Caution

This Kyber implementation is conformant with Kyber specification https://pq-crystals.org/kyber/data/kyber-specification-round3-20210804.pdf and I also try to make it constant-time but be informed that it is not yet audited. If you consider using it in production, be careful !

kyber

CRYSTALS-Kyber: Post-Quantum Public-key Encryption & Key-establishment Algorithm

Motivation

Kyber is being standardized by NIST as post-quantum secure key encapsulation mechanism (KEM), which can be used for key establishment.

Kyber offers an IND-CCA2-secure Key Encapsulation Mechanism - its security is based on the hardness of solving the learning-with-errors (LWE) problem in module (i.e. structured) lattices.

Kyber Key Encapsulation Mechanism is built on top of IND-CPA-secure Kyber Public Key Encryption, where two communicating parties, both generating their key pairs, while publishing their public keys to each other, can encrypt fixed length ( = 32 -bytes ) message using peer's public key. Cipher text can be decrypted by corresponding secret key ( which is private to the keypair owner ) and 32 -bytes message can be recovered back. Then a slightly tweaked Fujisaki–Okamoto (FO) transform is applied on IND-CPA-secure Kyber PKE - giving us the IND-CCA2-secure KEM construction. In KEM scheme, two parties interested in establishing a secure communication channel over public & insecure channel, can generate a shared secret key ( of arbitrary byte length ) from a key derivation function ( i.e. KDF which is SHAKE256 Xof in this context ) which is obtained by both of these parties as result of seeding SHAKE256 Xof with same secret. This secret is 32 -bytes and that's what is communicated by sender to receiver using underlying Kyber PKE scheme.

Algorithm	Input	Output
KEM KeyGen	-	Public Key and Secret Key
Encapsulation	Public Key	Cipher Text and SHAKE256 KDF
Decapsulation	Secret Key and Cipher Text	SHAKE256 KDF

Note

IND-CCA2-secure Kyber KEM can be used for synchronous secure communication such as TLS.

Here I'm maintaining kyber - a header-only and easy-to-use ( see more in usage ) C++ library implementing Kyber KEM, supporting Kyber-{512, 768, 1024} parameter sets, as defined in table 1 of Kyber specification. sha3 and subtle are two dependencies of this library, which are pinned to specific git commits, using git submodule.

Note

Find Kyber specification https://pq-crystals.org/kyber/data/kyber-specification-round3-20210804.pdf - this is the document that I followed when implementing Kyber. I suggest you go through the specification to get an in-depth understanding of Kyber PQC suite.

Note

Find progress of NIST PQC standardization effort @ https://csrc.nist.gov/projects/post-quantum-cryptography.

Prerequisites

• A C++ compiler with C++20 standard library such as clang++/ g++.

$ clang++ --version
Ubuntu clang version 17.0.2 (1~exp1ubuntu2.1)
Target: x86_64-pc-linux-gnu
Thread model: posix
InstalledDir: /usr/bin

$  g++ --version
g++ (Ubuntu 13.2.0-4ubuntu3) 13.2.0

• Build tools such as make, cmake.

$ make --version
GNU Make 4.3

$ cmake --version
cmake version 3.25.1

• For testing Kyber KEM implementation, you need to globally install google-test library and headers. Follow this guide, if you don't have it installed.
• For benchmarking Kyber KEM implementation, targeting CPU systems, you'll need to have google-benchmark header and library globally installed. I found guide @ https://github.com/google/benchmark#installation helpful.

Note

If you are on a machine running GNU/Linux kernel and you want to obtain CPU cycle count for KEM routines, you should consider building google-benchmark library with libPFM support, following https://gist.github.com/itzmeanjan/05dc3e946f635d00c5e0b21aae6203a7, a step-by-step guide. Find more about libPFM @ https://perfmon2.sourceforge.net.

Tip

Git submodule based dependencies will mostly be imported automatically, but in case that doesn't work, you can manually initialize and update them by issuing $ git submodule update --init from inside the root of this repository.

