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famoserGirgias
famoser
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Girgias
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ext/gmp: Add GMP ECC test (#18363)
Co-authored-by: Gina Peter Banyard <[email protected]>
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‎ext/gmp/tests/gmp_cryptography.phpt

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11
--TEST--
2-
test some of the simple operations done in ECC cryptography (GH-16870)
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test operations done in finite field and elliptic curve cryptography. (GH-16870)
3+
--DESCRIPTION--
4+
Test operations using gmp with number sizes useful in cryptography.
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To gather the to-be-executed operations, the gmp_cryptography_ecc.phpt and gmp_cryptography_ffc.phpt files have been analysed.
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For finite field crypto (FFC), the operations are executed in a 8192bit prime group, with a 512bit factor.
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This is the biggest prime that was standarized in https://datatracker.ietf.org/doc/html/rfc3526.
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Note that this is insufficient according to the NIST guidelines for the security strength 256bit.
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However, it is doubtful that such big groups (or even bigger ones) are used, as then elliptic curves are much more efficient.
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For elliptic curve crypto (EEC), the operations are executed in a 512bit prime group.
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This corresponds to the biggest curve standardized in https://www.secg.org/sec2-v2.pdf.
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Operations already executed as part of FCC are ommitted: As FFC operates on larger numbers, ECC operations are implicitly covered.
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Further context:
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- See https://www.keylength.com/en/4/ for an overview of the recommended key lengths by NIST.
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- See https://doi.org/10.6028/NIST.IR.8547.ipd for a public draft of NIST which proposes to fade-out FFC/ECC crypto by 2035.
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Factors were produced using
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$random = gmp_random_bits(512);
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$randomHex = strtoupper(gmp_strval($random, 16));
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echo chunk_split(chunk_split($randomHex, 8, " "), 54);
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--EXTENSIONS--
425
gmp
526
--FILE--
627
<?php
7-
$big_128 = gmp_init("275458973678998164972199298356823445708", 10);
8-
$big_256 = gmp_init("105897378200704506708747774951422238999742054168150946506894304230846229930690", 10);
9-
$big_384 = gmp_init("6416793922163250205142333121845147158821454739198730072980369042145699078647151545580979451456624745026383368515606", 10);
10-
$big_521 = gmp_init("1780138296718969229154737597263093326930734138014367844231086609903991655888322554437298817404082596582997382075361284417827317144352840347188199593652743789", 10);
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// 8192-bit MODP Group of https://datatracker.ietf.org/doc/html/rfc3526
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$generator = gmp_init(2);
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$prime = gmp_init('
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FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1
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29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD
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EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245
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E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
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EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D
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C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F
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83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
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670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B
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E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9
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DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510
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15728E5A 8AAAC42D AD33170D 04507A33 A85521AB DF1CBA64
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ECFB8504 58DBEF0A 8AEA7157 5D060C7D B3970F85 A6E1E4C7
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ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226 1AD2EE6B
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F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C
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BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31
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43DB5BFC E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7
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88719A10 BDBA5B26 99C32718 6AF4E23C 1A946834 B6150BDA
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2583E9CA 2AD44CE8 DBBBC2DB 04DE8EF9 2E8EFC14 1FBECAA6
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287C5947 4E6BC05D 99B2964F A090C3A2 233BA186 515BE7ED
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1F612970 CEE2D7AF B81BDD76 2170481C D0069127 D5B05AA9
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93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34028492
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36C3FAB4 D27C7026 C1D4DCB2 602646DE C9751E76 3DBA37BD
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F8FF9406 AD9E530E E5DB382F 413001AE B06A53ED 9027D831
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179727B0 865A8918 DA3EDBEB CF9B14ED 44CE6CBA CED4BB1B
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DB7F1447 E6CC254B 33205151 2BD7AF42 6FB8F401 378CD2BF
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5983CA01 C64B92EC F032EA15 D1721D03 F482D7CE 6E74FEF6
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D55E702F 46980C82 B5A84031 900B1C9E 59E7C97F BEC7E8F3
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23A97A7E 36CC88BE 0F1D45B7 FF585AC5 4BD407B2 2B4154AA
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CC8F6D7E BF48E1D8 14CC5ED2 0F8037E0 A79715EE F29BE328
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06A1D58B B7C5DA76 F550AA3D 8A1FBFF0 EB19CCB1 A313D55C
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DA56C9EC 2EF29632 387FE8D7 6E3C0468 043E8F66 3F4860EE
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12BF2D5B 0B7474D6 E694F91E 6DBE1159 74A3926F 12FEE5E4
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38777CB6 A932DF8C D8BEC4D0 73B931BA 3BC832B6 8D9DD300
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741FA7BF 8AFC47ED 2576F693 6BA42466 3AAB639C 5AE4F568
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3423B474 2BF1C978 238F16CB E39D652D E3FDB8BE FC848AD9
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22222E04 A4037C07 13EB57A8 1A23F0C7 3473FC64 6CEA306B
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4BCBC886 2F8385DD FA9D4B7F A2C087E8 79683303 ED5BDD3A
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062B3CF5 B3A278A6 6D2A13F8 3F44F82D DF310EE0 74AB6A36
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4597E899 A0255DC1 64F31CC5 0846851D F9AB4819 5DED7EA1
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B1D510BD 7EE74D73 FAF36BC3 1ECFA268 359046F4 EB879F92
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4009438B 481C6CD7 889A002E D5EE382B C9190DA6 FC026E47
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9558E447 5677E9AA 9E3050E2 765694DF C81F56E8 80B96E71
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60C980DD 98EDD3DF FFFFFFFF FFFFFFFF', 16);
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$factor512 = gmp_init('
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3F174D30 1AA08EF0 3556CF48 C6E53D8A 926067DA 50563B72
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42037431 C3144C7C A49937EF 1A6D940A 7228EC8E E2278808
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FD4C0344 D9E03882 A7C65C49 F47E843A', 16);
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80+
$factor = gmp_powm($generator, $factor512, $prime);
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var_dump(gmp_strval($factor, 16));
82+
83+
$result = gmp_add($factor, $prime);
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$result = gmp_mod($result, $prime);
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$result = gmp_sub($result, $factor);
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var_dump(gmp_cmp($result, 0) === 0);
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88+
$factor = gmp_random_range(0, $prime);
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$factorInverted = gmp_invert($factor, $prime);
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$result = gmp_mul($factor, $factorInverted);
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$result = gmp_mod($result, $prime);
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var_dump(gmp_cmp($result, 1) === 0);
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94+
$primeP = gmp_div($prime - 1, 2);
95+
var_dump(gmp_prob_prime($prime) > 0);
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97+
98+
// prime and b of secp521r1 from https://www.secg.org/sec2-v2.pdf
99+
$p = gmp_init('01FF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF
100+
FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF
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FFFFFFFF FFFFFFFF FFFFFFFF', 16);
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$b = gmp_init('0051 953EB961 8E1C9A1F 929A21A0 B68540EE A2DA725B 99B315F3
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B8B48991 8EF109E1 56193951 EC7E937B 1652C0BD 3BB1BF07 3573DF88
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3D2C34F1 EF451FD4 6B503F00', 16);
11105

