Caution
This Sphincs+ implementation is conformant with Sphincs+ specification @ https://sphincs.org/data/sphincs+-r3.1-specification.pdf. I also try to make it timing leakage free, using dudect (see https://github.com/oreparaz/dudect) -based tests, but be informed that this implementation is not yet audited. If you consider using it in production, be careful !
SPHINCS+: Stateless Hash-based Digital Signature Algorithm
SPHINCS+ is one of those post-quantum digital signature algorithms ( DSA ), which is selected by NIST for standardization. Quoting directly from SPHINCS+ specification
Note
SPHINCS+ is probably the most conservative design of a post-quantum signature scheme, on the other hand, it is rather inefficient in terms of signature size and speed.
SPHINCS+ builds on SPHINCS with various improvements. I suggest you read section 1.1 of the specification.
SPHINCS+ DSA offers following three APIs
keygen: Computes random keypair where secret key is 4n -bytes and public key is 2n -bytes | n = security parameter ( in bytes )
Note
SPHINCS+ secret key holds a copy of public key, which is used when signing messages.
sign: Given M ( > 0 ) -bytes message, SPHINCS+ secret key ( of 4n -bytes ) is used for signing message, by default deterministically. Though one might specifically ask for randomized signing, which will produce random signatures for same message, given that the caller supplies n -bytes random seed.verify: Given M ( > 0 ) -bytes message and SPHINCS+ signature, it uses SPHINCS+ public key ( of 2n -bytes ) for verifying signature, returning boolean result. Truth value is returned if signature is successfully verified.
Here I'm maintaining SPHINCS+ as a header-only, easy-to-use C++20 library, which implements SPHINCS+-SHAKE key generation/ signing/ verification algorithms, for all parameter sets ( encompassing NIST security levels {1, 3, 5} ), as suggested in section 7.2 and table 3 of the specification.
Tip
Find the SPHINCS+ specification @ https://sphincs.org/data/sphincs+-r3.1-specification.pdf, which was followed during this work.
Note
Follow progress of NIST PQC standardization effort here.
- A C++ compiler with C++20 standard library support such as
g++orclang++
$ 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
gcc (Ubuntu 13.2.0-4ubuntu3) 13.2.0- Build systems such as
makeandcmake.
$ make --version
GNU Make 4.3
$ cmake --version
cmake version 3.27.4- For testing correctness and compatibility of this SPHINCS+ implementation, you need to globally install
google-testlibrary and headers. Follow guide @ https://github.com/google/googletest/tree/main/googletest#standalone-cmake-project, if you don't have it installed. - For benchmarking, you'll need to have
google-benchmarksystem-wide 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 keygen, sign and verify 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 generally 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.
For ensuring that SPHINCS+ implementation is functionally correct and compliant with the specification @ https://sphincs.org/data/sphincs+-r3.1-specification.pdf, you may issue
Note
This implementation of SPHINCS+ specification is tested to be compatible and conformant with r3.1 of the specification. That's ensured by generating known answer tests ( KATs ) following https://gist.github.com/itzmeanjan/d483872509b8a1a7c4d6614ec9d43e6c and testing this implementation using those test vectors.
make -j # Run tests without any sort of sanitizers
make asan_test -j # Run tests with AddressSanitizer enabled
make ubsan_test -j # Run tests with UndefinedBehaviourSanitizer enabled[27/27] SphincsPlus.SphincsPlus192sRobustKnownAnswerTests (592956 ms)
PASSED TESTS (27/27):
17 ms: build/test.out SphincsPlus.WOTS_PlusNISTSecurityLevel5
18 ms: build/test.out SphincsPlus.WOTS_PlusNISTSecurityLevel1
20 ms: build/test.out SphincsPlus.WOTS_PlusNISTSecurityLevel3
1422 ms: build/test.out SphincsPlus.FORSNISTSecurityLevel1
2470 ms: build/test.out SphincsPlus.XMSSNISTSecurityLevel1
2470 ms: build/test.out SphincsPlus.XMSSNISTSecurityLevel5
3603 ms: build/test.out SphincsPlus.XMSSNISTSecurityLevel3
6446 ms: build/test.out SphincsPlus.FORSNISTSecurityLevel3
7932 ms: build/test.out SphincsPlus.HyperTreeNISTSecurityLevel1
8895 ms: build/test.out SphincsPlus.FORSNISTSecurityLevel5
11539 ms: build/test.out SphincsPlus.SphincsPlus128fSimpleKnownAnswerTests
12256 ms: build/test.out SphincsPlus.HyperTreeNISTSecurityLevel5
15019 ms: build/test.out SphincsPlus.HyperTreeNISTSecurityLevel3
21817 ms: build/test.out SphincsPlus.SphincsPlusNISTSecurityLevel1KeygenSignVerify
25749 ms: build/test.out SphincsPlus.SphincsPlusNISTSecurityLevel5KeygenSignVerify
26933 ms: build/test.out SphincsPlus.SphincsPlus192fSimpleKnownAnswerTests
31361 ms: build/test.out SphincsPlus.SphincsPlus128fRobustKnownAnswerTests
33611 ms: build/test.out SphincsPlus.SphincsPlusNISTSecurityLevel3KeygenSignVerify
34051 ms: build/test.out SphincsPlus.SphincsPlus192fRobustKnownAnswerTests
35977 ms: build/test.out SphincsPlus.SphincsPlus256fSimpleKnownAnswerTests
67307 ms: build/test.out SphincsPlus.SphincsPlus256fRobustKnownAnswerTests
206086 ms: build/test.out SphincsPlus.SphincsPlus128sSimpleKnownAnswerTests
333467 ms: build/test.out SphincsPlus.SphincsPlus256sSimpleKnownAnswerTests
367931 ms: build/test.out SphincsPlus.SphincsPlus192sSimpleKnownAnswerTests
413912 ms: build/test.out SphincsPlus.SphincsPlus128sRobustKnownAnswerTests
540031 ms: build/test.out SphincsPlus.SphincsPlus256sRobustKnownAnswerTests
592956 ms: build/test.out SphincsPlus.SphincsPlus192sRobustKnownAnswerTestsYou can run timing leakage tests, using dudect; execute following
Note
dudect is integrated into this library implementation of Sphincs+ DSA to find any sort of timing leakages. It checks for constant-timeness of most of both keygen and sign function implementations, for only one variant i.e. 128f-simple.
# Can only be built and run on x86_64 machine.
make dudect_test_build -j
# Before running the constant-time tests, it's a good idea to put all CPU cores on "performance" mode.
# You may find the guide @ https://github.com/google/benchmark/blob/main/docs/reducing_variance.md helpful.
# Given Sphincs+ is slow, compared to Dilithium/ Falcon, following tests are required to be run
# for longer, so that we can collect enough execution timing samples.
timeout 2h taskset -c 0 ./build/dudect/test_sphincs+_128f_simple_keygen.out
timeout 2h taskset -c 0 ./build/dudect/test_sphincs+_128f_simple_sign.outTip
dudect documentation says if t statistic is < 10, we're probably good, yes probably. You may want to read dudect documentation @ https://github.com/oreparaz/dudect. Also you might find the original paper @ https://ia.cr/2016/1123 interesting.
...
meas: 0.69 M, max t: +2.58, max tau: 3.11e-03, (5/tau)^2: 2.58e+06. For the moment, maybe constant time.
meas: 0.70 M, max t: +2.74, max tau: 3.27e-03, (5/tau)^2: 2.34e+06. For the moment, maybe constant time.
meas: 0.71 M, max t: +2.73, max tau: 3.24e-03, (5/tau)^2: 2.38e+06. For the moment, maybe constant time.
meas: 0.72 M, max t: +2.62, max tau: 3.09e-03, (5/tau)^2: 2.61e+06. For the moment, maybe constant time.
meas: 0.73 M, max t: +2.66, max tau: 3.11e-03, (5/tau)^2: 2.58e+06. For the moment, maybe constant time.
meas: 0.74 M, max t: +2.70, max tau: 3.14e-03, (5/tau)^2: 2.53e+06. For the moment, maybe constant time.
meas: 0.75 M, max t: +2.62, max tau: 3.03e-03, (5/tau)^2: 2.72e+06. For the moment, maybe constant time.
meas: 0.76 M, max t: +2.60, max tau: 2.99e-03, (5/tau)^2: 2.80e+06. For the moment, maybe constant time.
meas: 0.77 M, max t: +2.62, max tau: 2.99e-03, (5/tau)^2: 2.80e+06. For the moment, maybe constant time.
meas: 0.78 M, max t: +2.52, max tau: 2.85e-03, (5/tau)^2: 3.07e+06. For the moment, maybe constant time.
meas: 0.79 M, max t: +2.57, max tau: 2.89e-03, (5/tau)^2: 3.00e+06. For the moment, maybe constant time.
meas: 0.80 M, max t: +2.51, max tau: 2.81e-03, (5/tau)^2: 3.18e+06. For the moment, maybe constant time.
meas: 0.81 M, max t: +2.49, max tau: 2.77e-03, (5/tau)^2: 3.25e+06. For the moment, maybe constant time.
meas: 0.82 M, max t: +2.52, max tau: 2.78e-03, (5/tau)^2: 3.23e+06. For the moment, maybe constant time.Benchmarking key generation, signing and verification algorithms for various instantiations of SPHINCS+ digital signature scheme can be done, by issuing
make benchmark -j # If you haven't built google-benchmark library with libPFM support.
make perf -j # If you have built google-benchmark library with libPFM support.Note
Benchmarking expects presence of google-benchmark headers and library in global namespace ( so that it can be found by the compiler ) i.e. header and library path must live on $PATH.
Caution
Ensure you've put all your CPU cores on performance mode before running benchmarks, follow 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 SPHINCS+ signature scheme routines in terms of CPU cycles. Follow https://github.com/google/benchmark/blob/main/docs/perf_counters.md for more details. For x86_64 targets, notice rdtsc column, showing CPU ticks collected using RD (read) Time Stamp Counter.
Compiled with gcc version 13.2.0 (Ubuntu 13.2.0-4ubuntu3).
