OV signature

This project contains the reference and optimized implementations of the oil and vinegar (OV) signature system.

Licence

Public domain unless stated differently at the top of each file.

Parameters

Parameter	signature size	pk size	sk size	pkc size	compressed-sk size
GF(16),160,64	96	412,160	348,704	66,576	48
GF(256),112,44	128	278,432	237,896	43,576	48
GF(256),184,72	200	1,225,440	1,044,320	189,232	48
GF(256),244,96	260	2,869,440	2,436,704	446,992	48

Contents

• src : Source code.
• utils : utilities for AES, SHAKE, and PRNGs. The default setting calls openssl library.
• unit_tests : unit testers.

Generate NIST and SUPERCOP projects

1. NIST submission:

• creat basic nist project.

python3 ./create_nist_project.py

• generate KAT files. (I personally recommend skipping this step for version controls of the source code because the size of KATs are enomerous.)

cd pqov_nist_submission/Optimized_Implementation/avx2/
source ./generate_KAT.sh
mv KAT ../../
cd ../../../

• generate file descriptions required from NIST.

cd pqov_nist_submission/
ls -alR | python ../generate_filedescriptions_for_nist.py >> README
cd ../

2. SUPERCOP:

python3 ./create_supercop_project.py

Instructions for testing/benchmarks

Type make

make

for generating 3 executables:

1. sign_api-test : testing for API functions (crypto_keygen(), crypto_sign(), and crypto_verify()).
2. sign_api-benchmark: reporting performance numbers for signature API functions.
3. rec-sign-benchmark: reporting more detailed performance numbers for signature API functions. Number format: ''average /numbers of testing (1st quartile, median, 3rd quartile)''

Options for Parameters:

For compiling different parameters, we use the macros ( _OV256_112_44 / _OV256_184_72 / _OV256_244_96 / _OV16_160_64 ) to control the C source code.
The default setting is _OV256_112_44 defined in src/params.h.

The other option is to use our makefile:

1. _OV16_160_64 :

make PARAM=1

2. _OV256_112_44 :

make

or

make PARAM=3

3. _OV256_184_72 :

make PARAM=4

4. _OV256_244_96 :

make PARAM=5

Options for Variants:

For compiling different variants, we use the macros ( _OV_CLASSIC / _OV_PKC / _OV_PKC_SKC ) to control the C source code.
The default setting is _OV_CLASSIC defined in src/params.h.

The other option is to use our makefile:

1. _OV_CLASSIC :

make

or

make VARIANT=1

2. _OV_PKC :

make VARIANT=2

3. _OV_PKC_SKC :

make VARIANT=3

4. _OV256_244_96 and _OV_PKC :

make VARIANT=2 PARAM=5

Optimizations for Architectures:

Reference Version:

The reference uses (1) source code in the directories: src/ , src/ref/, and
(2) directories for utilities of AES, SHAKE, and randombytes() : utils/ .
The default implementation for AES and SHAKE is from openssl library, controlled by the macro _UTILS_OPENSSL_ defined in src/config.h.

Or, use our makefile:

1. Reference version (_OV256_112_44 and _OV_CLASSIC):

make

2. Reference version, _OV256_244_96 , and _OV_PKC :

make VARIANT=2 PARAM=5

To turn on the option of 4-round AES, one need to turn on the macro _4ROUND_AES_ defined in src/params.h.

AVX2 Version:

The AVX2 option uses (1) source code in the directories: src/ , src/amd64 , src/ssse3 , src/avx2, and
(2) directories for utilities of AES, SHAKE, and randombytes() : utils/, utils/x86aesni .
(3) One stil need to turn on the macros _BLAS_AVX2_, _MUL_WITH_MULTAB_, _UTILS_AESNI_ defined in src/config.h to enable AVX2 optimization.