Testing

For testing functional correctness and conformance with Kyber specification, you have to issue

Note

Known Answer Test (KAT) files living in this directory are generated by following (reproducible) steps, described in https://gist.github.com/itzmeanjan/c8f5bc9640d0f0bdd2437dfe364d7710.

make -j

Note: Randomizing tests' orders with a seed of 61247 .
[==========] Running 10 tests from 1 test suite.
[----------] Global test environment set-up.
[----------] 10 tests from KyberKEM
[ RUN      ] KyberKEM.ArithmeticOverZq
[       OK ] KyberKEM.ArithmeticOverZq (116 ms)
[ RUN      ] KyberKEM.NumberTheoreticTransform
[       OK ] KyberKEM.NumberTheoreticTransform (0 ms)
[ RUN      ] KyberKEM.Kyber768KnownAnswerTests
[       OK ] KyberKEM.Kyber768KnownAnswerTests (8 ms)
[ RUN      ] KyberKEM.Kyber512KnownAnswerTests
[       OK ] KyberKEM.Kyber512KnownAnswerTests (5 ms)
[ RUN      ] KyberKEM.CompressDecompressZq
[       OK ] KyberKEM.CompressDecompressZq (94 ms)
[ RUN      ] KyberKEM.Kyber1024KnownAnswerTests
[       OK ] KyberKEM.Kyber1024KnownAnswerTests (13 ms)
[ RUN      ] KyberKEM.Kyber768KeygenEncapsDecaps
[       OK ] KyberKEM.Kyber768KeygenEncapsDecaps (0 ms)
[ RUN      ] KyberKEM.Kyber512KeygenEncapsDecaps
[       OK ] KyberKEM.Kyber512KeygenEncapsDecaps (0 ms)
[ RUN      ] KyberKEM.PolynomialSerialization
[       OK ] KyberKEM.PolynomialSerialization (0 ms)
[ RUN      ] KyberKEM.Kyber1024KeygenEncapsDecaps
[       OK ] KyberKEM.Kyber1024KeygenEncapsDecaps (0 ms)
[----------] 10 tests from KyberKEM (238 ms total)

[----------] Global test environment tear-down
[==========] 10 tests from 1 test suite ran. (238 ms total)
[  PASSED  ] 10 tests.

Benchmarking

For benchmarking Kyber KEM routines ( i.e. keygen, encaps and decaps ) for various suggested parameter sets, you have to issue.

make benchmark  # If you haven't built google-benchmark library with libPFM support.
make perf       # If you have built google-benchmark library with libPFM support.

Note

Benchmarking expects presence of google-benchmark header and library in global namespace ( so that it can be found by the compiler ).

Caution

When benchmarking, ensure that you've disabled CPU frequency scaling, by following guide @ https://github.com/google/benchmark/blob/main/docs/reducing_variance.md.

Note

make perf - was issued when collecting following benchmarks. Notice, cycles column, denoting cost of executing Kyber KEM routines in terms of CPU cycles. Follow this for more details.

On 12th Gen Intel(R) Core(TM) i7-1260P ( compiled with GCC-13.2.0 )

