onuralver
Oct 7, 2017
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[[#list]]
<span style="background-color: #ffffff; color: #333333; display: block; font-family: 'Helvetica Neue',Helvetica,Arial,sans-serif; font-size: 14px;">
=<span style="color: inherit; font-family: inherit; font-size: 1.9em;">[[lbpe/CryptographyWithLB102|CryptographyWithLB103]]</span>=
<span style="display: block; vertical-align: middle;">
<span style="display: block; text-align: center; vertical-align: middle;"> Edit</span><span style="color: #333333; text-align: center; vertical-align: middle;">[[http://lbpe.wikispaces.com/page/history/CryptographyWithLB102| 6]]</span><span style="color: #333333; text-align: center; vertical-align: middle;">[[http://lbpe.wikispaces.com/page/menu/CryptographyWithLB102|…]]</span></span></span><span style="background-color: #ffffff; display: block; font-size: 14px;">
=[[#Cryptography with Liberty Basic]]Cryptography with Liberty Basic=
==[[#Cryptography with Liberty Basic-102: Classical Cryptography: DES]]103: Public Key Cryptography: RSA Algorithm==
==[[#Cryptography with Liberty Basic-By Onur Alver (CryptoMan)]]By Onur Alver (//CryptoMan//)==
----
==[[#Cryptography with Liberty Basic-INTRODUCTION]]INTRODUCTION==
=Table of Contents=
[[lbpe/CryptographyWithLB102#Cryptography%20with%20Liberty%20Basic|Cryptography with Liberty Basic]]
[[lbpe/CryptographyWithLB102#Cryptography%20with%20Liberty%20Basic-102:%20Classical%20Cryptography:%20DES|103: Public Key Cryptography: R]]SA Algorithm
We will continue in our series of articles about Cryptography with Public Key Cryptography.
----
[[#TranspositionCyper]]
==[[#Cryptography with Liberty Basic-TRANSPOSITION]]RSA ALGORITHM==
**RSA Algorithm is based on the assumption on the difficulty of factoring large composite numbers.**
|| <span style="font-size: 12px;">**Code:**</span>
<span style="font-size: 12px;"> </span><span style="font-family: Lucida Console,Monaco,monospace;">dim stats(11)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">dim SmallPrimes(1000)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 2, 3, 5, 7, 11, 13, 17, 19, 23, 29</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 31, 37, 41, 43, 47, 53, 59, 61, 67, 71</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 73, 79, 83, 89, 97, 101, 103, 107, 109, 113</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 127, 131, 137, 139, 149, 151, 157, 163, 167, 173</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 179, 181, 191, 193, 197, 199, 211, 223, 227, 229</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 233, 239, 241, 251, 257, 263, 269, 271, 277, 281</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 283, 293, 307, 311, 313, 317, 331, 337, 347, 349</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 353, 359, 367, 373, 379, 383, 389, 397, 401, 409</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 419, 421, 431, 433, 439, 443, 449, 457, 461, 463</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 467, 479, 487, 491, 499, 503, 509, 521, 523, 541</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 547, 557, 563, 569, 571, 577, 587, 593, 599, 601</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 607, 613, 617, 619, 631, 641, 643, 647, 653, 659</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 661, 673, 677, 683, 691, 701, 709, 719, 727, 733</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 739, 743, 751, 757, 761, 769, 773, 787, 797, 809</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 811, 821, 823, 827, 829, 839, 853, 857, 859, 863</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 877, 881, 883, 887, 907, 911, 919, 929, 937, 941</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829</span>
<span style="font-family: Lucida Console,Monaco,monospace;">data 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919</span>
<span style="font-family: Lucida Console,Monaco,monospace;">playwave "ding.wav", async</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print "Liberty Basic RSA Demonstration"</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print "Loading Small Primes"</span>
<span style="font-family: Lucida Console,Monaco,monospace;">for i=1 to 1000: read x : SmallPrimes(i)=x :next :NoOfSmallPrimes=1000</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print NoOfSmallPrimes;" Primes Loaded"</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print"Generating Random Primes"</span>
<span style="font-family: Lucida Console,Monaco,monospace;">'goto [Jump]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">for i=1 to 2</span>
<span style="font-family: Lucida Console,Monaco,monospace;">t1=time$("ms")</span>