$ uname -srm
Linux 6.5.0-14-generic x86_642024-01-12T23:13:17+04:00
Running ./build/perf.out
Run on (16 X 2807.24 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: 2.02, 1.24, 1.09
-----------------------------------------------------------------------------------------------------------------------
Benchmark Time CPU Iterations CYCLES items_per_second rdtsc
-----------------------------------------------------------------------------------------------------------------------
sphincs+-256f-simple/sign/32_mean 91.5 ms 91.5 ms 10 420.127M 10.9258/s 228.503M
sphincs+-256f-simple/sign/32_median 91.1 ms 91.1 ms 10 418.845M 10.9745/s 227.437M
sphincs+-256f-simple/sign/32_stddev 1.42 ms 1.42 ms 10 4.03714M 0.166404/s 3.55219M
sphincs+-256f-simple/sign/32_cv 1.55 % 1.56 % 10 0.96% 1.52% 1.55%
sphincs+-256f-simple/sign/32_min 90.3 ms 90.3 ms 10 415.334M 10.5449/s 225.314M
sphincs+-256f-simple/sign/32_max 94.8 ms 94.8 ms 10 424.867M 11.078/s 236.701M
sphincs+-192f-robust/sign/32_mean 134 ms 134 ms 10 624.985M 7.4607/s 335.143M
sphincs+-192f-robust/sign/32_median 138 ms 138 ms 10 646.056M 7.22728/s 345.356M
sphincs+-192f-robust/sign/32_stddev 5.87 ms 5.87 ms 10 28.2531M 0.332029/s 14.6609M
sphincs+-192f-robust/sign/32_cv 4.37 % 4.38 % 10 4.52% 4.45% 4.37%
sphincs+-192f-robust/sign/32_min 127 ms 127 ms 10 590.617M 7.15265/s 317.211M
sphincs+-192f-robust/sign/32_max 140 ms 140 ms 10 647.798M 7.86917/s 348.96M
sphincs+-192f-robust/verify/32_mean 9.61 ms 9.61 ms 10 44.7807M 104.398/s 23.9923M
sphincs+-192f-robust/verify/32_median 9.61 ms 9.61 ms 10 44.8682M 104.194/s 23.987M
sphincs+-192f-robust/verify/32_stddev 0.598 ms 0.598 ms 10 2.82949M 6.49884/s 1.492M
sphincs+-192f-robust/verify/32_cv 6.22 % 6.22 % 10 6.32% 6.23% 6.22%
sphincs+-192f-robust/verify/32_min 8.87 ms 8.87 ms 10 41.4316M 96.9217/s 22.1436M
sphincs+-192f-robust/verify/32_max 10.3 ms 10.3 ms 10 48.1533M 112.718/s 25.754M
sphincs+-256s-simple/sign/32_mean 867 ms 867 ms 10 3.95845G 1.15412/s 2.16327G
sphincs+-256s-simple/sign/32_median 863 ms 863 ms 10 3.95708G 1.15839/s 2.15476G
sphincs+-256s-simple/sign/32_stddev 14.4 ms 14.4 ms 10 43.5014M 0.0189863/s 35.9866M
sphincs+-256s-simple/sign/32_cv 1.66 % 1.66 % 10 1.10% 1.65% 1.66%
sphincs+-256s-simple/sign/32_min 846 ms 846 ms 10 3.91363G 1.12109/s 2.11081G
sphincs+-256s-simple/sign/32_max 892 ms 892 ms 10 4.00517G 1.18253/s 2.22644G
sphincs+-256s-robust/sign/32_mean 2444 ms 2444 ms 10 11.3212G 0.409781/s 6.10009G
sphincs+-256s-robust/sign/32_median 2386 ms 2386 ms 10 11.0348G 0.419183/s 5.95477G
sphincs+-256s-robust/sign/32_stddev 98.5 ms 98.5 ms 10 467.605M 0.0160907/s 245.903M
sphincs+-256s-robust/sign/32_cv 4.03 % 4.03 % 10 4.13% 3.93% 4.03%
sphincs+-256s-robust/sign/32_min 2363 ms 2363 ms 10 10.9753G 0.386185/s 5.89891G
sphincs+-256s-robust/sign/32_max 2590 ms 2589 ms 10 11.9996G 0.423137/s 6.46342G
sphincs+-256s-simple/verify/32_mean 1.24 ms 1.24 ms 10 5.68167M 806.459/s 3.0974M
sphincs+-256s-simple/verify/32_median 1.24 ms 1.24 ms 10 5.62389M 805.352/s 3.09937M
sphincs+-256s-simple/verify/32_stddev 0.036 ms 0.036 ms 10 121.113k 22.6866/s 89.1605k
sphincs+-256s-simple/verify/32_cv 2.88 % 2.87 % 10 2.13% 2.81% 2.88%
sphincs+-256s-simple/verify/32_min 1.20 ms 1.20 ms 10 5.58227M 760.8/s 3.00471M
sphincs+-256s-simple/verify/32_max 1.32 ms 1.31 ms 10 5.90764M 830.675/s 3.28238M
sphincs+-192f-simple/sign/32_mean 48.0 ms 48.0 ms 10 222.215M 20.817/s 119.914M
sphincs+-192f-simple/sign/32_median 48.1 ms 48.1 ms 10 222.493M 20.7849/s 120.091M
sphincs+-192f-simple/sign/32_stddev 0.459 ms 0.459 ms 10 1.81209M 0.199738/s 1.14573M
sphincs+-192f-simple/sign/32_cv 0.96 % 0.96 % 10 0.82% 0.96% 0.96%
sphincs+-192f-simple/sign/32_min 47.3 ms 47.3 ms 10 219.535M 20.5639/s 118.142M
sphincs+-192f-simple/sign/32_max 48.6 ms 48.6 ms 10 224.497M 21.1279/s 121.382M
sphincs+-192f-robust/keygen_mean 6.48 ms 6.48 ms 10 30.1237M 154.773/s 16.1682M
sphincs+-192f-robust/keygen_median 6.31 ms 6.31 ms 10 29.3171M 158.478/s 15.7504M
sphincs+-192f-robust/keygen_stddev 0.358 ms 0.358 ms 10 1.70474M 7.93803/s 894.109k
sphincs+-192f-robust/keygen_cv 5.53 % 5.53 % 10 5.66% 5.13% 5.53%
sphincs+-192f-robust/keygen_min 6.28 ms 6.28 ms 10 29.2526M 139.415/s 15.68M
sphincs+-192f-robust/keygen_max 7.17 ms 7.17 ms 10 33.3905M 159.183/s 17.9037M
sphincs+-192s-robust/verify/32_mean 3.33 ms 3.33 ms 10 15.477M 301.913/s 8.31031M
sphincs+-192s-robust/verify/32_median 3.33 ms 3.33 ms 10 15.4693M 301.365/s 8.30407M
sphincs+-192s-robust/verify/32_stddev 0.251 ms 0.251 ms 10 1.19271M 22.7708/s 626.523k
sphincs+-192s-robust/verify/32_cv 7.54 % 7.53 % 10 7.71% 7.54% 7.54%
sphincs+-192s-robust/verify/32_min 3.04 ms 3.04 ms 10 14.0979M 276.114/s 7.58682M
sphincs+-192s-robust/verify/32_max 3.63 ms 3.62 ms 10 16.8332M 328.988/s 9.04744M
sphincs+-128f-robust/sign/32_mean 80.7 ms 80.7 ms 10 375.056M 12.4156/s 201.382M
sphincs+-128f-robust/sign/32_median 78.7 ms 78.7 ms 10 365.035M 12.7095/s 196.41M
sphincs+-128f-robust/sign/32_stddev 3.52 ms 3.52 ms 10 16.8422M 0.523205/s 8.7823M
sphincs+-128f-robust/sign/32_cv 4.36 % 4.36 % 10 4.49% 4.21% 4.36%
sphincs+-128f-robust/sign/32_min 78.1 ms 78.1 ms 10 363.173M 11.6363/s 195.027M
sphincs+-128f-robust/sign/32_max 85.9 ms 85.9 ms 10 399.601M 12.799/s 214.511M
sphincs+-192s-simple/verify/32_mean 0.858 ms 0.858 ms 10 3.95577M 1.16656k/s 2.1415M
sphincs+-192s-simple/verify/32_median 0.857 ms 0.857 ms 10 3.96467M 1.16699k/s 2.1388M
sphincs+-192s-simple/verify/32_stddev 0.027 ms 0.027 ms 10 121.765k 36.1822/s 66.2661k
sphincs+-192s-simple/verify/32_cv 3.09 % 3.10 % 10 3.08% 3.10% 3.09%
sphincs+-192s-simple/verify/32_min 0.815 ms 0.815 ms 10 3.79805M 1.12043k/s 2.03505M
sphincs+-192s-simple/verify/32_max 0.893 ms 0.893 ms 10 4.13323M 1.22652k/s 2.22764M
sphincs+-128s-simple/sign/32_mean 589 ms 589 ms 10 2.69046G 1.69743/s 1.47078G
sphincs+-128s-simple/sign/32_median 586 ms 586 ms 10 2.70088G 1.70683/s 1.46236G
sphincs+-128s-simple/sign/32_stddev 8.79 ms 8.77 ms 10 36.9169M 0.0248951/s 21.9291M
sphincs+-128s-simple/sign/32_cv 1.49 % 1.49 % 10 1.37% 1.47% 1.49%
sphincs+-128s-simple/sign/32_min 580 ms 580 ms 10 2.59299G 1.64947/s 1.44785G
sphincs+-128s-simple/sign/32_max 606 ms 606 ms 10 2.72398G 1.72395/s 1.51328G
sphincs+-128s-robust/keygen_mean 284 ms 284 ms 10 1.3202G 3.528/s 709.484M
sphincs+-128s-robust/keygen_median 275 ms 275 ms 10 1.2751G 3.63081/s 687.468M
sphincs+-128s-robust/keygen_stddev 16.2 ms 16.2 ms 10 73.8294M 0.192319/s 40.4604M
sphincs+-128s-robust/keygen_cv 5.70 % 5.70 % 10 5.59% 5.45% 5.70%
sphincs+-128s-robust/keygen_min 272 ms 272 ms 10 1.27306G 3.23802/s 679.681M
sphincs+-128s-robust/keygen_max 309 ms 309 ms 10 1.4375G 3.67244/s 770.84M