Or, use our makefile:

1. AVX2 version (_OV256_112_44 and _OV_CLASSIC):

make PROJ=avx2

2. AVX2 version, _OV256_184_72, and _OV_PKC:

make PROJ=avx2 PARAM=4 VARIANT=2

NEON Version:

The NEON option uses (1) source code in the src/ , src/amd64 , src/neon, and
(2) directories for utilities of AES, SHAKE, and randombytes() : utils/, ( utils/neon_aesinst (Armv8 AES instruction) or utils/neon_aes(NEON bitslice AES implemetation) ).
(3) One stil need to turn on the macros _BLAS_NEON_ , _UTILS_NEONAES_ defined in src/config.h to enable NEON optimization.
(4) Depending on the CPUs and parameters, one can choose to define the macro _MUL_WITH_MULTAB_ for GF multiplication with MUL tables. We suggest to turn on it for the _OV16_160_64 parameter.

Or, use our makefile:

1. NEON version (_OV256_112_44 and _OV_CLASSIC):

make PROJ=neon

2. Another example: NEON version, _OV16_160_64, and _OV_PKC_SKC:

make PROJ=neon PARAM=1 VARIANT=3

Notes for Apple Mac M1:

1. We use

uname -s

to detect if running on Mac OS and

uname -m

to detect if is an Arm-based Mac. If uname -s returns Darwin and uname -m returns **arm64, we are running on an Arm-based Mac (e.g., Apple M1). The Makefile will then define the _APPLE_SILICON_ macro for enabling some optimization settings in the source code .
2. The program needs sudo to benchmark on Mac OS correctly.

Options for Algorithm of Solving Linear Equation while Signing:

1. Default setting: Gaussian Elimination and backward substitution.
2. Choose the algorithm of calculating inversion matrix with block matrix compution:
   (a) Define the _LDU_DECOMPOSE_ macro in src/parms.h.
   (b) Remove the _BACK_SUBSTITUTION_ macro in src/ov.c.

Benchmarks

1. AVX2 implementations on Intel(R) Xeon(R) CPU E3-1275 v5 @ 3.60GHz (Skylake), turbo boost off

Parameter	Key-generation cycles	signing cycles	sign-opening cycles
OV(16,160,64)-classic	4404165.040000 /100 (4328746,4332050,4337824)	116828.822000 /1000 (109180,109314,109476)	58255.892000 /1000 (57504,58274,59024)
OV(16,160,64)-cpk	4443962.080000 /100 (4372956,4376338,4381242)	117521.884000 /1000 (110712,110824,110980)	281266.102000 /1000 (280190,280946,281714)
OV(16,160,64)-cpk-csk	4517415.360000 /100 (4448068,4450838,4455366)	2480241.982000 /1000 (2471938,2473254,2475538)	276703.810000 /1000 (275764,276520,277334)
OV(256,112,44)-classic	2971691.280000 /100 (2901932,2903434,2905938)	105757.650000 /1000 (105176,105324,105472)	90378.776000 /1000 (89572,90336,91088)
OV(256,112,44)-cpk	2924426.540000 /100 (2857738,2858724,2861124)	107061.638000 /1000 (106332,106508,106688)	224355.520000 /1000 (223762,224006,224286)
OV(256,112,44)-cpk-csk	2913461.180000 /100 (2846270,2848774,2850886)	1877833.322000 /1000 (1874834,1876442,1878078)	224512.708000 /1000 (224076,224374,224684)
OV(256,184,72)-classic	17690951.620000 /100 (17599644,17603360,17607160)	300090.748000 /1000 (299110,299316,299532)	241705.192000 /1000 (241098,241588,242066)
OV(256,184,72)-cpk	17610902.060000 /100 (17532234,17534058,17537520)	300786.974000 /1000 (299790,300010,300258)	918983.580000 /1000 (916888,917402,918112)
OV(256,184,72)-cpk-csk	17248300.300000 /100 (17154892,17157802,17161764)	9950429.662000 /1000 (9898656,9965110,9995552)	921044.166000 /1000 (920010,920616,921214)
OV(256,244,96)-classic	48641435.640000 /100 (48457126,48480444,48500076)	595198.860000 /1000 (589688,591812,594184)	471052.054000 /1000 (468914,470886,472852)
OV(256,244,96)-cpk	46753567.760000 /100 (46652250,46656796,46660876)	597267.148000 /1000 (591802,594268,597160)	2042818.886000 /1000 (2036396,2038408,2041114)
OV(256,244,96)-cpk-csk	45627154.160000 /100 (45488036,45492216,45499014)	22993692.878000 /1000 (22986750,22992816,22998322)	2033715.538000 /1000 (2030920,2032992,2035192)