<span style="font-family: Lucida Console,Monaco,monospace;">[TryAnother]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print "Prime No ";i</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if i=1 then x=Random(30) else x=Random(30)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">iterations=0</span>
<span style="font-family: Lucida Console,Monaco,monospace;">[Loop]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">iterations=iterations+1</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if MillerRabin(x,7)=1 then</span>
<span style="font-family: Lucida Console,Monaco,monospace;">'print "Composite"</span>
<span style="font-family: Lucida Console,Monaco,monospace;">x=x+2</span>
<span style="font-family: Lucida Console,Monaco,monospace;">goto [Loop]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">else</span>
<span style="font-family: Lucida Console,Monaco,monospace;">t2=time$("ms")</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print x;" Probably Prime. Generated in ";t2-t1;" milliseconds"</span>
<span style="font-family: Lucida Console,Monaco,monospace;">playwave "tada.wav", async</span>
<span style="font-family: Lucida Console,Monaco,monospace;">end if</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if p then q=x else p=x</span>
<span style="font-family: Lucida Console,Monaco,monospace;">next i</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print</span>
<span style="font-family: Lucida Console,Monaco,monospace;">playwave "tada.wav", async</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print "p=";dechex$(p)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">[Retry]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">restore</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print "q=";dechex$(q)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">'Common modulus N=(p)(q)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">n=p*q</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print "Key Length ";len(dechex$(n))*4;" bits "</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print</span>
<span style="font-family: Lucida Console,Monaco,monospace;">'Euler Totient Number M=(p-1)(q-1)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">m=(p-1)*(q-1)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">'Choose a suitable prime E relatively prime to M</span>
<span style="font-family: Lucida Console,Monaco,monospace;">for i=1 to 12</span>
<span style="font-family: Lucida Console,Monaco,monospace;">read e</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if (GCD(e,m)=1) then goto [Start]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">next i</span>
<span style="font-family: Lucida Console,Monaco,monospace;">[Start]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print "Common Modulus, n=";dechex$(n)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print "Euler-Totient No, m=";dechex$(m)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print "Public Exponent, e=";dechex$(e)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">d=ExtBinEuclid( e, m )</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print "Secret Exponent, d=";dechex$(d)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">DIM TEST(10)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">DIM ENCR(10)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">DIM DECR(10)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">TEST(1)=TEXT2DEC("LIBERTY BASIC IS THE BEST")</span>
<span style="font-family: Lucida Console,Monaco,monospace;">TEST(2)=TEXT2DEC("WHICH BASIC CAN DO THIS ")</span>
<span style="font-family: Lucida Console,Monaco,monospace;">TEST(3)=TEXT2DEC("WITHOUT CALLING EXT DLL ?")</span>
<span style="font-family: Lucida Console,Monaco,monospace;">TEST(4)=TEXT2DEC("LB CAN DO BIG INTEGERS ! ")</span>
<span style="font-family: Lucida Console,Monaco,monospace;">TEST(5)=TEXT2DEC("UNDOCUMENTED LB FEATURE. ")</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print "RSA ENCRYPTION DEMO"</span>
<span style="font-family: Lucida Console,Monaco,monospace;">for i=1 to 5</span>
<span style="font-family: Lucida Console,Monaco,monospace;">t1=time$("ms")</span>
<span style="font-family: Lucida Console,Monaco,monospace;">ENCR(i)=FastExp(TEST(i), e, n)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">t2=time$("ms")</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print TEST(i);</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print " ";ENCR(i);</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print " ";t2-t1;" ms"</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print DEC2TEXT$( TEST(i) );" --> ";DEC2TEXT$( ENCR(i) )</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print</span>