sphincs+-192s-robust/sign/32_mean 2847 ms 2847 ms 10 13.2272G 0.35184/s 7.10542G
sphincs+-192s-robust/sign/32_median 2854 ms 2854 ms 10 13.273G 0.350796/s 7.12352G
sphincs+-192s-robust/sign/32_stddev 118 ms 118 ms 10 588.975M 0.0146597/s 295.654M
sphincs+-192s-robust/sign/32_cv 4.16 % 4.16 % 10 4.45% 4.17% 4.16%
sphincs+-192s-robust/sign/32_min 2715 ms 2715 ms 10 12.6173G 0.337405/s 6.77648G
sphincs+-192s-robust/sign/32_max 2964 ms 2964 ms 10 13.8004G 0.368342/s 7.39778G
sphincs+-256s-robust/keygen_mean 277 ms 277 ms 10 1.28877G 3.62681/s 690.389M
sphincs+-256s-robust/keygen_median 264 ms 264 ms 10 1.23017G 3.78344/s 659.714M
sphincs+-256s-robust/keygen_stddev 16.5 ms 16.5 ms 10 76.6499M 0.211597/s 41.2225M
sphincs+-256s-robust/keygen_cv 5.97 % 5.97 % 10 5.95% 5.83% 5.97%
sphincs+-256s-robust/keygen_min 263 ms 263 ms 10 1.22795G 3.36902/s 657.38M
sphincs+-256s-robust/keygen_max 297 ms 297 ms 10 1.37885G 3.79697/s 740.907M
sphincs+-192s-simple/sign/32_mean 1046 ms 1046 ms 10 4.78365G 0.956132/s 2.61182G
sphincs+-192s-simple/sign/32_median 1041 ms 1041 ms 10 4.75796G 0.9609/s 2.59762G
sphincs+-192s-simple/sign/32_stddev 24.0 ms 24.0 ms 10 48.2376M 0.0217202/s 59.9911M
sphincs+-192s-simple/sign/32_cv 2.30 % 2.30 % 10 1.01% 2.27% 2.30%
sphincs+-192s-simple/sign/32_min 1020 ms 1020 ms 10 4.73949G 0.92027/s 2.54581G
sphincs+-192s-simple/sign/32_max 1087 ms 1087 ms 10 4.85435G 0.980441/s 2.71234G
sphincs+-128s-robust/verify/32_mean 2.22 ms 2.22 ms 10 10.3345M 451.463/s 5.54406M
sphincs+-128s-robust/verify/32_median 2.25 ms 2.25 ms 10 10.4624M 445.209/s 5.60635M
sphincs+-128s-robust/verify/32_stddev 0.122 ms 0.122 ms 10 571.844k 24.838/s 304.253k
sphincs+-128s-robust/verify/32_cv 5.49 % 5.48 % 10 5.53% 5.50% 5.49%
sphincs+-128s-robust/verify/32_min 2.06 ms 2.06 ms 10 9.47653M 420.588/s 5.14351M
sphincs+-128s-robust/verify/32_max 2.38 ms 2.38 ms 10 11.0357M 485.272/s 5.93813M
sphincs+-128s-simple/verify/32_mean 0.718 ms 0.718 ms 10 3.31151M 1.39435k/s 1.79278M
sphincs+-128s-simple/verify/32_median 0.718 ms 0.718 ms 10 3.28631M 1.39237k/s 1.79272M
sphincs+-128s-simple/verify/32_stddev 0.029 ms 0.029 ms 10 144.956k 56.9857/s 73.4743k
sphincs+-128s-simple/verify/32_cv 4.10 % 4.10 % 10 4.38% 4.09% 4.10%
sphincs+-128s-simple/verify/32_min 0.670 ms 0.670 ms 10 3.11021M 1.29356k/s 1.67155M
sphincs+-128s-simple/verify/32_max 0.773 ms 0.773 ms 10 3.58344M 1.49323k/s 1.92951M
sphincs+-256f-simple/keygen_mean 4.70 ms 4.70 ms 10 21.7321M 212.849/s 11.729M
sphincs+-256f-simple/keygen_median 4.69 ms 4.69 ms 10 21.7256M 213.323/s 11.7026M
sphincs+-256f-simple/keygen_stddev 0.060 ms 0.060 ms 10 93.7117k 2.67482/s 150.166k
sphincs+-256f-simple/keygen_cv 1.28 % 1.28 % 10 0.43% 1.26% 1.28%
sphincs+-256f-simple/keygen_min 4.64 ms 4.64 ms 10 21.584M 206.227/s 11.5872M
sphincs+-256f-simple/keygen_max 4.85 ms 4.85 ms 10 21.851M 215.408/s 12.1036M
sphincs+-256s-simple/keygen_mean 74.7 ms 74.7 ms 10 346.436M 13.3867/s 186.466M
sphincs+-256s-simple/keygen_median 74.7 ms 74.7 ms 10 346.054M 13.3798/s 186.55M
sphincs+-256s-simple/keygen_stddev 0.518 ms 0.518 ms 10 1.38119M 0.0924487/s 1.29127M
sphincs+-256s-simple/keygen_cv 0.69 % 0.69 % 10 0.40% 0.69% 0.69%
sphincs+-256s-simple/keygen_min 74.1 ms 74.1 ms 10 344.587M 13.1929/s 184.856M
sphincs+-256s-simple/keygen_max 75.8 ms 75.8 ms 10 348.838M 13.5023/s 189.192M
sphincs+-128f-simple/keygen_mean 1.50 ms 1.50 ms 10 6.8694M 669.033/s 3.73398M
sphincs+-128f-simple/keygen_median 1.52 ms 1.52 ms 10 6.69887M 659.315/s 3.78587M
sphincs+-128f-simple/keygen_stddev 0.046 ms 0.046 ms 10 229.861k 20.6446/s 113.994k
sphincs+-128f-simple/keygen_cv 3.05 % 3.05 % 10 3.35% 3.09% 3.05%
sphincs+-128f-simple/keygen_min 1.44 ms 1.44 ms 10 6.67201M 648.602/s 3.58951M
sphincs+-128f-simple/keygen_max 1.54 ms 1.54 ms 10 7.19017M 695.389/s 3.84832M
sphincs+-256s-robust/verify/32_mean 4.72 ms 4.72 ms 10 21.9609M 212.737/s 11.7732M
sphincs+-256s-robust/verify/32_median 4.58 ms 4.58 ms 10 21.2866M 218.409/s 11.4283M
sphincs+-256s-robust/verify/32_stddev 0.294 ms 0.294 ms 10 1.39539M 13.021/s 732.843k
sphincs+-256s-robust/verify/32_cv 6.22 % 6.23 % 10 6.35% 6.12% 6.22%
sphincs+-256s-robust/verify/32_min 4.40 ms 4.40 ms 10 20.4143M 195.633/s 10.9807M
sphincs+-256s-robust/verify/32_max 5.11 ms 5.11 ms 10 23.7988M 227.301/s 12.7583M
sphincs+-128s-simple/keygen_mean 97.0 ms 97.0 ms 10 446.767M 10.3205/s 242.063M
sphincs+-128s-simple/keygen_median 98.2 ms 98.2 ms 10 455.303M 10.183/s 245.122M
sphincs+-128s-simple/keygen_stddev 2.98 ms 2.98 ms 10 14.7085M 0.322959/s 7.43731M
sphincs+-128s-simple/keygen_cv 3.07 % 3.07 % 10 3.29% 3.13% 3.07%
sphincs+-128s-simple/keygen_min 92.6 ms 92.6 ms 10 429.091M 9.96556/s 231.103M
sphincs+-128s-simple/keygen_max 100 ms 100 ms 10 461.192M 10.802/s 250.461M
sphincs+-192s-simple/keygen_mean 118 ms 118 ms 10 538.432M 8.48208/s 294.309M
sphincs+-192s-simple/keygen_median 118 ms 118 ms 10 539.079M 8.48371/s 294.209M
sphincs+-192s-simple/keygen_stddev 1.36 ms 1.36 ms 10 7.12578M 0.0979702/s 3.39988M
sphincs+-192s-simple/keygen_cv 1.16 % 1.15 % 10 1.32% 1.16% 1.16%
sphincs+-192s-simple/keygen_min 116 ms 116 ms 10 520.653M 8.32061/s 289.155M
sphincs+-192s-simple/keygen_max 120 ms 120 ms 10 546.704M 8.63248/s 300.002M
sphincs+-256f-robust/verify/32_mean 9.47 ms 9.47 ms 10 43.9846M 105.837/s 23.6443M
sphincs+-256f-robust/verify/32_median 9.30 ms 9.30 ms 10 43.2229M 107.476/s 23.2237M
sphincs+-256f-robust/verify/32_stddev 0.514 ms 0.514 ms 10 2.24695M 5.55579/s 1.2824M
sphincs+-256f-robust/verify/32_cv 5.42 % 5.42 % 10 5.11% 5.25% 5.42%
sphincs+-256f-robust/verify/32_min 8.92 ms 8.92 ms 10 41.6165M 95.9161/s 22.2664M
sphincs+-256f-robust/verify/32_max 10.4 ms 10.4 ms 10 47.7425M 112.103/s 26.0233M
sphincs+-128f-robust/keygen_mean 4.50 ms 4.50 ms 10 20.9405M 222.945/s 11.2344M
sphincs+-128f-robust/keygen_median 4.30 ms 4.30 ms 10 19.9286M 232.394/s 10.7406M
sphincs+-128f-robust/keygen_stddev 0.281 ms 0.281 ms 10 1.3306M 13.609/s 702.095k
sphincs+-128f-robust/keygen_cv 6.25 % 6.25 % 10 6.35% 6.10% 6.25%
sphincs+-128f-robust/keygen_min 4.26 ms 4.26 ms 10 19.8659M 206.167/s 10.6268M
sphincs+-128f-robust/keygen_max 4.85 ms 4.85 ms 10 22.5108M 234.881/s 12.1069M
sphincs+-192s-robust/keygen_mean 422 ms 422 ms 10 1.96139G 2.37499/s 1.05425G
sphincs+-192s-robust/keygen_median 407 ms 407 ms 10 1.89077G 2.4572/s 1.01582G
sphincs+-192s-robust/keygen_stddev 25.5 ms 25.5 ms 10 114.799M 0.136306/s 63.5318M
sphincs+-192s-robust/keygen_cv 6.03 % 6.03 % 10 5.85% 5.74% 6.03%
sphincs+-192s-robust/keygen_min 406 ms 405 ms 10 1.88824G 2.16501/s 1.01213G
sphincs+-192s-robust/keygen_max 462 ms 462 ms 10 2.13148G 2.46612/s 1.15289G
sphincs+-256f-simple/verify/32_mean 2.48 ms 2.48 ms 10 11.451M 403.013/s 6.1977M