12-
// in ecc crypto key lengths of 256, 384 and 521 (yes, 521, not 512) are typical,
13-
// and the calculations seem to include squaring and cubing the key,
14-
// so test those operations
15-
var_dump((string) gmp_pow($big_128, 2));
16-
var_dump((string) gmp_pow($big_128, 3));
106+
$jacobi = gmp_jacobi($b, $p);
107+
var_dump($jacobi === 1);
17108

18-
var_dump((string) gmp_pow($big_256, 2));
19-
var_dump((string) gmp_pow($big_256, 3));
109+
$result = gmp_and($p, $b);
110+
var_dump(gmp_cmp($result, $b) === 0);
20111

21-
var_dump((string) gmp_pow($big_384, 2));
22-
var_dump((string) gmp_pow($big_384, 3));
112+
$result = gmp_xor($p, $p);
113+
var_dump(gmp_cmp($result, 0) === 0);
23114

24-
var_dump((string) gmp_pow($big_521, 2));
25-
var_dump((string) gmp_pow($big_521, 3));
115+
$result = gmp_pow($b, 3);
116+
var_dump(gmp_strval($result, 16));
26117

27118
?>
28119
--EXPECT--
29-
string(77) "75877646180287003845291692588996321992008024509271171205840397374930023621264"
30-
string(116) "20901178542000013443295783507452967008255111311111391381095411786512605029527130998551663048238767676593252458334912"
31-
string(155) "11214254709783046066761897074581165564696209875788503860615296581570239055173596662994580613114615553617959320367624022951770022252133452732995602203876100"
32-
string(232) "1187560172240926986956555551805946700914014146395850601682624192167183140821546786142042010581624015945796617035803644080855311724420346850512769661608026325318823192181186500090109111010574371273491473985103578154963883352347509000"
33-
string(230) "41175244239511227932271803271789465275501438128816738161335879819867157609061333189838579416997011220296835767015204168726569753974321567200401024149587401209307771709029048946370759582286096704404540466667318675170269947865547236"
34-
string(345) "264213056979683026715444213001489498112251992104549535125497320782388835160296854596249682279610208850530256165562505337646325742090947380083481042994421218556776724906795900034870043631716997303728488772811762108912277655229349137086580494553471889656657230883768271890897138746582039089128053875620299138149315547875444447674573987934196165016"
35-
string(313) "3168892355445512933444812965909472020409957119791476182178991646344151155563236535370283312345943041041662641584330401473731788344553589640556705580180081371688996848117690101021660395072221488243400947129794119144961728431002781350889740682623487619845390287149216977767858293453242551076767446272230208078076521"
36-
string(469) "5641066640108537808257411937508162073054596465771071759059984994432846497317882144255197676537588304873835452821393566559424565939427398239568910381599042586683472720047480341060077571873252225062218300704671408283921205864218742798766467986541832811143938893251282757214673131758780892167922492222473153470483402146144945253685265421614344082690235633775622262137908096304889066587289890823326962594240368957840634699139830536223598719285051876381571976198029149478069"
120+
string(2048) "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"
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bool(true)
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bool(true)
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bool(true)
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bool(true)
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bool(true)
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bool(true)
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string(389) "84916bf590f1bad61b6ede6cd6da703bca41cfb661c94b8cf66a1c92f0e2ebb24ad4683b908600ddf7145cac3b4808d6bbed18332d58d93c8ced3e0d3d19fd214a987f86116dd46c9709fd7d8a2b8ade79ba75e41df983b02082e89e3f729de3c6f42613a6b79b5e1967ab712e34cfb79e0d6f6168f7f758c2785da8ac1c36624fbb421a6502b2bbe9ad035c2577864aa12eee3173db7ffb915fce65a918041b95239d66d339de820a7d162cfccdfbd2222c91383ef0c4e903128cbd04dc0bf000000"

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