<span style="font-family: Lucida Console,Monaco,monospace;">next i</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print "________________________________________________________________________________________________________________"</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print "RSA DECRYPTION DEMO"</span>
<span style="font-family: Lucida Console,Monaco,monospace;">for i=1 to 5</span>
<span style="font-family: Lucida Console,Monaco,monospace;">t1=time$("ms")</span>
<span style="font-family: Lucida Console,Monaco,monospace;">DECR(i)=FastExp(ENCR(i), d, n)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">t2=time$("ms")</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print ENCR(i);</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print " ";DECR(i);</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print " ";t2-t1;" ms"</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print DEC2TEXT$( ENCR(i) );" --> ";DEC2TEXT$( DECR(i) )</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print</span>
<span style="font-family: Lucida Console,Monaco,monospace;">next i</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print " "</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print</span>
<span style="font-family: Lucida Console,Monaco,monospace;">print "RSA Demo Finished."</span>
<span style="font-family: Lucida Console,Monaco,monospace;">playwave "ding.wav", async</span>
<span style="font-family: Lucida Console,Monaco,monospace;">[stop]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">END</span>
<span style="font-family: Lucida Console,Monaco,monospace;">Function GCD( m,n )</span>
<span style="font-family: Lucida Console,Monaco,monospace;">' Find greatest common divisor with Extend Euclidian Algorithm</span>
<span style="font-family: Lucida Console,Monaco,monospace;">' Knuth Vol 1 P.13 Algorithm E</span>
<span style="font-family: Lucida Console,Monaco,monospace;">ap =1 :b =1 :a =0 :bp =0: c =m :d =n</span>
<span style="font-family: Lucida Console,Monaco,monospace;">[StepE2]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">q = int(c/d) :r = c-q*d</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if r<>0 then</span>
<span style="font-family: Lucida Console,Monaco,monospace;">c=d :d=r :t=ap :ap=a :a=t-q*a :t=bp :bp=b :b=t-q*b</span>
<span style="font-family: Lucida Console,Monaco,monospace;">'print ap;" ";b;" ";a;" ";bp;" ";c;" ";d;" ";t;" ";q</span>
<span style="font-family: Lucida Console,Monaco,monospace;">goto [StepE2]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">end if</span>
<span style="font-family: Lucida Console,Monaco,monospace;">GCD=a*m+b*n</span>
<span style="font-family: Lucida Console,Monaco,monospace;">'print ap;" ";b;" ";a;" ";bp;" ";c;" ";d;" ";t;" ";q</span>
<span style="font-family: Lucida Console,Monaco,monospace;">End Function 'Extended Euclidian GCD</span>
<span style="font-family: Lucida Console,Monaco,monospace;">Function ExtBinEuclid( u, v )</span>
<span style="font-family: Lucida Console,Monaco,monospace;">k=0 :t1=0 :t2=0 :t3=0</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if u<v then</span>
<span style="font-family: Lucida Console,Monaco,monospace;">temp=u</span>
<span style="font-family: Lucida Console,Monaco,monospace;">u=v</span>
<span style="font-family: Lucida Console,Monaco,monospace;">v=temp</span>
<span style="font-family: Lucida Console,Monaco,monospace;">end if</span>
<span style="font-family: Lucida Console,Monaco,monospace;">while (IsEven( u ) and IsEven( v ))</span>
<span style="font-family: Lucida Console,Monaco,monospace;">k = k+1</span>
<span style="font-family: Lucida Console,Monaco,monospace;">u = int(u/2)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">v = int(v/2)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">wend</span>
<span style="font-family: Lucida Console,Monaco,monospace;">u1 = 1: u2 = 0: u3 =u: t1 =v: t2 =u-1: t3 =v</span>
<span style="font-family: Lucida Console,Monaco,monospace;">[Loop1]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">[Loop2]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">' print "*"</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if (IsEven(u3)) then</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if IsOdd(u1) or IsOdd(u2) then</span>
<span style="font-family: Lucida Console,Monaco,monospace;">u1=u1+v</span>
<span style="font-family: Lucida Console,Monaco,monospace;">u2=u2+u</span>
<span style="font-family: Lucida Console,Monaco,monospace;">end if</span>
<span style="font-family: Lucida Console,Monaco,monospace;">u1=int(u1/2)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">u2=int(u2/2)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">u3=int(u3/2)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">end if</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if IsEven(t3) or (u3<t3) then</span>