sphincs+-256f-simple/verify/32_median 2.49 ms 2.49 ms 10 11.4558M 401.26/s 6.22053M
sphincs+-256f-simple/verify/32_stddev 0.069 ms 0.069 ms 10 217.412k 11.1668/s 172.034k
sphincs+-256f-simple/verify/32_cv 2.78 % 2.77 % 10 1.90% 2.77% 2.78%
sphincs+-256f-simple/verify/32_min 2.39 ms 2.39 ms 10 11.1266M 384.212/s 5.96912M
sphincs+-256f-simple/verify/32_max 2.60 ms 2.60 ms 10 11.7495M 418.146/s 6.49669M
sphincs+-128f-simple/sign/32_mean 29.5 ms 29.5 ms 10 134.362M 33.8729/s 73.7389M
sphincs+-128f-simple/sign/32_median 29.2 ms 29.2 ms 10 134.076M 34.209/s 72.9678M
sphincs+-128f-simple/sign/32_stddev 0.821 ms 0.821 ms 10 1.31186M 0.921139/s 2.04878M
sphincs+-128f-simple/sign/32_cv 2.78 % 2.78 % 10 0.98% 2.72% 2.78%
sphincs+-128f-simple/sign/32_min 28.8 ms 28.8 ms 10 132.826M 32.1265/s 71.8145M
sphincs+-128f-simple/sign/32_max 31.1 ms 31.1 ms 10 136.533M 34.7588/s 77.6969M
sphincs+-256f-robust/keygen_mean 16.9 ms 16.9 ms 10 78.4116M 59.3191/s 42.1649M
sphincs+-256f-robust/keygen_median 16.5 ms 16.5 ms 10 76.4857M 60.4722/s 41.2757M
sphincs+-256f-robust/keygen_stddev 0.838 ms 0.838 ms 10 4.15786M 2.75161/s 2.09243M
sphincs+-256f-robust/keygen_cv 4.96 % 4.96 % 10 5.30% 4.64% 4.96%
sphincs+-256f-robust/keygen_min 16.4 ms 16.4 ms 10 76.1167M 53.9547/s 40.9161M
sphincs+-256f-robust/keygen_max 18.5 ms 18.5 ms 10 86.4745M 61.0025/s 46.2608M
sphincs+-256f-robust/sign/32_mean 264 ms 264 ms 10 1.22088G 3.79742/s 658.22M
sphincs+-256f-robust/sign/32_median 258 ms 258 ms 10 1.19213G 3.8782/s 643.623M
sphincs+-256f-robust/sign/32_stddev 10.4 ms 10.4 ms 10 51.9519M 0.146041/s 25.9863M
sphincs+-256f-robust/sign/32_cv 3.95 % 3.95 % 10 4.26% 3.85% 3.95%
sphincs+-256f-robust/sign/32_min 255 ms 255 ms 10 1.18222G 3.5812/s 636.553M
sphincs+-256f-robust/sign/32_max 279 ms 279 ms 10 1.29621G 3.92142/s 696.97M
sphincs+-128f-robust/verify/32_mean 6.30 ms 6.30 ms 10 28.8489M 159.303/s 15.7294M
sphincs+-128f-robust/verify/32_median 6.13 ms 6.13 ms 10 28.5194M 163.059/s 15.3076M
sphincs+-128f-robust/verify/32_stddev 0.428 ms 0.427 ms 10 1.93596M 9.88859/s 1.06862M
sphincs+-128f-robust/verify/32_cv 6.79 % 6.78 % 10 6.71% 6.21% 6.79%
sphincs+-128f-robust/verify/32_min 5.90 ms 5.90 ms 10 27.0366M 137.308/s 14.7324M
sphincs+-128f-robust/verify/32_max 7.28 ms 7.28 ms 10 34.0488M 169.435/s 18.1779M
sphincs+-192f-simple/keygen_mean 1.86 ms 1.86 ms 10 8.57268M 538.593/s 4.63516M
sphincs+-192f-simple/keygen_median 1.86 ms 1.86 ms 10 8.58642M 539.071/s 4.63055M
sphincs+-192f-simple/keygen_stddev 0.024 ms 0.024 ms 10 104.115k 6.81469/s 58.744k
sphincs+-192f-simple/keygen_cv 1.27 % 1.27 % 10 1.21% 1.27% 1.27%
sphincs+-192f-simple/keygen_min 1.81 ms 1.81 ms 10 8.44192M 524.712/s 4.52966M
sphincs+-192f-simple/keygen_max 1.91 ms 1.91 ms 10 8.70338M 551.114/s 4.75695M
sphincs+-128s-robust/sign/32_mean 1600 ms 1600 ms 10 7.42044G 0.626036/s 3.9931G
sphincs+-128s-robust/sign/32_median 1563 ms 1563 ms 10 7.22637G 0.639876/s 3.90083G
sphincs+-128s-robust/sign/32_stddev 66.5 ms 66.5 ms 10 337.655M 0.0251806/s 165.887M
sphincs+-128s-robust/sign/32_cv 4.15 % 4.15 % 10 4.55% 4.02% 4.15%
sphincs+-128s-robust/sign/32_min 1549 ms 1549 ms 10 7.16617G 0.589586/s 3.86614G
sphincs+-128s-robust/sign/32_max 1696 ms 1696 ms 10 7.92219G 0.645632/s 4.23358G
sphincs+-128f-simple/verify/32_mean 2.04 ms 2.04 ms 10 9.41893M 491.639/s 5.08112M
sphincs+-128f-simple/verify/32_median 2.05 ms 2.05 ms 10 9.41325M 486.859/s 5.1268M
sphincs+-128f-simple/verify/32_stddev 0.062 ms 0.062 ms 10 254.028k 15.0478/s 153.721k
sphincs+-128f-simple/verify/32_cv 3.03 % 3.03 % 10 2.70% 3.06% 3.03%
sphincs+-128f-simple/verify/32_min 1.93 ms 1.93 ms 10 8.98453M 471.983/s 4.81112M
sphincs+-128f-simple/verify/32_max 2.12 ms 2.12 ms 10 9.7153M 518.815/s 5.28825M
sphincs+-192f-simple/verify/32_mean 2.50 ms 2.50 ms 10 11.4917M 400.155/s 6.24137M
sphincs+-192f-simple/verify/32_median 2.49 ms 2.49 ms 10 11.4568M 402.159/s 6.20668M
sphincs+-192f-simple/verify/32_stddev 0.062 ms 0.061 ms 10 110.948k 9.45317/s 154.275k
sphincs+-192f-simple/verify/32_cv 2.47 % 2.45 % 10 0.97% 2.36% 2.47%
sphincs+-192f-simple/verify/32_min 2.44 ms 2.44 ms 10 11.3713M 376.921/s 6.09303M
sphincs+-192f-simple/verify/32_max 2.66 ms 2.65 ms 10 11.718M 409.659/s 6.6275MCompiled with gcc version 13.2.0 (Ubuntu 13.2.0-4ubuntu3).
$ uname -srm
Linux 6.5.0-1008-raspi aarch642024-01-12T23:28:17+04:00
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: 7.92, 3.65, 1.44
------------------------------------------------------------------------------------------------------------
Benchmark Time CPU Iterations CYCLES items_per_second
------------------------------------------------------------------------------------------------------------
sphincs+-192f-robust/verify/32_mean 29.2 ms 29.2 ms 10 52.5442M 34.2041/s
sphincs+-192f-robust/verify/32_median 29.2 ms 29.2 ms 10 52.4877M 34.2379/s
sphincs+-192f-robust/verify/32_stddev 0.315 ms 0.315 ms 10 566.246k 0.367411/s
sphincs+-192f-robust/verify/32_cv 1.08 % 1.08 % 10 1.08% 1.07%
sphincs+-192f-robust/verify/32_min 28.8 ms 28.8 ms 10 51.8265M 33.6664/s
sphincs+-192f-robust/verify/32_max 29.7 ms 29.7 ms 10 53.3866M 34.6774/s
sphincs+-256s-simple/sign/32_mean 3757 ms 3757 ms 10 6.75193G 0.266196/s
sphincs+-256s-simple/sign/32_median 3757 ms 3757 ms 10 6.75191G 0.266199/s
sphincs+-256s-simple/sign/32_stddev 0.306 ms 0.213 ms 10 276.976k 15.1265u/s
sphincs+-256s-simple/sign/32_cv 0.01 % 0.01 % 10 0.00% 0.01%
sphincs+-256s-simple/sign/32_min 3757 ms 3756 ms 10 6.75161G 0.266164/s
sphincs+-256s-simple/sign/32_max 3758 ms 3757 ms 10 6.75242G 0.266214/s
sphincs+-192s-simple/verify/32_mean 3.59 ms 3.59 ms 10 6.4491M 278.747/s
sphincs+-192s-simple/verify/32_median 3.58 ms 3.58 ms 10 6.44003M 279.021/s
sphincs+-192s-simple/verify/32_stddev 0.071 ms 0.071 ms 10 127.691k 5.43984/s
sphincs+-192s-simple/verify/32_cv 1.98 % 1.98 % 10 1.98% 1.95%
sphincs+-192s-simple/verify/32_min 3.49 ms 3.49 ms 10 6.27699M 267.388/s
sphincs+-192s-simple/verify/32_max 3.74 ms 3.74 ms 10 6.72122M 286.3/s
sphincs+-192s-robust/verify/32_mean 11.1 ms 11.1 ms 10 19.881M 90.4526/s
sphincs+-192s-robust/verify/32_median 11.1 ms 11.1 ms 10 19.9672M 89.999/s
sphincs+-192s-robust/verify/32_stddev 0.305 ms 0.305 ms 10 547.952k 2.50817/s
sphincs+-192s-robust/verify/32_cv 2.76 % 2.76 % 10 2.76% 2.77%
sphincs+-192s-robust/verify/32_min 10.5 ms 10.5 ms 10 18.8613M 86.4954/s
sphincs+-192s-robust/verify/32_max 11.6 ms 11.6 ms 10 20.7782M 95.2843/s
sphincs+-256f-simple/sign/32_mean 379 ms 379 ms 10 680.846M 2.63983/s
sphincs+-256f-simple/sign/32_median 379 ms 379 ms 10 680.831M 2.63997/s
sphincs+-256f-simple/sign/32_stddev 0.119 ms 0.118 ms 10 220.738k 821.658u/s
sphincs+-256f-simple/sign/32_cv 0.03 % 0.03 % 10 0.03% 0.03%