2. With 4RAES macro, AVX2 implementations on Intel(R) Xeon(R) CPU E3-1275 v5 @ 3.60GHz (Skylake), turbo boost off

Parameter	Key-generation cycles	signing cycles	sign-opening cycles
OV(16,160,64)-classic	4430025.800000 /100 (4356148,4358736,4364702)	116570.692000 /1000 (109868,109996,110148)	58059.062000 /1000 (57294,58050,58798)
OV(16,160,64)-cpk	4405616.080000 /100 (4334642,4337958,4343666)	117115.824000 /1000 (110470,110602,110760)	168166.006000 /1000 (167288,167886,168470)
OV(16,160,64)-cpk-csk	4318530.000000 /100 (4247340,4252570,4257254)	2373560.138000 /1000 (2365812,2366766,2368256)	168930.000000 /1000 (168132,168830,169436)
OV(256,112,44)-classic	2868175.480000 /100 (2796552,2798734,2804066)	106530.948000 /1000 (105906,106098,106268)	89335.626000 /1000 (88582,89296,90126)
OV(256,112,44)-cpk	2881418.040000 /100 (2814360,2815902,2819468)	106800.630000 /1000 (106160,106336,106526)	151526.502000 /1000 (150976,151236,151506)
OV(256,112,44)-cpk-csk	2926573.520000 /100 (2858332,2861082,2867376)	1819385.352000 /1000 (1817018,1818690,1819480)	151029.002000 /1000 (150656,150902,151204)
OV(256,184,72)-classic	17362839.880000 /100 (17272786,17274800,17278294)	301435.272000 /1000 (299614,299818,300032)	241093.452000 /1000 (240294,240958,241602)
OV(256,184,72)-cpk	17518167.760000 /100 (17437532,17441792,17447672)	301554.380000 /1000 (300466,300716,300982)	591127.750000 /1000 (589324,589846,590356)
OV(256,184,72)-cpk-csk	17001182.380000 /100 (16905392,16909288,16914922)	9613919.664000 /1000 (9598624,9603518,9605894)	591259.966000 /1000 (590390,590902,591422)
OV(256,244,96)-classic	48088795.340000 /100 (47909346,47918484,47931396)	589577.194000 /1000 (586850,587744,589090)	461104.490000 /1000 (459508,460642,461702)
OV(256,244,96)-cpk	45604738.980000 /100 (45505002,45508552,45512622)	627582.498000 /1000 (620602,624774,629524)	1286277.362000 /1000 (1279818,1282392,1285530)
OV(256,244,96)-cpk-csk	44926343.860000 /100 (44787368,44792434,44801692)	21833937.212000 /1000 (21817004,21823506,21830864)	1271237.518000 /1000 (1266868,1268998,1270808)

