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ext/gmp: add test for uses of gmp_pow with number sizes commonly used in cryptography (#16896)
With common number sizes used there --------- Co-authored-by: Florian Moser <git@famoser.ch>
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‎ext/gmp/tests/gmp_cryptography.phpt

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--TEST--
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test some of the simple operations done in ECC cryptography (GH-16870)
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--EXTENSIONS--
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gmp
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--FILE--
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<?php
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$big_128 = gmp_init("275458973678998164972199298356823445708", 10);
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$big_256 = gmp_init("105897378200704506708747774951422238999742054168150946506894304230846229930690", 10);
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$big_384 = gmp_init("6416793922163250205142333121845147158821454739198730072980369042145699078647151545580979451456624745026383368515606", 10);
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$big_521 = gmp_init("1780138296718969229154737597263093326930734138014367844231086609903991655888322554437298817404082596582997382075361284417827317144352840347188199593652743789", 10);
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// in ecc crypto key lengths of 256, 384 and 521 (yes, 521, not 512) are typical,
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// and the calculations seem to include squaring and cubing the key,
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// so test those operations
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var_dump((string) gmp_pow($big_128, 2));
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var_dump((string) gmp_pow($big_128, 3));
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var_dump((string) gmp_pow($big_256, 2));
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var_dump((string) gmp_pow($big_256, 3));
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var_dump((string) gmp_pow($big_384, 2));
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var_dump((string) gmp_pow($big_384, 3));
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var_dump((string) gmp_pow($big_521, 2));
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var_dump((string) gmp_pow($big_521, 3));
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?>
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--EXPECT--
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string(77) "75877646180287003845291692588996321992008024509271171205840397374930023621264"
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string(116) "20901178542000013443295783507452967008255111311111391381095411786512605029527130998551663048238767676593252458334912"
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string(155) "11214254709783046066761897074581165564696209875788503860615296581570239055173596662994580613114615553617959320367624022951770022252133452732995602203876100"
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string(232) "1187560172240926986956555551805946700914014146395850601682624192167183140821546786142042010581624015945796617035803644080855311724420346850512769661608026325318823192181186500090109111010574371273491473985103578154963883352347509000"
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string(230) "41175244239511227932271803271789465275501438128816738161335879819867157609061333189838579416997011220296835767015204168726569753974321567200401024149587401209307771709029048946370759582286096704404540466667318675170269947865547236"
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string(345) "264213056979683026715444213001489498112251992104549535125497320782388835160296854596249682279610208850530256165562505337646325742090947380083481042994421218556776724906795900034870043631716997303728488772811762108912277655229349137086580494553471889656657230883768271890897138746582039089128053875620299138149315547875444447674573987934196165016"
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string(313) "3168892355445512933444812965909472020409957119791476182178991646344151155563236535370283312345943041041662641584330401473731788344553589640556705580180081371688996848117690101021660395072221488243400947129794119144961728431002781350889740682623487619845390287149216977767858293453242551076767446272230208078076521"
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string(469) "5641066640108537808257411937508162073054596465771071759059984994432846497317882144255197676537588304873835452821393566559424565939427398239568910381599042586683472720047480341060077571873252225062218300704671408283921205864218742798766467986541832811143938893251282757214673131758780892167922492222473153470483402146144945253685265421614344082690235633775622262137908096304889066587289890823326962594240368957840634699139830536223598719285051876381571976198029149478069"