sphincs+-256f-simple/sign/32_min 379 ms 379 ms 10 680.547M 2.63796/s
sphincs+-256f-simple/sign/32_max 379 ms 379 ms 10 681.326M 2.64085/s
sphincs+-128s-robust/keygen_mean 884 ms 884 ms 10 1.58877G 1.13127/s
sphincs+-128s-robust/keygen_median 884 ms 884 ms 10 1.58872G 1.13134/s
sphincs+-128s-robust/keygen_stddev 0.146 ms 0.131 ms 10 195.493k 167.023u/s
sphincs+-128s-robust/keygen_cv 0.02 % 0.01 % 10 0.01% 0.01%
sphincs+-128s-robust/keygen_min 884 ms 884 ms 10 1.58859G 1.13083/s
sphincs+-128s-robust/keygen_max 884 ms 884 ms 10 1.58929G 1.1314/s
sphincs+-192f-robust/keygen_mean 20.4 ms 20.4 ms 10 36.5784M 49.1341/s
sphincs+-192f-robust/keygen_median 20.4 ms 20.4 ms 10 36.579M 49.1315/s
sphincs+-192f-robust/keygen_stddev 0.010 ms 0.010 ms 10 17.532k 0.0243131/s
sphincs+-192f-robust/keygen_cv 0.05 % 0.05 % 10 0.05% 0.05%
sphincs+-192f-robust/keygen_min 20.3 ms 20.3 ms 10 36.5374M 49.1065/s
sphincs+-192f-robust/keygen_max 20.4 ms 20.4 ms 10 36.6029M 49.1956/s
sphincs+-256s-robust/sign/32_mean 9611 ms 9610 ms 10 17.2721G 0.104058/s
sphincs+-256s-robust/sign/32_median 9611 ms 9610 ms 10 17.2716G 0.104061/s
sphincs+-256s-robust/sign/32_stddev 0.798 ms 0.887 ms 10 1.80482M 9.60673u/s
sphincs+-256s-robust/sign/32_cv 0.01 % 0.01 % 10 0.01% 0.01%
sphincs+-256s-robust/sign/32_min 9611 ms 9609 ms 10 17.2701G 0.104034/s
sphincs+-256s-robust/sign/32_max 9613 ms 9612 ms 10 17.2768G 0.10407/s
sphincs+-128s-simple/sign/32_mean 2203 ms 2202 ms 10 3.95806G 0.454082/s
sphincs+-128s-simple/sign/32_median 2203 ms 2202 ms 10 3.95808G 0.454073/s
sphincs+-128s-simple/sign/32_stddev 0.254 ms 0.238 ms 10 435.256k 49.0597u/s
sphincs+-128s-simple/sign/32_cv 0.01 % 0.01 % 10 0.01% 0.01%
sphincs+-128s-simple/sign/32_min 2202 ms 2202 ms 10 3.95751G 0.454024/s
sphincs+-128s-simple/sign/32_max 2203 ms 2203 ms 10 3.95872G 0.454153/s
sphincs+-192s-robust/sign/32_mean 10773 ms 10771 ms 10 19.359G 0.0928392/s
sphincs+-192s-robust/sign/32_median 10773 ms 10771 ms 10 19.359G 0.0928388/s
sphincs+-192s-robust/sign/32_stddev 0.645 ms 0.521 ms 10 632.096k 4.4882u/s
sphincs+-192s-robust/sign/32_cv 0.01 % 0.00 % 10 0.00% 0.00%
sphincs+-192s-robust/sign/32_min 10772 ms 10770 ms 10 19.3579G 0.0928314/s
sphincs+-192s-robust/sign/32_max 10774 ms 10772 ms 10 19.36G 0.0928465/s
sphincs+-192f-robust/sign/32_mean 461 ms 461 ms 10 828.263M 2.16978/s
sphincs+-192f-robust/sign/32_median 461 ms 461 ms 10 828.251M 2.16964/s
sphincs+-192f-robust/sign/32_stddev 0.137 ms 0.117 ms 10 188.681k 550.978u/s
sphincs+-192f-robust/sign/32_cv 0.03 % 0.03 % 10 0.02% 0.03%
sphincs+-192f-robust/sign/32_min 461 ms 461 ms 10 827.996M 2.16912/s
sphincs+-192f-robust/sign/32_max 461 ms 461 ms 10 828.495M 2.17053/s
sphincs+-192f-simple/sign/32_mean 188 ms 188 ms 10 337.478M 5.3247/s
sphincs+-192f-simple/sign/32_median 188 ms 188 ms 10 337.471M 5.32499/s
sphincs+-192f-simple/sign/32_stddev 0.128 ms 0.121 ms 10 221.551k 3.41885m/s
sphincs+-192f-simple/sign/32_cv 0.07 % 0.06 % 10 0.07% 0.06%
sphincs+-192f-simple/sign/32_min 188 ms 188 ms 10 337.104M 5.31868/s
sphincs+-192f-simple/sign/32_max 188 ms 188 ms 10 337.88M 5.32962/s
sphincs+-256f-robust/verify/32_mean 33.5 ms 33.5 ms 10 60.1374M 29.8849/s
sphincs+-256f-robust/verify/32_median 33.6 ms 33.6 ms 10 60.3595M 29.7745/s
sphincs+-256f-robust/verify/32_stddev 0.448 ms 0.449 ms 10 806.298k 0.403911/s
sphincs+-256f-robust/verify/32_cv 1.34 % 1.34 % 10 1.34% 1.35%
sphincs+-256f-robust/verify/32_min 32.7 ms 32.7 ms 10 58.7467M 29.407/s
sphincs+-256f-robust/verify/32_max 34.0 ms 34.0 ms 10 61.1033M 30.5847/s
sphincs+-128f-simple/keygen_mean 5.01 ms 5.01 ms 10 9.00288M 199.6/s
sphincs+-128f-simple/keygen_median 5.01 ms 5.01 ms 10 9.0034M 199.605/s
sphincs+-128f-simple/keygen_stddev 0.002 ms 0.001 ms 10 1.74969k 0.0500185/s
sphincs+-128f-simple/keygen_cv 0.04 % 0.03 % 10 0.02% 0.03%
sphincs+-128f-simple/keygen_min 5.01 ms 5.01 ms 10 9.00022M 199.541/s
sphincs+-128f-simple/keygen_max 5.01 ms 5.01 ms 10 9.00534M 199.699/s
sphincs+-192s-robust/keygen_mean 1476 ms 1476 ms 10 2.65293G 0.677468/s
sphincs+-192s-robust/keygen_median 1476 ms 1476 ms 10 2.65287G 0.677478/s
sphincs+-192s-robust/keygen_stddev 0.185 ms 0.170 ms 10 249.868k 78.0824u/s
sphincs+-192s-robust/keygen_cv 0.01 % 0.01 % 10 0.01% 0.01%
sphincs+-192s-robust/keygen_min 1476 ms 1476 ms 10 2.65261G 0.677291/s
sphincs+-192s-robust/keygen_max 1477 ms 1476 ms 10 2.65355G 0.677581/s
sphincs+-192s-simple/sign/32_mean 4145 ms 4145 ms 10 7.44952G 0.241274/s
sphincs+-192s-simple/sign/32_median 4145 ms 4145 ms 10 7.44953G 0.241272/s
sphincs+-192s-simple/sign/32_stddev 0.276 ms 0.217 ms 10 357.825k 12.656u/s
sphincs+-192s-simple/sign/32_cv 0.01 % 0.01 % 10 0.00% 0.01%
sphincs+-192s-simple/sign/32_min 4145 ms 4144 ms 10 7.44895G 0.24125/s
sphincs+-192s-simple/sign/32_max 4146 ms 4145 ms 10 7.45012G 0.241292/s
sphincs+-192f-simple/verify/32_mean 10.2 ms 10.2 ms 10 18.3144M 98.1658/s
sphincs+-192f-simple/verify/32_median 10.2 ms 10.2 ms 10 18.2726M 98.3337/s
sphincs+-192f-simple/verify/32_stddev 0.244 ms 0.244 ms 10 437.779k 2.36102/s
sphincs+-192f-simple/verify/32_cv 2.40 % 2.40 % 10 2.39% 2.41%
sphincs+-192f-simple/verify/32_min 9.76 ms 9.76 ms 10 17.5367M 94.4989/s
sphincs+-192f-simple/verify/32_max 10.6 ms 10.6 ms 10 19.0174M 102.469/s
sphincs+-128s-simple/keygen_mean 321 ms 320 ms 10 575.972M 3.12029/s
sphincs+-128s-simple/keygen_median 321 ms 321 ms 10 576.046M 3.11984/s
sphincs+-128s-simple/keygen_stddev 0.161 ms 0.134 ms 10 217.014k 1.30309m/s
sphincs+-128s-simple/keygen_cv 0.05 % 0.04 % 10 0.04% 0.04%
sphincs+-128s-simple/keygen_min 320 ms 320 ms 10 575.557M 3.11909/s
sphincs+-128s-simple/keygen_max 321 ms 321 ms 10 576.168M 3.12252/s
sphincs+-256f-robust/sign/32_mean 1044 ms 1044 ms 10 1.87618G 0.957925/s
sphincs+-256f-robust/sign/32_median 1044 ms 1044 ms 10 1.87608G 0.957973/s
sphincs+-256f-robust/sign/32_stddev 0.333 ms 0.335 ms 10 618.912k 307.615u/s
sphincs+-256f-robust/sign/32_cv 0.03 % 0.03 % 10 0.03% 0.03%
sphincs+-256f-robust/sign/32_min 1044 ms 1043 ms 10 1.8753G 0.957384/s
sphincs+-256f-robust/sign/32_max 1045 ms 1045 ms 10 1.87718G 0.958403/s
sphincs+-256f-robust/keygen_mean 60.6 ms 60.6 ms 10 108.892M 16.5027/s
sphincs+-256f-robust/keygen_median 60.6 ms 60.6 ms 10 108.889M 16.5037/s
sphincs+-256f-robust/keygen_stddev 0.025 ms 0.021 ms 10 30.144k 5.76279m/s
sphincs+-256f-robust/keygen_cv 0.04 % 0.03 % 10 0.03% 0.03%
sphincs+-256f-robust/keygen_min 60.6 ms 60.6 ms 10 108.849M 16.4928/s
sphincs+-256f-robust/keygen_max 60.6 ms 60.6 ms 10 108.956M 16.5109/s
sphincs+-256s-simple/keygen_mean 310 ms 310 ms 10 556.533M 3.22939/s
sphincs+-256s-simple/keygen_median 310 ms 310 ms 10 556.56M 3.22921/s