3. AVX2 implementations on Intel(R) Xeon(R) CPU E3-1230L v3 @ 1.80GHz (Haswell)), turbo boost off

Parameter	Key-generation cycles	signing cycles	sign-opening cycles
OV(16,160,64)-classic	5016036.240000 /100 (4937420,4945376,4954124)	131392.752000 /1000 (123156,123376,123620)	60904.608000 /1000 (60076,60832,61504)
OV(16,160,64)-cpk	5067757.040000 /100 (4992400,5002756,5013412)	130966.108000 /1000 (123668,123908,124156)	399596.960000 /1000 (397648,398596,399556)
OV(16,160,64)-cpk-csk	5515641.200000 /100 (5443368,5448272,5457180)	3052952.056000 /1000 (3038012,3042756,3052016)	400434.368000 /1000 (398800,399724,400624)
OV(256,112,44)-classic	3403510.500000 /100 (3304036,3311188,3317840)	122641.960000 /1000 (121632,121772,121948)	82859.460000 /1000 (82420,82668,83012)
OV(256,112,44)-cpk	3459328.000000 /100 (3391588,3393872,3400424)	116985.104000 /1000 (113816,116624,118816)	313062.148000 /1000 (311876,312284,312712)
OV(256,112,44)-cpk-csk	3360401.360000 /100 (3280040,3287336,3294824)	2253385.692000 /1000 (2244896,2251440,2257484)	312037.884000 /1000 (311328,311720,312160)
OV(256,184,72)-classic	22138835.280000 /100 (22044264,22046680,22049832)	350406.368000 /1000 (346180,346528,346836)	275809.088000 /1000 (274848,275216,275652)
OV(256,184,72)-cpk	22470932.960000 /100 (22385912,22389144,22394876)	348133.452000 /1000 (345920,346424,346868)	1282573.512000 /1000 (1278228,1280160,1281668)
OV(256,184,72)-cpk-csk	21868033.520000 /100 (21777396,21779704,21782444)	11381519.284000 /1000 (11368148,11381092,11388020)	1283091.132000 /1000 (1279344,1281232,1282876)
OV(256,244,96)-classic	58309948.240000 /100 (58156052,58162124,58172156)	695597.460000 /1000 (689308,690752,693412)	515532.460000 /1000 (513292,514100,515140)
OV(256,244,96)-cpk	57414118.200000 /100 (57310516,57315504,57325072)	734795.140000 /1000 (724380,726632,735368)	2846586.460000 /1000 (2837992,2842448,2847740)
OV(256,244,96)-cpk-csk	57445240.400000 /100 (57301900,57306980,57313992)	26031018.856000 /1000 (26013280,26021784,26031760)	2843408.596000 /1000 (2838024,2842416,2846564)

4. Wit 4RAES macro, AVX2 implementations on Intel(R) Xeon(R) CPU E3-1230L v3 @ 1.80GHz (Haswell)), turbo boost off

Parameter	Key-generation cycles	signing cycles	sign-opening cycles
OV(16,160,64)-classic	4975791.120000 /100 (4898016,4904192,4913388)	130077.300000 /1000 (123308,123560,123808)	60423.632000 /1000 (59592,60364,61092)
OV(16,160,64)-cpk	4867485.520000 /100 (4795252,4799564,4809548)	123498.396000 /1000 (117820,117948,118128)	206137.548000 /1000 (204728,205504,206312)
OV(16,160,64)-cpk-csk	4878610.640000 /100 (4803228,4810612,4819392)	2764608.984000 /1000 (2751324,2755060,2765580)	208606.620000 /1000 (207436,208188,208912)
OV(256,112,44)-classic	3286078.300000 /100 (3197572,3204260,3214664)	122923.608000 /1000 (121896,122028,122152)	96773.664000 /1000 (96208,96644,97064)
OV(256,112,44)-cpk	3196467.980000 /100 (3122680,3130128,3138036)	115342.300000 /1000 (113108,114012,114976)	196975.472000 /1000 (195972,196404,196840)
OV(256,112,44)-cpk-csk	3219533.400000 /100 (3146820,3154404,3159528)	2115833.688000 /1000 (2109292,2113924,2119136)	182389.296000 /1000 (181824,182100,182376)
OV(256,184,72)-classic	21494207.180000 /100 (21367644,21370252,21373736)	348552.644000 /1000 (346504,346820,347232)	275686.680000 /1000 (274668,275024,275476)
OV(256,184,72)-cpk	21505762.640000 /100 (21416272,21419104,21423720)	349823.884000 /1000 (348344,348756,349204)	716735.288000 /1000 (713804,714252,714844)
OV(256,184,72)-cpk-csk	21294242.160000 /100 (21200464,21203604,21206856)	11222585.880000 /1000 (11211988,11222092,11229120)	717092.608000 /1000 (714928,715432,716136)
OV(256,244,96)-classic	57179699.360000 /100 (57023616,57049260,57070560)	695777.216000 /1000 (687932,690340,695824)	514094.544000 /1000 (511824,512628,513604)
OV(256,244,96)-cpk	56078502.040000 /100 (55973132,55983388,55991336)	740858.864000 /1000 (718072,723628,758304)	1522603.924000 /1000 (1515360,1516652,1518708)
OV(256,244,96)-cpk-csk	56273885.840000 /100 (56131464,56136556,56145308)	24832148.256000 /1000 (24816540,24824672,24835632)	1556615.036000 /1000 (1550748,1552732,1556188)