<span style="font-family: Lucida Console,Monaco,monospace;">temp=u1: u1=t1: t1=temp</span>
<span style="font-family: Lucida Console,Monaco,monospace;">temp=u2: u2=t2: t2=temp</span>
<span style="font-family: Lucida Console,Monaco,monospace;">temp=u3: u3=t3: t3=temp</span>
<span style="font-family: Lucida Console,Monaco,monospace;">end if</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if IsEven(u3) then</span>
<span style="font-family: Lucida Console,Monaco,monospace;">goto [Loop2]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">end if</span>
<span style="font-family: Lucida Console,Monaco,monospace;">while u1<t1 OR u2<t2</span>
<span style="font-family: Lucida Console,Monaco,monospace;">u1=u1+v: u2=u2+u</span>
<span style="font-family: Lucida Console,Monaco,monospace;">wend</span>
<span style="font-family: Lucida Console,Monaco,monospace;">u1=u1-t1: u2=u2-t2: u3=u3-t3</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if (t3>0) then</span>
<span style="font-family: Lucida Console,Monaco,monospace;">goto [Loop1]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">end if</span>
<span style="font-family: Lucida Console,Monaco,monospace;">while u1>=v AND u2>=u</span>
<span style="font-family: Lucida Console,Monaco,monospace;">u1=ul-v: u2=u2-u</span>
<span style="font-family: Lucida Console,Monaco,monospace;">wend</span>
<span style="font-family: Lucida Console,Monaco,monospace;">ExtBinEuclid=u-u2</span>
<span style="font-family: Lucida Console,Monaco,monospace;">End Function</span>
<span style="font-family: Lucida Console,Monaco,monospace;">function IsEven( x )</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if ( x MOD 2 )=0 then</span>
<span style="font-family: Lucida Console,Monaco,monospace;">IsEven=1</span>
<span style="font-family: Lucida Console,Monaco,monospace;">else</span>
<span style="font-family: Lucida Console,Monaco,monospace;">IsEven=0</span>
<span style="font-family: Lucida Console,Monaco,monospace;">end if</span>
<span style="font-family: Lucida Console,Monaco,monospace;">end function</span>
<span style="font-family: Lucida Console,Monaco,monospace;">function IsOdd( x )</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if ( x MOD 2 )=0 then</span>
<span style="font-family: Lucida Console,Monaco,monospace;">IsOdd=0</span>
<span style="font-family: Lucida Console,Monaco,monospace;">else</span>
<span style="font-family: Lucida Console,Monaco,monospace;">IsOdd=1</span>
<span style="font-family: Lucida Console,Monaco,monospace;">end if</span>
<span style="font-family: Lucida Console,Monaco,monospace;">end function</span>
<span style="font-family: Lucida Console,Monaco,monospace;">Function FastExp(x, y, N)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if (y=1) then 'MOD(x,N)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">FastExp=x-int(x/N)*N</span>
<span style="font-family: Lucida Console,Monaco,monospace;">goto [ExitFunction]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">end if</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if ( y and 1) = 0 then</span>
<span style="font-family: Lucida Console,Monaco,monospace;">dum1=y/2</span>
<span style="font-family: Lucida Console,Monaco,monospace;">dum2=y-int(y/2)*2 'MOD(y,2)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">temp=FastExp(x,dum1,N)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">z=temp*temp</span>
<span style="font-family: Lucida Console,Monaco,monospace;">FastExp=z-int(z/N)*N 'MOD(temp*temp,N)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">goto [ExitFunction]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">else</span>
<span style="font-family: Lucida Console,Monaco,monospace;">dum1=y-1</span>
<span style="font-family: Lucida Console,Monaco,monospace;">dum1=dum1/2</span>
<span style="font-family: Lucida Console,Monaco,monospace;">temp=FastExp(x,dum1,N)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">dum2=temp*temp</span>
<span style="font-family: Lucida Console,Monaco,monospace;">temp=dum2-int(dum2/N)*N 'MOD(dum2,N)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">z=temp*x</span>
<span style="font-family: Lucida Console,Monaco,monospace;">FastExp=z-int(z/N)*N 'MOD(temp*x,N)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">goto [ExitFunction]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">end if</span>
<span style="font-family: Lucida Console,Monaco,monospace;">[ExitFunction]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">end function</span>
<span style="font-family: Lucida Console,Monaco,monospace;">Function PowMod( a, n, m)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">r = 1</span>