sphincs+-256s-simple/keygen_stddev 0.112 ms 0.113 ms 10 212.021k 1.17704m/s
sphincs+-256s-simple/keygen_cv 0.04 % 0.04 % 10 0.04% 0.04%
sphincs+-256s-simple/keygen_min 309 ms 309 ms 10 556.234M 3.22758/s
sphincs+-256s-simple/keygen_max 310 ms 310 ms 10 556.872M 3.23116/s
sphincs+-128s-robust/verify/32_mean 6.63 ms 6.63 ms 10 11.9081M 151.038/s
sphincs+-128s-robust/verify/32_median 6.64 ms 6.64 ms 10 11.9309M 150.638/s
sphincs+-128s-robust/verify/32_stddev 0.207 ms 0.207 ms 10 371.353k 4.71517/s
sphincs+-128s-robust/verify/32_cv 3.12 % 3.12 % 10 3.12% 3.12%
sphincs+-128s-robust/verify/32_min 6.28 ms 6.28 ms 10 11.2947M 142.958/s
sphincs+-128s-robust/verify/32_max 7.00 ms 7.00 ms 10 12.5684M 159.129/s
sphincs+-256f-simple/verify/32_mean 10.2 ms 10.2 ms 10 18.3038M 98.1893/s
sphincs+-256f-simple/verify/32_median 10.2 ms 10.2 ms 10 18.3288M 98.0286/s
sphincs+-256f-simple/verify/32_stddev 0.150 ms 0.150 ms 10 269.937k 1.45888/s
sphincs+-256f-simple/verify/32_cv 1.47 % 1.48 % 10 1.47% 1.49%
sphincs+-256f-simple/verify/32_min 9.93 ms 9.92 ms 10 17.8289M 96.29/s
sphincs+-256f-simple/verify/32_max 10.4 ms 10.4 ms 10 18.6597M 100.767/s
sphincs+-256s-robust/verify/32_mean 16.5 ms 16.5 ms 10 29.6917M 60.5499/s
sphincs+-256s-robust/verify/32_median 16.6 ms 16.6 ms 10 29.8024M 60.3059/s
sphincs+-256s-robust/verify/32_stddev 0.352 ms 0.351 ms 10 630.552k 1.28124/s
sphincs+-256s-robust/verify/32_cv 2.13 % 2.13 % 10 2.12% 2.12%
sphincs+-256s-robust/verify/32_min 16.1 ms 16.1 ms 10 28.9572M 58.29/s
sphincs+-256s-robust/verify/32_max 17.2 ms 17.2 ms 10 30.8239M 62.0663/s
sphincs+-128f-robust/keygen_mean 13.8 ms 13.8 ms 10 24.8303M 72.3769/s
sphincs+-128f-robust/keygen_median 13.8 ms 13.8 ms 10 24.8305M 72.3734/s
sphincs+-128f-robust/keygen_stddev 0.003 ms 0.002 ms 10 2.47394k 0.010313/s
sphincs+-128f-robust/keygen_cv 0.02 % 0.01 % 10 0.01% 0.01%
sphincs+-128f-robust/keygen_min 13.8 ms 13.8 ms 10 24.8261M 72.3687/s
sphincs+-128f-robust/keygen_max 13.8 ms 13.8 ms 10 24.8334M 72.4024/s
sphincs+-128f-simple/verify/32_mean 9.13 ms 9.13 ms 10 16.4055M 109.646/s
sphincs+-128f-simple/verify/32_median 9.10 ms 9.10 ms 10 16.3469M 109.928/s
sphincs+-128f-simple/verify/32_stddev 0.301 ms 0.301 ms 10 540.292k 3.60203/s
sphincs+-128f-simple/verify/32_cv 3.30 % 3.30 % 10 3.29% 3.29%
sphincs+-128f-simple/verify/32_min 8.63 ms 8.63 ms 10 15.5097M 103.48/s
sphincs+-128f-simple/verify/32_max 9.66 ms 9.66 ms 10 17.3681M 115.885/s
sphincs+-192s-simple/keygen_mean 486 ms 486 ms 10 873.566M 2.05734/s
sphincs+-192s-simple/keygen_median 486 ms 486 ms 10 873.567M 2.05728/s
sphincs+-192s-simple/keygen_stddev 0.159 ms 0.156 ms 10 271.325k 659.867u/s
sphincs+-192s-simple/keygen_cv 0.03 % 0.03 % 10 0.03% 0.03%
sphincs+-192s-simple/keygen_min 486 ms 486 ms 10 873.193M 2.05647/s
sphincs+-192s-simple/keygen_max 486 ms 486 ms 10 873.958M 2.05823/s
sphincs+-128f-robust/sign/32_mean 271 ms 270 ms 10 486.071M 3.69712/s
sphincs+-128f-robust/sign/32_median 270 ms 270 ms 10 486.09M 3.69715/s
sphincs+-128f-robust/sign/32_stddev 0.113 ms 0.088 ms 10 134.21k 1.20834m/s
sphincs+-128f-robust/sign/32_cv 0.04 % 0.03 % 10 0.03% 0.03%
sphincs+-128f-robust/sign/32_min 270 ms 270 ms 10 485.891M 3.69513/s
sphincs+-128f-robust/sign/32_max 271 ms 271 ms 10 486.265M 3.69906/s
sphincs+-128s-robust/sign/32_mean 5465 ms 5464 ms 10 9.82046G 0.18301/s
sphincs+-128s-robust/sign/32_median 5465 ms 5464 ms 10 9.82043G 0.18301/s
sphincs+-128s-robust/sign/32_stddev 0.166 ms 0.141 ms 10 294.814k 4.70817u/s
sphincs+-128s-robust/sign/32_cv 0.00 % 0.00 % 10 0.00% 0.00%
sphincs+-128s-robust/sign/32_min 5465 ms 5464 ms 10 9.82011G 0.183/s
sphincs+-128s-robust/sign/32_max 5465 ms 5464 ms 10 9.821G 0.183017/s
sphincs+-128s-simple/verify/32_mean 3.01 ms 3.01 ms 10 5.40181M 332.845/s
sphincs+-128s-simple/verify/32_median 3.01 ms 3.01 ms 10 5.40749M 332.315/s
sphincs+-128s-simple/verify/32_stddev 0.076 ms 0.077 ms 10 138.072k 8.53613/s
sphincs+-128s-simple/verify/32_cv 2.54 % 2.55 % 10 2.56% 2.56%
sphincs+-128s-simple/verify/32_min 2.89 ms 2.89 ms 10 5.18755M 321.462/s
sphincs+-128s-simple/verify/32_max 3.11 ms 3.11 ms 10 5.58958M 346.409/s
sphincs+-128f-robust/verify/32_mean 19.7 ms 19.7 ms 10 35.3166M 50.9193/s
sphincs+-128f-robust/verify/32_median 19.9 ms 19.9 ms 10 35.6877M 50.3482/s
sphincs+-128f-robust/verify/32_stddev 0.523 ms 0.524 ms 10 943.007k 1.40489/s
sphincs+-128f-robust/verify/32_cv 2.66 % 2.67 % 10 2.67% 2.76%
sphincs+-128f-robust/verify/32_min 18.5 ms 18.5 ms 10 33.1682M 49.3277/s
sphincs+-128f-robust/verify/32_max 20.3 ms 20.3 ms 10 36.4365M 54.1802/s
sphincs+-256s-robust/keygen_mean 978 ms 978 ms 10 1.75689G 1.023/s
sphincs+-256s-robust/keygen_median 978 ms 978 ms 10 1.75694G 1.02298/s
sphincs+-256s-robust/keygen_stddev 0.190 ms 0.186 ms 10 362.628k 194.701u/s
sphincs+-256s-robust/keygen_cv 0.02 % 0.02 % 10 0.02% 0.02%
sphincs+-256s-robust/keygen_min 977 ms 977 ms 10 1.75612G 1.02275/s
sphincs+-256s-robust/keygen_max 978 ms 978 ms 10 1.75734G 1.02345/s
sphincs+-128f-simple/sign/32_mean 120 ms 120 ms 10 215.957M 8.32063/s
sphincs+-128f-simple/sign/32_median 120 ms 120 ms 10 215.943M 8.32141/s
sphincs+-128f-simple/sign/32_stddev 0.036 ms 0.043 ms 10 86.1536k 2.98705m/s
sphincs+-128f-simple/sign/32_cv 0.03 % 0.04 % 10 0.04% 0.04%
sphincs+-128f-simple/sign/32_min 120 ms 120 ms 10 215.836M 8.31591/s
sphincs+-128f-simple/sign/32_max 120 ms 120 ms 10 216.091M 8.32442/s
sphincs+-256s-simple/verify/32_mean 5.06 ms 5.06 ms 10 9.08566M 197.822/s
sphincs+-256s-simple/verify/32_median 5.05 ms 5.05 ms 10 9.07831M 197.898/s
sphincs+-256s-simple/verify/32_stddev 0.091 ms 0.091 ms 10 164.307k 3.54907/s
sphincs+-256s-simple/verify/32_cv 1.80 % 1.80 % 10 1.81% 1.79%
sphincs+-256s-simple/verify/32_min 4.91 ms 4.91 ms 10 8.82804M 191.356/s
sphincs+-256s-simple/verify/32_max 5.23 ms 5.23 ms 10 9.39158M 203.543/s
sphincs+-192f-simple/keygen_mean 7.62 ms 7.62 ms 10 13.6917M 131.24/s
sphincs+-192f-simple/keygen_median 7.62 ms 7.62 ms 10 13.6914M 131.247/s
sphincs+-192f-simple/keygen_stddev 0.008 ms 0.007 ms 10 13.1032k 0.128408/s
sphincs+-192f-simple/keygen_cv 0.10 % 0.10 % 10 0.10% 0.10%
sphincs+-192f-simple/keygen_min 7.61 ms 7.61 ms 10 13.6672M 131.036/s
sphincs+-192f-simple/keygen_max 7.63 ms 7.63 ms 10 13.7111M 131.48/s
sphincs+-256f-simple/keygen_mean 19.4 ms 19.4 ms 10 34.8104M 51.6241/s
sphincs+-256f-simple/keygen_median 19.4 ms 19.4 ms 10 34.808M 51.6292/s
sphincs+-256f-simple/keygen_stddev 0.008 ms 0.008 ms 10 13.7667k 0.0207193/s
sphincs+-256f-simple/keygen_cv 0.04 % 0.04 % 10 0.04% 0.04%
sphincs+-256f-simple/keygen_min 19.4 ms 19.4 ms 10 34.7937M 51.5876/s
sphincs+-256f-simple/keygen_max 19.4 ms 19.4 ms 10 34.8376M 51.6496/sCompiled with Apple clang version 15.0.0 (clang-1500.1.0.2.5).