5. neon implementation on Apple M1

Parameter	Key-generation cycles	signing cycles	sign-opening cycles
OV(16,160,64)-classic	3393202.048000 /1000 (3389693,3391967,3395605)	79649.492100 /10000 (74491,74633,74814)	45974.790500 /10000 (44777,45908,47078)
OV(16,160,64)-cpk	3366171.190000 /1000 (3359391,3360648,3363265)	79637.568200 /10000 (74612,74757,74938)	138389.038700 /10000 (136221,138541,140629)
OV(16,160,64)-cpk-csk	3399677.154000 /1000 (3390185,3393812,3397537)	2094305.040600 /10000 (2088941,2089131,2089364)	138383.778500 /10000 (136248,138496,140612)
OV(256,112,44)-classic	1797428.261000 /1000 (1791766,1793119,1794443)	55554.494500 /10000 (55244,55320,55413)	49796.923700 /10000 (49550,49719,49976)
OV(256,112,44)-cpk	1779785.786000 /1000 (1774902,1775826,1776591)	55520.226000 /10000 (55203,55289,55391)	113035.876400 /10000 (112739,112934,113235)
OV(256,112,44)-cpk-csk	1781368.708000 /1000 (1773490,1774748,1775610)	1056925.781800 /10000 (1056437,1056617,1056802)	113889.868100 /10000 (113626,113805,114074)
OV(256,184,72)-classic	9842855.186000 /1000 (9833331,9836359,9842447)	149716.423600 /10000 (148561,149280,149439)	189911.501600 /10000 (189580,189837,190151)
OV(256,184,72)-cpk	9808371.327000 /1000 (9801978,9803637,9805500)	148068.639000 /10000 (147459,147564,147708)	462334.340400 /10000 (461835,462306,462730)
OV(256,184,72)-cpk-csk	9761487.225000 /1000 (9749338,9751198,9753375)	6353695.307200 /10000 (6353126,6353401,6353665)	462173.811200 /10000 (461515,461896,462369)
OV(256,244,96)-classic	28294004.860000 /1000 (28275650,28286979,28297149)	298569.667200 /10000 (293517,293826,294532)	376079.556800 /10000 (375692,376000,376372)
OV(256,244,96)-cpk	26889989.542000 /1000 (26710677,26743866,26754034)	310212.719500 /10000 (308849,309159,309459)	1012621.870400 /10000 (1012091,1012482,1012937)
OV(256,244,96)-cpk-csk	26750917.303000 /1000 (26661383,26663940,26674888)	15836867.328600 /10000 (15829550,15830169,15831069)	1015436.129700 /10000 (1010911,1011331,1012047)