2023-12-05T22:33:52+04:00
Running ./build/perf.out
Run on (16 X 504.568 MHz CPU s)
CPU Caches:
  L1 Data 48 KiB (x8)
  L1 Instruction 32 KiB (x8)
  L2 Unified 1280 KiB (x8)
  L3 Unified 18432 KiB (x1)
Load Average: 0.44, 0.51, 0.51
----------------------------------------------------------------------------------------------
Benchmark                        Time             CPU   Iterations     CYCLES items_per_second
----------------------------------------------------------------------------------------------
kyber512/keygen_mean          14.4 us         14.4 us            8   67.3437k       69.4709k/s
kyber512/keygen_median        14.4 us         14.4 us            8   67.4082k       69.3937k/s
kyber512/keygen_stddev       0.042 us        0.043 us            8    176.213        210.232/s
kyber512/keygen_cv            0.29 %          0.30 %             8      0.26%            0.30%
kyber1024/decap_mean          48.5 us         48.5 us            8    226.76k       20.6092k/s
kyber1024/decap_median        48.5 us         48.5 us            8   226.561k       20.6251k/s
kyber1024/decap_stddev       0.165 us        0.157 us            8    426.061        66.8334/s
kyber1024/decap_cv            0.34 %          0.32 %             8      0.19%            0.32%
kyber512/decap_mean           20.7 us         20.6 us            8   96.5275k       48.4359k/s
kyber512/decap_median         20.6 us         20.6 us            8   96.3069k       48.5757k/s
kyber512/decap_stddev        0.134 us        0.135 us            8    582.227         313.68/s
kyber512/decap_cv             0.65 %          0.65 %             8      0.60%            0.65%
kyber768/keygen_mean          24.7 us         24.7 us            8     114.9k       40.5314k/s
kyber768/keygen_median        24.6 us         24.6 us            8   115.106k       40.6451k/s
kyber768/keygen_stddev       0.177 us        0.169 us            8    687.033        274.976/s
kyber768/keygen_cv            0.72 %          0.69 %             8      0.60%            0.68%
kyber768/decap_mean           33.3 us         33.2 us            8    155.52k       30.0789k/s
kyber768/decap_median         33.2 us         33.2 us            8    155.26k       30.0966k/s
kyber768/decap_stddev        0.147 us        0.139 us            8    552.726        125.078/s
kyber768/decap_cv             0.44 %          0.42 %             8      0.36%            0.42%
kyber1024/encap_mean          44.3 us         44.3 us            8   206.579k       22.5924k/s
kyber1024/encap_median        44.3 us         44.3 us            8   206.455k       22.5788k/s
kyber1024/encap_stddev       0.147 us        0.145 us            8    549.686        74.1456/s
kyber1024/encap_cv            0.33 %          0.33 %             8      0.27%            0.33%
kyber512/encap_mean           18.0 us         18.0 us            8    84.133k       55.5064k/s
kyber512/encap_median         18.0 us         18.0 us            8   84.1549k       55.5051k/s
kyber512/encap_stddev        0.064 us        0.061 us            8    151.114        186.754/s
kyber512/encap_cv             0.36 %          0.34 %             8      0.18%            0.34%
kyber768/encap_mean           29.7 us         29.7 us            8   138.837k       33.6446k/s
kyber768/encap_median         29.7 us         29.7 us            8   138.648k       33.7164k/s
kyber768/encap_stddev        0.161 us        0.158 us            8    633.267        178.415/s
kyber768/encap_cv             0.54 %          0.53 %             8      0.46%            0.53%
kyber1024/keygen_mean         38.8 us         38.8 us            8   180.897k       25.7986k/s
kyber1024/keygen_median       38.9 us         38.8 us            8   181.344k       25.7401k/s
kyber1024/keygen_stddev      0.268 us        0.267 us            8   1.09543k        179.632/s
kyber1024/keygen_cv           0.69 %          0.69 %             8      0.61%            0.70%

On 12th Gen Intel(R) Core(TM) i7-1260P ( compiled with Clang-17.0.2 )

