bit preimage resistance.

== Implementation Support

|===
| Implementation | OpenSSL | libb2 | NSS | ACC | gcrypt | Nettle| CL  |
| SHA-1          | 🗸       |       | 🗸   | 🗸   | 🗸      | 🗸     | {1} |
| BLAKE2b        | f       | 🗸     |     |     | 🗸      |       | {2} |
| BLAKE2bp       |         | 🗸     |     |     |        |       |     |
| KangarooTwelve |         |       |     |     |        |       |     |
| SHA-256        | 🗸       |       | 🗸   |  🗸  | 🗸      | 🗸     | {1} |
| SHA-512/256    | 🗸       |       |     |     |        | 🗸     | {3} |
| SHA3-256       | 🗸       |       |     |     | 🗸      | 🗸     | {4} |
| SHAKE128       | 🗸       |       |     |     | 🗸      |       | {5} |
|===

f: future version (expected 1.2.0)
ACC: Apple Common Crypto
CL: Command-line

:1: OpenSSL, coreutils, Perl Digest::SHA. :2: OpenSSL, coreutils. :3: OpenSSL :4: OpenSSL, Perl Digest::SHA3. :5: Perl Digest::SHA3.

=== Performance Analysis

The test system used below is my personal laptop, a 2016 Lenovo ThinkPad X1 Carbon with an Intel i7-6600U CPU (2.60 GHz) running Debian unstable.

I implemented a test tool helper to compute speed much like OpenSSL does. Below is a comparison of speeds. The columns indicate the speed in KiB/s for chunks of the given size. The runs are representative of multiple similar runs.

256 and 1024 bytes were chosen to represent common tree and commit object sizes and the 8 KiB is an approximate average blob size.

Algorithms are sorted by performance on the 1 KiB column.

|===
| Implementation             | 256 B  | 1 KiB  | 8 KiB  | 16 KiB |
| SHA-1 (OpenSSL)            | 513963 | 685966 | 748993 | 754270 |
| BLAKE2b (libb2)            | 488123 | 552839 | 576246 | 579292 |
| SHA-512/256 (OpenSSL)      | 181177 | 349002 | 499113 | 495169 |
| BLAKE2bp (libb2)           | 139891 | 344786 | 488390 | 522575 |
| SHA-256 (OpenSSL)          | 264276 | 333560 | 357830 | 355761 |
| KangarooTwelve             | 239305 | 307300 | 355257 | 364261 |
| SHAKE128 (OpenSSL)         | 154775 | 253344 | 337811 | 346732 |
| SHA3-256 (OpenSSL)         | 128597 | 185381 | 198931 | 207365 |
| BLAKE2bp (libb2; threaded) |  12223 |  49306 | 132833 | 179616 |
|===

SUPERCOP (a crypto benchmarking tool; https://bench.cr.yp.to/results-hash.html) has also benchmarked these algorithms. Note that BLAKE2bp is not listed, KangarooTwelve is k12, SHA-512/256 is equivalent to sha512, SHA3-256 is keccakc512, and SHAKE128 is keccakc256.

Information is for kizomba, a Kaby Lake system. Counts are in cycles per byte (smaller is better; sorted by 1536 B column):

|===
| Algorithm      | 576 B | 1536 B | 4096 B | long |
| BLAKE2b        |  3.51 |   3.10 |   3.08 | 3.07 |
| SHA-1          |  4.36 |   3.81 |   3.59 | 3.49 |
| KangarooTwelve |  4.99 |   4.57 |   4.13 | 3.86 |
| SHA-512/256    |  6.39 |   5.76 |   5.31 | 5.05 |
| SHAKE128       |  8.23 |   7.67 |   7.17 | 6.97 |
| SHA-256        |  8.90 |   8.08 |   7.77 | 7.59 |
| SHA3-256       | 10.26 |   9.15 |   8.84 | 8.57 |
|===

Numbers for genji262, an AMD Ryzen System, which has SHA acceleration:

|===
| Algorithm      | 576 B | 1536 B | 4096 B | long |
| SHA-1          |  1.87 |   1.69 |   1.60 | 1.54 |
| SHA-256        |  1.95 |   1.72 |   1.68 | 1.64 |
| BLAKE2b        |  2.94 |   2.59 |   2.59 | 2.59 |
| KangarooTwelve |  4.09 |   3.65 |   3.35 | 3.17 |
| SHA-512/256    |  5.54 |   5.08 |   4.71 | 4.48 |
| SHAKE128       |  6.95 |   6.23 |   5.71 | 5.49 |
| SHA3-256       |  8.29 |   7.35 |   7.04 | 6.81 |
|===

Note that no mid- to high-end Intel processors provide acceleration. AMD Ryzen and some ARM64 processors do.

== Summary

The algorithms with the greatest implementation availability are SHA-256, SHA3-256, BLAKE2b, and SHAKE128.

In terms of command-line availability, BLAKE2b, SHA-256, SHA-512/256, and SHA3-256 should be available in the near future on a reasonably small Debian, Ubuntu, or Fedora install.

As far as security, the most conservative choices appear to be SHA-256, SHA-512/256, and SHA3-256.

The performance winners are BLAKE2b unaccelerated and SHA-256 accelerated.