6. neon implementation on Apple M1, defining 4RAES macro

Parameter	Key-generation cycles	signing cycles	sign-opening cycles
OV(16,160,64)-classic	3354871.311000 /1000 (3348860,3349853,3351112)	79175.906800 /10000 (74372,74515,74696)	45800.548600 /10000 (44629,45711,46863)
OV(16,160,64)-cpk	3327670.425000 /1000 (3321012,3324331,3326806)	79323.975100 /10000 (74366,74503,74679)	97395.223100 /10000 (95793,97391,98984)
OV(16,160,64)-cpk-csk	3352449.915000 /1000 (3342295,3349000,3351955)	2050209.412400 /10000 (2044850,2045042,2045331)	97323.289600 /10000 (95756,97325,98867)
OV(256,112,44)-classic	1766518.643000 /1000 (1761364,1762817,1763931)	55363.380500 /10000 (55097,55175,55267)	49893.352300 /10000 (49644,49808,50070)
OV(256,112,44)-cpk	1749851.720000 /1000 (1745637,1746623,1747825)	55542.583600 /10000 (55244,55329,55431)	83097.113800 /10000 (82796,83021,83311)
OV(256,112,44)-cpk-csk	1751771.015000 /1000 (1746535,1748646,1750924)	1027002.902200 /10000 (1026583,1026701,1026841)	84001.746000 /10000 (83738,83920,84191)
OV(256,184,72)-classic	9694194.041000 /1000 (9688797,9690791,9692931)	149529.498900 /10000 (148460,149120,149299)	189887.573600 /10000 (189566,189817,190140)
OV(256,184,72)-cpk	9645633.052000 /1000 (9639195,9640984,9643113)	147986.401300 /10000 (147396,147524,147666)	330573.232900 /10000 (330084,330463,330877)
OV(256,184,72)-cpk-csk	9650337.274000 /1000 (9644063,9645510,9648015)	6222689.873100 /10000 (6221007,6221280,6221588)	331661.876800 /10000 (330625,331074,331700)
OV(256,244,96)-classic	27859451.168000 /1000 (27846303,27852840,27859809)	299725.738900 /10000 (292736,293117,308054)	376210.326900 /10000 (375814,376132,376506)
OV(256,244,96)-cpk	26580995.262000 /1000 (26298820,26305292,26340264)	309852.521500 /10000 (308127,308410,308684)	707297.318200 /10000 (706823,707217,707643)
OV(256,244,96)-cpk-csk	26643439.819000 /1000 (26289085,26298657,26354765)	15526142.527500 /10000 (15522021,15522513,15523170)	706816.234400 /10000 (704644,704986,705439)

7. neon implementation on ARM Cortex-A72(v8) @ 1.8GHz (Raspberry pi 4, aarch64, no aes extension)

Parameter	Key-generation cycles	signing cycles	sign-opening cycles
OV(16,160,64)-classic	29290685.950000 /500 (29239158,29269925,29310858)	494872.201800 /10000 (458114,460655,470144)	143442.171400 /10000 (139658,141528,143558)
OV(16,160,64)-cpk	28936858.182000 /500 (28894743,28906183,28925222)	1580336802.216000 /10000 (542228,549105,559817)	5080532.816700 /10000 (4993594,5087095,5174934)
OV(16,160,64)-cpk-csk	29483404.598000 /500 (29451741,29467684,29491076)	1395940904.282800 /10000 (16401080,16413501,16435793)	1844672822620759.000000 /10000 (4974918,5070253,5156379)
OV(256,112,44)-classic	11188099.140000 /500 (11163154,11172204,11185089)	247106.639500 /10000 (244375,245095,245897)	143717.544900 /10000 (142618,142868,143161)
OV(256,112,44)-cpk	11224762.366000 /500 (11186542,11193794,11198712)	256224.640400 /10000 (251210,253324,255524)	3678706.104100 /10000 (3668527,3681898,3684604)
OV(256,112,44)-cpk-csk	11295081.128000 /500 (11219457,11229231,11318013)	7621048.374000 /10000 (7616217,7617137,7618574)	3674931.824400 /10000 (3666397,3677844,3679458)
OV(256,184,72)-classic	66931801.010000 /500 (66731124,66871027,67029434)	1557611.746800 /10000 (1520321,1542143,1587587)	588840.363000 /10000 (571977,574080,589334)
OV(256,184,72)-cpk	66570566.088000 /500 (66275754,66554826,66793786)	1659039.631200 /10000 (1623087,1632966,1692327)	1374057048.781200 /10000 (17122760,17161246,17200844)
OV(256,184,72)-cpk-csk	64199301.720000 /500 (64056764,64147364,64275590)	42820542.201000 /10000 (42746359,42794977,42855995)	1336706755.118000 /10000 (17338010,17369004,17405721)
OV(256,244,96)-classic	313822979.386000 /500 (313313865,313814250,314327646)	3347921.603300 /10000 (3272056,3337536,3403568)	1342670.939700 /10000 (1310429,1319092,1390676)
OV(256,244,96)-cpk	306220128.888000 /500 (305215682,305700907,306292823)	3324891.704800 /10000 (3245750,3316413,3385823)	39345343.824300 /10000 (39295821,39337795,39385602)
OV(256,244,96)-cpk-csk	312769807.848000 /500 (312264832,312729427,313148491)	107318888.779000 /10000 (107227206,107305680,107381535)	39389996.820300 /10000 (39326493,39390657,39452436)

