ext/gmp: add test with examples of the usage of gmp for cryptography

Author: famoser

ext/gmp/tests/gmp_cryptography_ffc.phpt

@@ -0,0 +1,108 @@
+--TEST--
+Examples of the usage of gmp for finite field cryptography.
+--DESCRIPTION--
+This executes basic operations (addition, multiplication, inverse, exponentiation) as the "base operations".
+Then, it performs a primality check, and finally diffie-hellman as the "application".
+All operations are done in the 4096-bit MODP Group from RFC 3526: https://www.ietf.org/rfc/rfc3526.txt
+
+Omitted are calculations on elliptic curves, which are also common, because of the complexity of these algorithms.
+Elliptic curves generally operate on smaller values, so their use-case is somewhat covered here,
+but curve calculations may need additional operations not used here.
+
+Further, omitted is explicit demonstration of (public-key) encryption, commitments, zero-knowledge proofs or similar common applications.
+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.
+
+$a, $b, and $c generated with
+$random = gmp_random_range(0, $prime);
+$randomHex = strtoupper(gmp_strval($random, 16));
+echo chunk_split(chunk_split($randomHex, 8, " "), 54);
+--EXTENSIONS--
+gmp
+--FILE--
+<?php
+
+$prime = gmp_init('
+FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1
+29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD
+EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245
+E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
+EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D
+C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F
+83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
+670C354E 4ABC9804 F1746C08 CA237327 FFFFFFFF FFFFFFFF', 16);
+
+$a = gmp_init('
+BE774B3A 56642360 4B32CCF8 B721F519 E1FAD10F C8AB6109
+D7B98E79 8A541A9B 5A747CC3 2927A1F9 AA8BFA3E 3F31858D
+03DA94D5 B076FE11 35CBB577 70E8FF40 8B0F7E01 354C3436
+1827ADF1 794E3C96 2BDBC8B9 6B894EF0 7CF67367 5F2B0B4F
+0F6304FE A9F48EB9 D8D08C16 C00716F6 956AEEA5 9B7BB16A
+7B29C225 1AF3988D 0F2381B2 6DDD130A 605BACD0 DE0104F9
+71B1F8C9 43217768 D556A6BA AB2C5DED 69DC3CA3 79D6BBEA
+8E9A8522 CCD6DD95 FA295909 C593D444 08A8832A A5429BFA', 16);
+
+$b = gmp_init('
+CA1CAE83 DBC72ACC 0BDA48CA 5AFF77D1 055F1CEA 0B4E3089
+E2BC1661 F4878AF1 F28DE016 350F4182 ECF2DC26 691AAE10
+BA6CB81B 375A1460 068CCB45 B948855B 3CE7FB9C 2754D50F
+CE4B45F9 FF101B47 2F76A39B 707D1D0F F2EAA747 0E6AEB4B
+37D582B3 2E724769 BB4D8088 FD2DB183 B67BB11F 3A61DF60
+7C3029C9 33475CE6 9E3872EA 764AD8B4 CA42FDA0 04931B8C
+046B2283 E06E291F 5CFE9369 7CC5A21B 13156554 59B11B21
+CE206802 5738B90D EC4DB008 AA5B2BB3 1DCFE633 E05B91D9', 16);
+
+$c = gmp_init('
+8CA047D8 C5270CEF D43F181D 94901BF7 354BC803 AEFD1A1B
+210B1500 C520C021 19CA1AE7 1422AD02 B326BBF3 19545111
+FF5C284F 2A1083C5 31E9363E A98256F8 6F6B274C F44665F0
+02FA45DD B3A1BF03 3A9BB662 EA5573AA 86BCD6A1 18E62597
+A4B760A6 A393B406 265E4884 279B8C4E 209B3338 5A1A7D53
+9D0F619A 18F967EF A0758D32 9E117136 F9ADDAE1 8AAF4718
+837B4772 386C3B7D 988F8343 78F59991 81812F2D 93310E7E
+9ED63DB7 5999C790 69D29570 08B7C39C 259BFFD2 74DC5E81', 16);
+
+// check commutativity addition (a+b)+c = a+(b,c)
+$d = gmp_mod(gmp_add($a, $b), $prime);
+$left = gmp_mod(gmp_add($d, $c), $prime);
+$d = gmp_mod(gmp_add($b, $c), $prime);
+$right = gmp_mod(gmp_add($a, $d), $prime);
+var_dump(gmp_cmp($left, $right) === 0);
+
+// check distribution multiplication a(b+c) = ab + ac
+$d = gmp_mod(gmp_add($b, $c), $prime);
+$left = gmp_mod(gmp_mul($a, $d), $prime);
+$d1 = gmp_mod(gmp_mul($a, $b), $prime);
+$d2 = gmp_mod(gmp_mul($a, $c), $prime);
+$right = gmp_mod(gmp_add($d1, $d2), $prime);
+var_dump(gmp_cmp($left, $right) === 0);
+
+// check inversion a * a^(-1) = 1
+$inverse = gmp_invert($a, $prime);
+$product = gmp_mod(gmp_mul($a, $inverse), $prime);
+var_dump(gmp_cmp($product, 1) === 0);
+
+// check exponentiation by group order a ^ (p-1) = 1
+$groupOrder = gmp_sub($prime, 1);
+$product = gmp_powm($a, $groupOrder, $prime);
+var_dump(gmp_cmp($product, 1) === 0);
+
+// check whether q is a safe prime (that is, p=(q-1)/2 is also prime)
+$primeP = gmp_div($prime - 1, 2);
+var_dump(gmp_prob_prime($primeP) > 0);
+
+// diffie-hellman key exchange (g^a)^b = (g^b)^a
+$generator = gmp_init(2);
+$factorA = gmp_random_range(1, $primeP);
+$factorB = gmp_random_range(1, $primeP);
+$left = gmp_powm(gmp_powm($generator, $factorA, $primeP), $factorB, $primeP);
+$right = gmp_powm(gmp_powm($generator, $factorB, $primeP), $factorA, $primeP);
+var_dump(gmp_cmp($left, $right) === 0);
+
+?>
+--EXPECT--
+bool(true)
+bool(true)
+bool(true)
+bool(true)
+bool(true)
+bool(true)