2023-12-05T22:32:40+04:00
Running ./build/perf.out
Run on (16 X 1113.91 MHz CPU s)
CPU Caches:
  L1 Data 48 KiB (x8)
  L1 Instruction 32 KiB (x8)
  L2 Unified 1280 KiB (x8)
  L3 Unified 18432 KiB (x1)
Load Average: 0.70, 0.54, 0.52
----------------------------------------------------------------------------------------------
Benchmark                        Time             CPU   Iterations     CYCLES items_per_second
----------------------------------------------------------------------------------------------
kyber1024/encap_mean          39.4 us         39.4 us            8   184.447k       25.3726k/s
kyber1024/encap_median        39.4 us         39.4 us            8   184.349k       25.4044k/s
kyber1024/encap_stddev       0.111 us        0.110 us            8    666.498        70.9216/s
kyber1024/encap_cv            0.28 %          0.28 %             8      0.36%            0.28%
kyber768/encap_mean           25.2 us         25.2 us            8   118.269k       39.6068k/s
kyber768/encap_median         25.2 us         25.2 us            8   118.098k       39.6763k/s
kyber768/encap_stddev        0.190 us        0.191 us            8    944.954        296.817/s
kyber768/encap_cv             0.75 %          0.76 %             8      0.80%            0.75%
kyber768/decap_mean           27.4 us         27.4 us            8   128.276k       36.4705k/s
kyber768/decap_median         27.4 us         27.4 us            8   128.023k       36.5011k/s
kyber768/decap_stddev        0.148 us        0.147 us            8    725.711        194.118/s
kyber768/decap_cv             0.54 %          0.54 %             8      0.57%            0.53%
kyber512/keygen_mean          11.7 us         11.7 us            8   54.4158k       85.6074k/s
kyber512/keygen_median        11.6 us         11.6 us            8   54.4761k       85.8637k/s
kyber512/keygen_stddev       0.157 us        0.157 us            8    230.812        1.1305k/s
kyber512/keygen_cv            1.35 %          1.35 %             8      0.42%            1.32%
kyber1024/keygen_mean         31.2 us         31.2 us            8   146.117k       32.0219k/s
kyber1024/keygen_median       31.3 us         31.3 us            8   146.447k       31.9462k/s
kyber1024/keygen_stddev      0.443 us        0.443 us            8   2.14262k        460.613/s
kyber1024/keygen_cv           1.42 %          1.42 %             8      1.47%            1.44%
kyber512/decap_mean           16.8 us         16.8 us            8    78.599k       59.5481k/s
kyber512/decap_median         16.8 us         16.8 us            8   78.6311k       59.5517k/s
kyber512/decap_stddev        0.154 us        0.154 us            8    750.744        545.456/s
kyber512/decap_cv             0.92 %          0.92 %             8      0.96%            0.92%
kyber512/encap_mean           15.4 us         15.4 us            8   71.9738k       65.0018k/s
kyber512/encap_median         15.3 us         15.3 us            8   71.6988k       65.2546k/s
kyber512/encap_stddev        0.172 us        0.172 us            8    790.241        725.525/s
kyber512/encap_cv             1.12 %          1.12 %             8      1.10%            1.12%
kyber768/keygen_mean          20.5 us         20.5 us            8   95.9542k        48.737k/s
kyber768/keygen_median        20.5 us         20.5 us            8   95.9397k       48.6711k/s
kyber768/keygen_stddev       0.096 us        0.096 us            8    523.379        227.911/s
kyber768/keygen_cv            0.47 %          0.47 %             8      0.55%            0.47%
kyber1024/decap_mean          41.8 us         41.8 us            8   194.826k       23.9134k/s
kyber1024/decap_median        41.7 us         41.7 us            8   194.774k       24.0016k/s
kyber1024/decap_stddev       0.526 us        0.523 us            8    573.604        291.732/s
kyber1024/decap_cv            1.26 %          1.25 %             8      0.29%            1.22%

On ARM Cortex-A72 i.e. Raspberry Pi 4B ( compiled with GCC-13.2.0 )

2023-12-06T00:37:57+05:30
Running ./build/perf.out
Run on (4 X 1800 MHz CPU s)
CPU Caches:
  L1 Data 32 KiB (x4)
  L1 Instruction 48 KiB (x4)
  L2 Unified 1024 KiB (x1)
Load Average: 0.69, 1.28, 1.13
Performance counters not supported.
-----------------------------------------------------------------------------------
Benchmark                        Time             CPU   Iterations items_per_second
-----------------------------------------------------------------------------------
kyber1024/encap_mean           220 us          220 us           10       4.53661k/s
kyber1024/encap_median         220 us          220 us           10       4.53843k/s
kyber1024/encap_stddev       0.775 us        0.776 us           10        15.9613/s
kyber1024/encap_cv            0.35 %          0.35 %            10            0.35%
kyber768/encap_mean            147 us          146 us           10       6.82666k/s
kyber768/encap_median          146 us          146 us           10       6.82827k/s
kyber768/encap_stddev        0.370 us        0.357 us           10        16.6515/s
kyber768/encap_cv             0.25 %          0.24 %            10            0.24%
kyber1024/keygen_mean          189 us          189 us           10       5.30215k/s
kyber1024/keygen_median        188 us          188 us           10       5.30614k/s
kyber1024/keygen_stddev      0.588 us        0.590 us           10        16.5559/s
kyber1024/keygen_cv           0.31 %          0.31 %            10            0.31%
kyber512/decap_mean            106 us          106 us           10       9.45067k/s
kyber512/decap_median          106 us          106 us           10       9.45608k/s
kyber512/decap_stddev        0.243 us        0.250 us           10        22.2866/s
kyber512/decap_cv             0.23 %          0.24 %            10            0.24%
kyber768/decap_mean            169 us          169 us           10       5.91167k/s
kyber768/decap_median          169 us          169 us           10       5.91724k/s
kyber768/decap_stddev        0.639 us        0.623 us           10        21.6423/s
kyber768/decap_cv             0.38 %          0.37 %            10            0.37%
kyber512/encap_mean           89.0 us         89.0 us           10        11.236k/s
kyber512/encap_median         89.0 us         89.0 us           10       11.2376k/s
kyber512/encap_stddev        0.216 us        0.222 us           10        28.0647/s
kyber512/encap_cv             0.24 %          0.25 %            10            0.25%
kyber768/keygen_mean           119 us          119 us           10       8.37056k/s
kyber768/keygen_median         119 us          119 us           10       8.38088k/s
kyber768/keygen_stddev       0.623 us        0.615 us           10        42.9127/s
kyber768/keygen_cv            0.52 %          0.51 %            10            0.51%
kyber1024/decap_mean           249 us          249 us           10       4.02233k/s
kyber1024/decap_median         249 us          249 us           10       4.02281k/s
kyber1024/decap_stddev       0.721 us        0.706 us           10        11.4051/s
kyber1024/decap_cv            0.29 %          0.28 %            10            0.28%
kyber512/keygen_mean          70.1 us         70.0 us           10       14.2774k/s
kyber512/keygen_median        70.1 us         70.1 us           10       14.2713k/s
kyber512/keygen_stddev       0.198 us        0.196 us           10        40.0484/s
kyber512/keygen_cv            0.28 %          0.28 %            10            0.28%