7. neon implementation on ARM Cortex-A72(v8) @ 1.8GHz, defining 4RAES macro (Raspberry pi 4, aarch64, no aes extension)

Parameter	Key-generation cycles	signing cycles	sign-opening cycles
OV(16,160,64)-classic	26104042.366000 /500 (26055865,26079083,26109987)	479892.969200 /10000 (445703,448188,454231)	135681.459000 /10000 (131743,133721,136119)
OV(16,160,64)-cpk	25712346.908000 /500 (25690772,25698880,25710821)	550544.434100 /10000 (508517,517451,530845)	2308786.814100 /10000 (2264483,2309671,2354513)
OV(16,160,64)-cpk-csk	28350136.382000 /500 (28308338,28324760,28346176)	13374690.195600 /10000 (13328127,13333557,13351565)	2263162.810800 /10000 (2223998,2266233,2304816)
OV(256,112,44)-classic	9491444.574000 /500 (9419551,9436542,9450911)	257070.261600 /10000 (252719,254211,255892)	153938.584600 /10000 (151079,152130,153527)
OV(256,112,44)-cpk	9196501.852000 /500 (9181131,9191247,9197749)	253417.475800 /10000 (248689,249910,252309)	1678078.192600 /10000 (1671641,1672544,1686208)
OV(256,112,44)-cpk-csk	9478628.272000 /500 (9466694,9473513,9481548)	5631076.342600 /10000 (5625684,5627393,5637580)	1678325.878400 /10000 (1673384,1674207,1683582)
OV(256,184,72)-classic	2371867147.266000 /500 (57079160,57311639,57579767)	1595025.065900 /10000 (1558627,1569429,1623583)	587322.646100 /10000 (570475,572965,586951)
OV(256,184,72)-cpk	56918872.966000 /500 (56663215,56890636,57122899)	1758320.144800 /10000 (1720138,1729733,1797286)	8319356.344400 /10000 (8282039,8318527,8349960)
OV(256,184,72)-cpk-csk	56859414.722000 /500 (56676866,56815652,56969672)	1844673000101042.500000 /10000 (34488140,34533235,34600256)	8636187.722000 /10000 (8602234,8634365,8663370)
OV(256,244,96)-classic	295923082.904000 /500 (295058951,295693403,296663039)	3352007.747000 /10000 (3270463,3339648,3408099)	1352412.647500 /10000 (1320262,1328232,1398580)
OV(256,244,96)-cpk	36893485758928136.000000 /500 (282248561,282742682,283172951)	3387885.507700 /10000 (3312617,3376153,3440469)	18848531.373100 /10000 (18789243,18831724,18894871)
OV(256,244,96)-cpk-csk	291461557.636000 /500 (290948203,291438637,291896182)	1419459809.967000 /10000 (86648551,86727909,86825980)	18629406.251200 /10000 (18521783,18602008,18724379)