‎ext/gmp/tests/gmp_cryptography_ffc.phpt

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--TEST--
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Examples of the usage of gmp for finite field cryptography.
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--DESCRIPTION--
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This executes basic operations (addition, multiplication, inverse, exponentiation) as the "base operations".
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Then, it performs a primality check, and finally diffie-hellman as the "application".
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All operations are done in the 4096-bit MODP Group from RFC 3526: https://www.ietf.org/rfc/rfc3526.txt
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Omitted are calculations on elliptic curves, which are also common, because of the complexity of these algorithms.
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Elliptic curves generally operate on smaller values, so their use-case is somewhat covered here,
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but curve calculations may need additional operations not used here.
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Further, omitted is explicit demonstration of (public-key) encryption, commitments, zero-knowledge proofs or similar common applications.
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However, the operation used in the diffie-hellman is at the core of all these other applications, hence these use-cases are implicitly covered, too.
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$a, $b, and $c generated with
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$random = gmp_random_range(0, $prime);
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$randomHex = strtoupper(gmp_strval($random, 16));
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echo chunk_split(chunk_split($randomHex, 8, " "), 54);
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--EXTENSIONS--
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gmp
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--FILE--
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<?php
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$prime = gmp_init('
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FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1
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29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD
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EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245
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E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
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EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D
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C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F
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83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
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670C354E 4ABC9804 F1746C08 CA237327 FFFFFFFF FFFFFFFF', 16);
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$a = gmp_init('
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BE774B3A 56642360 4B32CCF8 B721F519 E1FAD10F C8AB6109
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D7B98E79 8A541A9B 5A747CC3 2927A1F9 AA8BFA3E 3F31858D
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03DA94D5 B076FE11 35CBB577 70E8FF40 8B0F7E01 354C3436
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1827ADF1 794E3C96 2BDBC8B9 6B894EF0 7CF67367 5F2B0B4F
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0F6304FE A9F48EB9 D8D08C16 C00716F6 956AEEA5 9B7BB16A
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7B29C225 1AF3988D 0F2381B2 6DDD130A 605BACD0 DE0104F9
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71B1F8C9 43217768 D556A6BA AB2C5DED 69DC3CA3 79D6BBEA
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8E9A8522 CCD6DD95 FA295909 C593D444 08A8832A A5429BFA', 16);
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$b = gmp_init('
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CA1CAE83 DBC72ACC 0BDA48CA 5AFF77D1 055F1CEA 0B4E3089
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E2BC1661 F4878AF1 F28DE016 350F4182 ECF2DC26 691AAE10
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BA6CB81B 375A1460 068CCB45 B948855B 3CE7FB9C 2754D50F
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CE4B45F9 FF101B47 2F76A39B 707D1D0F F2EAA747 0E6AEB4B
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37D582B3 2E724769 BB4D8088 FD2DB183 B67BB11F 3A61DF60
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7C3029C9 33475CE6 9E3872EA 764AD8B4 CA42FDA0 04931B8C
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046B2283 E06E291F 5CFE9369 7CC5A21B 13156554 59B11B21
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CE206802 5738B90D EC4DB008 AA5B2BB3 1DCFE633 E05B91D9', 16);
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$c = gmp_init('
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8CA047D8 C5270CEF D43F181D 94901BF7 354BC803 AEFD1A1B
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210B1500 C520C021 19CA1AE7 1422AD02 B326BBF3 19545111
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FF5C284F 2A1083C5 31E9363E A98256F8 6F6B274C F44665F0
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02FA45DD B3A1BF03 3A9BB662 EA5573AA 86BCD6A1 18E62597
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A4B760A6 A393B406 265E4884 279B8C4E 209B3338 5A1A7D53
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9D0F619A 18F967EF A0758D32 9E117136 F9ADDAE1 8AAF4718
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837B4772 386C3B7D 988F8343 78F59991 81812F2D 93310E7E
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9ED63DB7 5999C790 69D29570 08B7C39C 259BFFD2 74DC5E81', 16);
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// check commutativity addition (a+b)+c = a+(b,c)
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$d = gmp_mod(gmp_add($a, $b), $prime);
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$left = gmp_mod(gmp_add($d, $c), $prime);
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$d = gmp_mod(gmp_add($b, $c), $prime);
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$right = gmp_mod(gmp_add($a, $d), $prime);
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var_dump(gmp_cmp($left, $right) === 0);
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// check distribution multiplication a(b+c) = ab + ac
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$d = gmp_mod(gmp_add($b, $c), $prime);
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$left = gmp_mod(gmp_mul($a, $d), $prime);
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$d1 = gmp_mod(gmp_mul($a, $b), $prime);
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$d2 = gmp_mod(gmp_mul($a, $c), $prime);
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$right = gmp_mod(gmp_add($d1, $d2), $prime);
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var_dump(gmp_cmp($left, $right) === 0);
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// check inversion a * a^(-1) = 1
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$inverse = gmp_invert($a, $prime);
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$product = gmp_mod(gmp_mul($a, $inverse), $prime);
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var_dump(gmp_cmp($product, 1) === 0);
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// check exponentiation by group order a ^ (p-1) = 1
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$groupOrder = gmp_sub($prime, 1);
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$product = gmp_powm($a, $groupOrder, $prime);
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var_dump(gmp_cmp($product, 1) === 0);
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// check whether q is a safe prime (that is, p=(q-1)/2 is also prime)
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$primeP = gmp_div($prime - 1, 2);
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var_dump(gmp_prob_prime($primeP) > 0);
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// diffie-hellman key exchange (g^a)^b = (g^b)^a
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$generator = gmp_init(2);
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$factorA = gmp_random_range(1, $primeP);
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$factorB = gmp_random_range(1, $primeP);
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$left = gmp_powm(gmp_powm($generator, $factorA, $primeP), $factorB, $primeP);
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$right = gmp_powm(gmp_powm($generator, $factorB, $primeP), $factorA, $primeP);
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var_dump(gmp_cmp($left, $right) === 0);
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?>
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--EXPECT--
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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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