uname -srm
Darwin 23.2.0 arm642024-01-22T20:57:36+04:00
Running ./build/bench.out
Run on (10 X 24 MHz CPU s)
CPU Caches:
L1 Data 64 KiB
L1 Instruction 128 KiB
L2 Unified 4096 KiB (x10)
Load Average: 4.08, 1.88, 1.82
-------------------------------------------------------------------------------------------------
Benchmark Time CPU Iterations items_per_second
-------------------------------------------------------------------------------------------------
sphincs+-256s-simple/sign/32_mean 956 ms 955 ms 10 1.04694/s
sphincs+-256s-simple/sign/32_median 952 ms 951 ms 10 1.05179/s
sphincs+-256s-simple/sign/32_stddev 14.2 ms 14.3 ms 10 0.0151226/s
sphincs+-256s-simple/sign/32_cv 1.48 % 1.50 % 10 1.44%
sphincs+-256s-simple/sign/32_min 952 ms 951 ms 10 1.0039/s
sphincs+-256s-simple/sign/32_max 997 ms 996 ms 10 1.05184/s
sphincs+-192f-simple/verify/32_mean 2.63 ms 2.63 ms 10 380.76/s
sphincs+-192f-simple/verify/32_median 2.64 ms 2.63 ms 10 379.595/s
sphincs+-192f-simple/verify/32_stddev 0.047 ms 0.047 ms 10 6.92005/s
sphincs+-192f-simple/verify/32_cv 1.80 % 1.81 % 10 1.82%
sphincs+-192f-simple/verify/32_min 2.55 ms 2.55 ms 10 370.813/s
sphincs+-192f-simple/verify/32_max 2.70 ms 2.70 ms 10 392.735/s
sphincs+-192s-simple/sign/32_mean 1088 ms 1087 ms 10 0.920116/s
sphincs+-192s-simple/sign/32_median 1088 ms 1087 ms 10 0.920072/s
sphincs+-192s-simple/sign/32_stddev 0.163 ms 0.110 ms 10 93.278u/s
sphincs+-192s-simple/sign/32_cv 0.01 % 0.01 % 10 0.01%
sphincs+-192s-simple/sign/32_min 1088 ms 1087 ms 10 0.920022/s
sphincs+-192s-simple/sign/32_max 1088 ms 1087 ms 10 0.920261/s
sphincs+-128s-simple/keygen_mean 83.2 ms 83.1 ms 10 12.0375/s
sphincs+-128s-simple/keygen_median 83.2 ms 83.1 ms 10 12.0375/s
sphincs+-128s-simple/keygen_stddev 0.022 ms 0.005 ms 10 733.148u/s
sphincs+-128s-simple/keygen_cv 0.03 % 0.01 % 10 0.01%
sphincs+-128s-simple/keygen_min 83.1 ms 83.1 ms 10 12.0364/s
sphincs+-128s-simple/keygen_max 83.2 ms 83.1 ms 10 12.0387/s
sphincs+-256s-robust/sign/32_mean 1726 ms 1724 ms 10 0.580078/s
sphincs+-256s-robust/sign/32_median 1719 ms 1716 ms 10 0.582602/s
sphincs+-256s-robust/sign/32_stddev 18.0 ms 18.0 ms 10 5.92884m/s
sphincs+-256s-robust/sign/32_cv 1.04 % 1.04 % 10 1.02%
sphincs+-256s-robust/sign/32_min 1718 ms 1716 ms 10 0.564604/s
sphincs+-256s-robust/sign/32_max 1774 ms 1771 ms 10 0.582721/s
sphincs+-128f-simple/keygen_mean 1.30 ms 1.30 ms 10 770.521/s
sphincs+-128f-simple/keygen_median 1.30 ms 1.30 ms 10 770.518/s
sphincs+-128f-simple/keygen_stddev 0.001 ms 0.000 ms 10 0.0452933/s
sphincs+-128f-simple/keygen_cv 0.04 % 0.01 % 10 0.01%
sphincs+-128f-simple/keygen_min 1.30 ms 1.30 ms 10 770.46/s
sphincs+-128f-simple/keygen_max 1.30 ms 1.30 ms 10 770.625/s
sphincs+-256f-simple/keygen_mean 5.01 ms 5.01 ms 10 199.687/s
sphincs+-256f-simple/keygen_median 5.01 ms 5.01 ms 10 199.689/s
sphincs+-256f-simple/keygen_stddev 0.001 ms 0.000 ms 10 0.0144266/s
sphincs+-256f-simple/keygen_cv 0.03 % 0.01 % 10 0.01%
sphincs+-256f-simple/keygen_min 5.01 ms 5.01 ms 10 199.663/s
sphincs+-256f-simple/keygen_max 5.02 ms 5.01 ms 10 199.712/s
sphincs+-256s-robust/verify/32_mean 2.55 ms 2.55 ms 10 392.218/s
sphincs+-256s-robust/verify/32_median 2.56 ms 2.55 ms 10 391.584/s
sphincs+-256s-robust/verify/32_stddev 0.040 ms 0.040 ms 10 6.19041/s
sphincs+-256s-robust/verify/32_cv 1.59 % 1.57 % 10 1.58%
sphincs+-256s-robust/verify/32_min 2.48 ms 2.48 ms 10 383.864/s
sphincs+-256s-robust/verify/32_max 2.61 ms 2.61 ms 10 403.425/s
sphincs+-256s-simple/keygen_mean 80.2 ms 80.1 ms 10 12.4794/s
sphincs+-256s-simple/keygen_median 80.2 ms 80.1 ms 10 12.4797/s
sphincs+-256s-simple/keygen_stddev 0.030 ms 0.012 ms 10 1.88862m/s
sphincs+-256s-simple/keygen_cv 0.04 % 0.02 % 10 0.02%
sphincs+-256s-simple/keygen_min 80.2 ms 80.1 ms 10 12.4759/s
sphincs+-256s-simple/keygen_max 80.3 ms 80.2 ms 10 12.4817/s
sphincs+-192f-simple/keygen_mean 1.90 ms 1.90 ms 10 527.157/s
sphincs+-192f-simple/keygen_median 1.90 ms 1.90 ms 10 527.158/s
sphincs+-192f-simple/keygen_stddev 0.001 ms 0.000 ms 10 0.0439028/s
sphincs+-192f-simple/keygen_cv 0.04 % 0.01 % 10 0.01%
sphincs+-192f-simple/keygen_min 1.90 ms 1.90 ms 10 527.081/s
sphincs+-192f-simple/keygen_max 1.90 ms 1.90 ms 10 527.223/s
sphincs+-128s-robust/sign/32_mean 1173 ms 1172 ms 10 0.853268/s
sphincs+-128s-robust/sign/32_median 1173 ms 1172 ms 10 0.853432/s
sphincs+-128s-robust/sign/32_stddev 0.992 ms 0.812 ms 10 590.275u/s
sphincs+-128s-robust/sign/32_cv 0.08 % 0.07 % 10 0.07%
sphincs+-128s-robust/sign/32_min 1173 ms 1172 ms 10 0.851615/s
sphincs+-128s-robust/sign/32_max 1176 ms 1174 ms 10 0.853585/s
sphincs+-192f-robust/keygen_mean 3.56 ms 3.56 ms 10 281.038/s
sphincs+-192f-robust/keygen_median 3.56 ms 3.56 ms 10 281.015/s
sphincs+-192f-robust/keygen_stddev 0.001 ms 0.001 ms 10 0.0645186/s
sphincs+-192f-robust/keygen_cv 0.03 % 0.02 % 10 0.02%
sphincs+-192f-robust/keygen_min 3.56 ms 3.56 ms 10 280.978/s
sphincs+-192f-robust/keygen_max 3.56 ms 3.56 ms 10 281.162/s
sphincs+-192f-simple/sign/32_mean 48.9 ms 48.8 ms 10 20.4728/s
sphincs+-192f-simple/sign/32_median 48.9 ms 48.8 ms 10 20.4818/s
sphincs+-192f-simple/sign/32_stddev 0.073 ms 0.069 ms 10 0.0286755/s
sphincs+-192f-simple/sign/32_cv 0.15 % 0.14 % 10 0.14%
sphincs+-192f-simple/sign/32_min 48.8 ms 48.8 ms 10 20.3917/s
sphincs+-192f-simple/sign/32_max 49.1 ms 49.0 ms 10 20.4852/s
sphincs+-128f-simple/sign/32_mean 30.3 ms 30.3 ms 10 33.0301/s
sphincs+-128f-simple/sign/32_median 30.3 ms 30.3 ms 10 33.0311/s
sphincs+-128f-simple/sign/32_stddev 0.013 ms 0.010 ms 10 0.010819/s
sphincs+-128f-simple/sign/32_cv 0.04 % 0.03 % 10 0.03%
sphincs+-128f-simple/sign/32_min 30.3 ms 30.3 ms 10 33.0129/s
sphincs+-128f-simple/sign/32_max 30.3 ms 30.3 ms 10 33.0478/s
sphincs+-192f-robust/verify/32_mean 5.09 ms 5.08 ms 10 196.916/s
sphincs+-192f-robust/verify/32_median 5.09 ms 5.08 ms 10 196.843/s
sphincs+-192f-robust/verify/32_stddev 0.107 ms 0.107 ms 10 4.14326/s
sphincs+-192f-robust/verify/32_cv 2.11 % 2.11 % 10 2.10%
sphincs+-192f-robust/verify/32_min 4.92 ms 4.92 ms 10 190.444/s
sphincs+-192f-robust/verify/32_max 5.26 ms 5.25 ms 10 203.318/s
sphincs+-128f-robust/verify/32_mean 3.44 ms 3.44 ms 10 290.687/s
sphincs+-128f-robust/verify/32_median 3.45 ms 3.44 ms 10 290.344/s
sphincs+-128f-robust/verify/32_stddev 0.042 ms 0.043 ms 10 3.61899/s
sphincs+-128f-robust/verify/32_cv 1.23 % 1.24 % 10 1.24%
sphincs+-128f-robust/verify/32_min 3.37 ms 3.37 ms 10 286.211/s
sphincs+-128f-robust/verify/32_max 3.50 ms 3.49 ms 10 296.826/s
sphincs+-128s-simple/sign/32_mean 631 ms 630 ms 10 1.58651/s
sphincs+-128s-simple/sign/32_median 631 ms 630 ms 10 1.58658/s
sphincs+-128s-simple/sign/32_stddev 0.207 ms 0.118 ms 10 297.925u/s
sphincs+-128s-simple/sign/32_cv 0.03 % 0.02 % 10 0.02%
sphincs+-128s-simple/sign/32_min 631 ms 630 ms 10 1.58568/s
sphincs+-128s-simple/sign/32_max 632 ms 631 ms 10 1.58671/s
sphincs+-128f-robust/sign/32_mean 56.4 ms 56.3 ms 10 17.7478/s
sphincs+-128f-robust/sign/32_median 56.4 ms 56.3 ms 10 17.7467/s
sphincs+-128f-robust/sign/32_stddev 0.026 ms 0.026 ms 10 8.2731m/s
sphincs+-128f-robust/sign/32_cv 0.05 % 0.05 % 10 0.05%
sphincs+-128f-robust/sign/32_min 56.4 ms 56.3 ms 10 17.7384/s
sphincs+-128f-robust/sign/32_max 56.4 ms 56.4 ms 10 17.7621/s
sphincs+-128f-simple/verify/32_mean 1.80 ms 1.80 ms 10 556.312/s
sphincs+-128f-simple/verify/32_median 1.79 ms 1.79 ms 10 559.06/s
sphincs+-128f-simple/verify/32_stddev 0.049 ms 0.049 ms 10 14.9518/s
sphincs+-128f-simple/verify/32_cv 2.70 % 2.71 % 10 2.69%
sphincs+-128f-simple/verify/32_min 1.73 ms 1.72 ms 10 532.058/s
sphincs+-128f-simple/verify/32_max 1.88 ms 1.88 ms 10 580.051/s
sphincs+-192s-simple/keygen_mean 121 ms 121 ms 10 8.24687/s
sphincs+-192s-simple/keygen_median 121 ms 121 ms 10 8.24698/s
sphincs+-192s-simple/keygen_stddev 0.033 ms 0.011 ms 10 772.41u/s
sphincs+-192s-simple/keygen_cv 0.03 % 0.01 % 10 0.01%
sphincs+-192s-simple/keygen_min 121 ms 121 ms 10 8.24579/s
sphincs+-192s-simple/keygen_max 121 ms 121 ms 10 8.24797/s
sphincs+-256f-simple/sign/32_mean 101 ms 100 ms 10 9.96101/s
sphincs+-256f-simple/sign/32_median 100 ms 100 ms 10 9.96204/s
sphincs+-256f-simple/sign/32_stddev 0.053 ms 0.039 ms 10 3.91328m/s
sphincs+-256f-simple/sign/32_cv 0.05 % 0.04 % 10 0.04%