On ARM Cortex-A72 i.e. Raspberry Pi 4B ( compiled with Clang-17.0.2 )

2023-12-06T00:36:20+05:30
Running ./build/perf.out
Run on (4 X 1800 MHz CPU s)
CPU Caches:
  L1 Data 32 KiB (x4)
  L1 Instruction 48 KiB (x4)
  L2 Unified 1024 KiB (x1)
Load Average: 0.73, 1.55, 1.20
Performance counters not supported.
-----------------------------------------------------------------------------------
Benchmark                        Time             CPU   Iterations items_per_second
-----------------------------------------------------------------------------------
kyber1024/encap_mean           297 us          297 us           10       3.36489k/s
kyber1024/encap_median         297 us          297 us           10       3.36366k/s
kyber1024/encap_stddev        1.08 us         1.09 us           10        12.2899/s
kyber1024/encap_cv            0.36 %          0.37 %            10            0.37%
kyber1024/keygen_mean          254 us          254 us           10       3.93546k/s
kyber1024/keygen_median        254 us          254 us           10       3.93845k/s
kyber1024/keygen_stddev       1.05 us         1.05 us           10        16.2184/s
kyber1024/keygen_cv           0.41 %          0.41 %            10            0.41%
kyber512/decap_mean            129 us          129 us           10       7.72535k/s
kyber512/decap_median          130 us          129 us           10       7.72301k/s
kyber512/decap_stddev        0.293 us        0.284 us           10        16.9731/s
kyber512/decap_cv             0.23 %          0.22 %            10            0.22%
kyber768/encap_mean            193 us          193 us           10       5.16967k/s
kyber768/encap_median          193 us          193 us           10       5.17074k/s
kyber768/encap_stddev        0.416 us        0.426 us           10        11.3712/s
kyber768/encap_cv             0.22 %          0.22 %            10            0.22%
kyber1024/decap_mean           320 us          320 us           10       3.12381k/s
kyber1024/decap_median         320 us          320 us           10       3.12274k/s
kyber1024/decap_stddev       0.813 us        0.805 us           10        7.85819/s
kyber1024/decap_cv            0.25 %          0.25 %            10            0.25%
kyber768/decap_mean            211 us          211 us           10       4.73723k/s
kyber768/decap_median          211 us          211 us           10       4.73735k/s
kyber768/decap_stddev        0.374 us        0.391 us           10        8.77749/s
kyber768/decap_cv             0.18 %          0.19 %            10            0.19%
kyber512/encap_mean            116 us          116 us           10       8.59258k/s
kyber512/encap_median          116 us          116 us           10       8.59042k/s
kyber512/encap_stddev        0.222 us        0.216 us           10        15.9794/s
kyber512/encap_cv             0.19 %          0.19 %            10            0.19%
kyber512/keygen_mean          92.6 us         92.6 us           10       10.7953k/s
kyber512/keygen_median        92.4 us         92.4 us           10       10.8198k/s
kyber512/keygen_stddev       0.692 us        0.695 us           10        79.7935/s
kyber512/keygen_cv            0.75 %          0.75 %            10            0.74%
kyber768/keygen_mean           159 us          159 us           10       6.29988k/s
kyber768/keygen_median         159 us          159 us           10       6.30371k/s
kyber768/keygen_stddev       0.714 us        0.712 us           10         28.124/s
kyber768/keygen_cv            0.45 %          0.45 %            10            0.45%

Usage

kyber is written as a header-only C++ library, majorly targeting 64 -bit platforms and it's pretty easy to get started with. All you need to do is following.

• Clone kyber repository.

cd

# Multi-step cloning and importing of submodules
git clone https://github.com/itzmeanjan/kyber.git && pushd kyber && git submodule update --init && popd
# Or do single step cloning and importing of submodules
git clone https://github.com/itzmeanjan/kyber.git --recurse-submodules

• Write your program while including proper header files ( based on which variant of Kyber KEM you want to use, see include directory ), which includes declarations ( and definitions ) of all required KEM routines and constants ( such as byte length of public/ private keys and cipher text ).

// main.cpp

#include "kyber512_kem.hpp"
#include <algorithm>
#include <array>
#include <cassert>

int
main()
{
  std::array<uint8_t, 32> d{}; // seed
  std::array<uint8_t, 32> z{}; // seed
  std::array<uint8_t, kyber512_kem::PKEY_LEN> pkey{};
  std::array<uint8_t, kyber512_kem::SKEY_LEN> skey{};
  std::array<uint8_t, 32> m{}; // seed
  std::array<uint8_t, kyber512_kem::CIPHER_LEN> cipher{};

  // Be careful !
  //
  // Read API documentation in include/prng.hpp
  prng::prng_t prng;

  prng.read(d);
  prng.read(z);
  prng.read(m);

  kyber512_kem::keygen(d, z, pkey, skey);
  auto skdf = kyber512_kem::encapsulate(m, pkey, cipher);
  auto rkdf = kyber512_kem::decapsulate(skey, cipher);

  std::array<uint8_t, 32> sender_key{};
  skdf.squeeze(sender_key);

  std::array<uint8_t, 32> receiver_key{};
  rkdf.squeeze(receiver_key);

  assert(std::ranges::equal(sender_key, receiver_key));
  return 0;
}

• When compiling your program, let your compiler know where it can find kyber, sha3 and subtle headers, which includes their definitions ( kyber being a header-only library ) too.

# Assuming `kyber` was cloned just under $HOME

KYBER_HEADERS=~/kyber/include
SHA3_HEADERS=~/kyber/sha3/include
SUBTLE_HEADERS=~/kyber/subtle/include

g++ -std=c++20 -Wall -O3 -march=native -I $KYBER_HEADERS -I $SHA3_HEADERS -I $SUBTLE_HEADERS main.cpp

Kyber KEM Variant	Namespace	Header
Kyber512 KEM Routines	kyber512_kem::	include/kyber512_kem.hpp
Kyber768 KEM Routines	kyber768_kem::	include/kyber768_kem.hpp
Kyber1024 KEM Routines	kyber1024_kem::	include/kyber1024_kem.hpp

Note

Kyber parameter sets are selected from table 1 of Kyber specification https://pq-crystals.org/kyber/data/kyber-specification-round3-20210804.pdf.

See example program, where I show how to use Kyber512 KEM API. You can almost similarly use Kyber768 or Kyber1024 KEM API, by just importing correct header file and using KEM functions/ constants from respective namespace.

g++ -std=c++20 -Wall -Wextra -pedantic -O3 -march=native -I ./include -I ./sha3/include -I ./subtle/include/ examples/kyber512_kem.cpp && ./a.out

Kyber512 KEM

pubkey        : 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
seckey        : 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
cipher        : 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
shared secret : 508ac79bf97e90d75267159ba5189b73c48ab41a91aec0f32edd6cd1e66465b5

Caution

Before you consider using Psuedo Random Number Generator which comes with this library implementation, I strongly advice you to go through include/prng.hpp.

Note

Looking at API documentation, in header files, can give you good idea of how to use Kyber KEM API. Note, this library doesn't expose any raw pointer based interface, rather everything is wrapped under statically defined std::span - which one can easily create from std::{array, vector}. I opt for using statically defined std::span based function interfaces because we always know, at compile-time, how many bytes the seeds/ keys/ cipher-texts/ shared-secrets are, for various different Kyber KEM parameters. This gives much better type safety and compile-time error reporting.