sphincs+-256f-simple/sign/32_min 100 ms 100 ms 10 9.95045/s
sphincs+-256f-simple/sign/32_max 101 ms 100 ms 10 9.96393/s
sphincs+-192s-robust/sign/32_mean 1988 ms 1985 ms 10 0.503742/s
sphincs+-192s-robust/sign/32_median 1986 ms 1983 ms 10 0.504245/s
sphincs+-192s-robust/sign/32_stddev 6.13 ms 5.98 ms 10 1.50493m/s
sphincs+-192s-robust/sign/32_cv 0.31 % 0.30 % 10 0.30%
sphincs+-192s-robust/sign/32_min 1985 ms 1983 ms 10 0.49947/s
sphincs+-192s-robust/sign/32_max 2005 ms 2002 ms 10 0.504295/s
sphincs+-128s-simple/verify/32_mean 0.618 ms 0.617 ms 10 1.62283k/s
sphincs+-128s-simple/verify/32_median 0.616 ms 0.615 ms 10 1.62509k/s
sphincs+-128s-simple/verify/32_stddev 0.022 ms 0.022 ms 10 57.5421/s
sphincs+-128s-simple/verify/32_cv 3.57 % 3.56 % 10 3.55%
sphincs+-128s-simple/verify/32_min 0.586 ms 0.585 ms 10 1.52839k/s
sphincs+-128s-simple/verify/32_max 0.655 ms 0.654 ms 10 1.70824k/s
sphincs+-128s-robust/verify/32_mean 1.17 ms 1.17 ms 10 854.079/s
sphincs+-128s-robust/verify/32_median 1.17 ms 1.17 ms 10 857.166/s
sphincs+-128s-robust/verify/32_stddev 0.031 ms 0.031 ms 10 22.3277/s
sphincs+-128s-robust/verify/32_cv 2.64 % 2.65 % 10 2.61%
sphincs+-128s-robust/verify/32_min 1.13 ms 1.13 ms 10 813.641/s
sphincs+-128s-robust/verify/32_max 1.23 ms 1.23 ms 10 885.665/s
sphincs+-256f-robust/sign/32_mean 186 ms 186 ms 10 5.38278/s
sphincs+-256f-robust/sign/32_median 186 ms 186 ms 10 5.39002/s
sphincs+-256f-robust/sign/32_stddev 0.715 ms 0.747 ms 10 0.0214275/s
sphincs+-256f-robust/sign/32_cv 0.38 % 0.40 % 10 0.40%
sphincs+-256f-robust/sign/32_min 186 ms 186 ms 10 5.32189/s
sphincs+-256f-robust/sign/32_max 188 ms 188 ms 10 5.39049/s
sphincs+-128s-robust/keygen_mean 156 ms 156 ms 10 6.41065/s
sphincs+-128s-robust/keygen_median 156 ms 156 ms 10 6.41071/s
sphincs+-128s-robust/keygen_stddev 0.052 ms 0.014 ms 10 574.443u/s
sphincs+-128s-robust/keygen_cv 0.03 % 0.01 % 10 0.01%
sphincs+-128s-robust/keygen_min 156 ms 156 ms 10 6.40968/s
sphincs+-128s-robust/keygen_max 156 ms 156 ms 10 6.41161/s
sphincs+-256f-simple/verify/32_mean 2.68 ms 2.68 ms 10 373.394/s
sphincs+-256f-simple/verify/32_median 2.69 ms 2.69 ms 10 371.807/s
sphincs+-256f-simple/verify/32_stddev 0.047 ms 0.047 ms 10 6.60918/s
sphincs+-256f-simple/verify/32_cv 1.75 % 1.77 % 10 1.77%
sphincs+-256f-simple/verify/32_min 2.61 ms 2.60 ms 10 361.898/s
sphincs+-256f-simple/verify/32_max 2.76 ms 2.76 ms 10 384.206/s
sphincs+-192s-robust/verify/32_mean 1.73 ms 1.72 ms 10 580.372/s
sphincs+-192s-robust/verify/32_median 1.74 ms 1.74 ms 10 575.88/s
sphincs+-192s-robust/verify/32_stddev 0.040 ms 0.040 ms 10 13.6261/s
sphincs+-192s-robust/verify/32_cv 2.32 % 2.33 % 10 2.35%
sphincs+-192s-robust/verify/32_min 1.66 ms 1.66 ms 10 561.004/s
sphincs+-192s-robust/verify/32_max 1.79 ms 1.78 ms 10 603.469/s
sphincs+-256s-simple/verify/32_mean 1.32 ms 1.32 ms 10 758.553/s
sphincs+-256s-simple/verify/32_median 1.32 ms 1.32 ms 10 759.077/s
sphincs+-256s-simple/verify/32_stddev 0.023 ms 0.023 ms 10 13.5255/s
sphincs+-256s-simple/verify/32_cv 1.77 % 1.77 % 10 1.78%
sphincs+-256s-simple/verify/32_min 1.28 ms 1.27 ms 10 741.999/s
sphincs+-256s-simple/verify/32_max 1.35 ms 1.35 ms 10 784.793/s
sphincs+-256f-robust/verify/32_mean 5.19 ms 5.18 ms 10 192.933/s
sphincs+-256f-robust/verify/32_median 5.19 ms 5.18 ms 10 193.06/s
sphincs+-256f-robust/verify/32_stddev 0.097 ms 0.097 ms 10 3.63415/s
sphincs+-256f-robust/verify/32_cv 1.88 % 1.87 % 10 1.88%
sphincs+-256f-robust/verify/32_min 5.01 ms 5.00 ms 10 187.86/s
sphincs+-256f-robust/verify/32_max 5.33 ms 5.32 ms 10 199.816/s
sphincs+-192f-robust/sign/32_mean 90.0 ms 89.9 ms 10 11.1264/s
sphincs+-192f-robust/sign/32_median 90.0 ms 89.9 ms 10 11.1257/s
sphincs+-192f-robust/sign/32_stddev 0.024 ms 0.016 ms 10 2.01766m/s
sphincs+-192f-robust/sign/32_cv 0.03 % 0.02 % 10 0.02%
sphincs+-192f-robust/sign/32_min 89.9 ms 89.8 ms 10 11.1239/s
sphincs+-192f-robust/sign/32_max 90.0 ms 89.9 ms 10 11.1303/s
sphincs+-192s-simple/verify/32_mean 0.902 ms 0.901 ms 10 1.11103k/s
sphincs+-192s-simple/verify/32_median 0.897 ms 0.896 ms 10 1.11658k/s
sphincs+-192s-simple/verify/32_stddev 0.029 ms 0.029 ms 10 34.9975/s
sphincs+-192s-simple/verify/32_cv 3.20 % 3.19 % 10 3.15%
sphincs+-192s-simple/verify/32_min 0.871 ms 0.870 ms 10 1.05571k/s
sphincs+-192s-simple/verify/32_max 0.948 ms 0.947 ms 10 1.14974k/s
sphincs+-256s-robust/keygen_mean 152 ms 151 ms 10 6.6089/s
sphincs+-256s-robust/keygen_median 151 ms 151 ms 10 6.60882/s
sphincs+-256s-robust/keygen_stddev 0.050 ms 0.015 ms 10 639.449u/s
sphincs+-256s-robust/keygen_cv 0.03 % 0.01 % 10 0.01%
sphincs+-256s-robust/keygen_min 151 ms 151 ms 10 6.60812/s
sphincs+-256s-robust/keygen_max 152 ms 151 ms 10 6.60995/s
sphincs+-256f-robust/keygen_mean 9.47 ms 9.46 ms 10 105.719/s
sphincs+-256f-robust/keygen_median 9.47 ms 9.46 ms 10 105.724/s
sphincs+-256f-robust/keygen_stddev 0.005 ms 0.003 ms 10 0.0296424/s
sphincs+-256f-robust/keygen_cv 0.05 % 0.03 % 10 0.03%
sphincs+-256f-robust/keygen_min 9.47 ms 9.46 ms 10 105.645/s
sphincs+-256f-robust/keygen_max 9.48 ms 9.47 ms 10 105.746/s
sphincs+-192s-robust/keygen_mean 228 ms 228 ms 10 4.39032/s
sphincs+-192s-robust/keygen_median 228 ms 228 ms 10 4.39021/s
sphincs+-192s-robust/keygen_stddev 0.070 ms 0.048 ms 10 929.561u/s
sphincs+-192s-robust/keygen_cv 0.03 % 0.02 % 10 0.02%
sphincs+-192s-robust/keygen_min 228 ms 228 ms 10 4.38935/s
sphincs+-192s-robust/keygen_max 228 ms 228 ms 10 4.39282/s
sphincs+-128f-robust/keygen_mean 2.44 ms 2.44 ms 10 410.636/s
sphincs+-128f-robust/keygen_median 2.44 ms 2.44 ms 10 410.644/s
sphincs+-128f-robust/keygen_stddev 0.001 ms 0.000 ms 10 0.0326569/s
sphincs+-128f-robust/keygen_cv 0.04 % 0.01 % 10 0.01%
sphincs+-128f-robust/keygen_min 2.44 ms 2.44 ms 10 410.568/s
sphincs+-128f-robust/keygen_max 2.44 ms 2.44 ms 10 410.672/ssphincs+ is a header-only C++20 library which is pretty easy to use. To get started
- Clone SPHINCS+ repository
cd
# Multi-step cloning and importing of submodules
git clone https://github.com/itzmeanjan/sphincs-plus.git && pushd sphincs-plus && git submodule update --init && popd
# Or do single step cloning and importing of submodules
git clone https://github.com/itzmeanjan/sphincs-plus.git --recurse-submodules- Write a program which makes use of SPHINCS+-{128,192,256}{s,f}-{robust,simple} key generation, signing and verification API ( all of these routines and constants, representing how many bytes to allocate for holding public key, secret key and signature, live under
sphincs_plus_{128,192,256}{s,f}_{robust,simple}::namespace ), while importing correct header file. - Finally compile your program, while letting your compiler know where it can find SPHINCS+ and Sha3 headers.
# Assuming `sphincs-plus` was cloned just under $HOME
SPHINCS_PLUS_HEADERS=~/sphincs-plus/include
SHA3_HEADERS=~/sphincs-plus/sha3/include
g++ -std=c++20 -Wall -Wextra -pedantic -O3 -march=native -I $SPHINCS_PLUS_HEADERS -I $SHA3_HEADERS main.cppTip
For recommended parameter sets, find table 3 of SPHINCS+ specification.
See the example program sphincs+_shake_128s_robust.cpp, demonstrating usage of keygen/ sign/ verify API.
pushd examples; g++ -std=c++20 -Wall -Wextra -pedantic -O3 -march=native -I ../include -I ../sha3/include sphincs+_shake_128s_robust.cpp && ./a.out; popd
SPHINCS+-SHAKE-128s-robust @ NIST Security Level 1
Secret Key : 49a5ca3d5f151f2c9c0f197d324724c9c2313bdb69720a1bc615434b4874ba41949e000ab275dd6da569ff32757c021586eb2036e1ba14483e809ffa0c5505f5
Public Key : 949e000ab275dd6da569ff32757c021586eb2036e1ba14483e809ffa0c5505f5
Message : 80bce832fab336eefdceef28ab89838667d164d255298fe888344760199a8c3c
Signature : 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Verified : trueCaution
Before you consider using Psuedo Random Number Generator, which comes with this library implementation, I strongly advice you to go through the comments in include/prng.hpp.
Note
Looking at the API documentation, in header files, can give you a pretty good idea of how to use Sphincs+ 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/ signatures are, for various different Sphincs+ instantiations. This gives much better type safety and compile-time error reporting.