<span style="font-family: Lucida Console,Monaco,monospace;">while (n > 0)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if (n AND 1) then '/* test lowest bit */</span>
<span style="font-family: Lucida Console,Monaco,monospace;">r = MulMod(r, a, m) '/* multiply (mod m) */</span>
<span style="font-family: Lucida Console,Monaco,monospace;">end if</span>
<span style="font-family: Lucida Console,Monaco,monospace;">a = MulMod(a, a, m) '/* square */</span>
<span style="font-family: Lucida Console,Monaco,monospace;">n = int(n/2) '/* divided by 2 */</span>
<span style="font-family: Lucida Console,Monaco,monospace;">wend</span>
<span style="font-family: Lucida Console,Monaco,monospace;">PowMod=r</span>
<span style="font-family: Lucida Console,Monaco,monospace;">End Function</span>
<span style="font-family: Lucida Console,Monaco,monospace;">Function MulMod( a, b, m)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if (m = 0) then</span>
<span style="font-family: Lucida Console,Monaco,monospace;">MulMod=a * b ' /* (mod 0) */</span>
<span style="font-family: Lucida Console,Monaco,monospace;">Else</span>
<span style="font-family: Lucida Console,Monaco,monospace;">r = 0</span>
<span style="font-family: Lucida Console,Monaco,monospace;">while (a > 0)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if (a AND 1) then ' /* test lowest bit */</span>
<span style="font-family: Lucida Console,Monaco,monospace;">r= r+b</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if (r > m) then</span>
<span style="font-family: Lucida Console,Monaco,monospace;">r = (r MOD m) ' /* add (mod m) */</span>
<span style="font-family: Lucida Console,Monaco,monospace;">end if</span>
<span style="font-family: Lucida Console,Monaco,monospace;">end if</span>
<span style="font-family: Lucida Console,Monaco,monospace;">a = int(a/2) ' /* divided by 2 */</span>
<span style="font-family: Lucida Console,Monaco,monospace;">b = b*2</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if (b > m) then</span>
<span style="font-family: Lucida Console,Monaco,monospace;">b = (b MOD m) ' /* times 2 (mod m) */</span>
<span style="font-family: Lucida Console,Monaco,monospace;">end if</span>
<span style="font-family: Lucida Console,Monaco,monospace;">wend</span>
<span style="font-family: Lucida Console,Monaco,monospace;">MulMod=r</span>
<span style="font-family: Lucida Console,Monaco,monospace;">End If</span>
<span style="font-family: Lucida Console,Monaco,monospace;">End Function</span>
<span style="font-family: Lucida Console,Monaco,monospace;">Function rand( x )</span>
<span style="font-family: Lucida Console,Monaco,monospace;">x=x*5</span>
<span style="font-family: Lucida Console,Monaco,monospace;">x=x+1</span>
<span style="font-family: Lucida Console,Monaco,monospace;">rand=x</span>
<span style="font-family: Lucida Console,Monaco,monospace;">End Function</span>
<span style="font-family: Lucida Console,Monaco,monospace;">Function MillerRabin(n,b)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">'print "Miller Rabin"</span>
<span style="font-family: Lucida Console,Monaco,monospace;">'t1=time$("ms")</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if IsEven(n) then</span>
<span style="font-family: Lucida Console,Monaco,monospace;">MillerRabin=1</span>
<span style="font-family: Lucida Console,Monaco,monospace;">goto [ExtFn]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">end if</span>
<span style="font-family: Lucida Console,Monaco,monospace;">i=0</span>
<span style="font-family: Lucida Console,Monaco,monospace;">[Loop]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">i=i+1</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if i>1000 then goto [Continue]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if ( n MOD SmallPrimes(i) )=0 then</span>
<span style="font-family: Lucida Console,Monaco,monospace;">MillerRabin=1</span>
<span style="font-family: Lucida Console,Monaco,monospace;">goto [ExtFn]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">end if</span>
<span style="font-family: Lucida Console,Monaco,monospace;">goto [Loop]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">[Continue]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if GCD(n,b)>1 then</span>
<span style="font-family: Lucida Console,Monaco,monospace;">MillerRabin=1</span>
<span style="font-family: Lucida Console,Monaco,monospace;">goto [ExtFn]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">end if</span>
<span style="font-family: Lucida Console,Monaco,monospace;">q=n-1</span>
<span style="font-family: Lucida Console,Monaco,monospace;">t=0</span>
<span style="font-family: Lucida Console,Monaco,monospace;">while (int(q) AND 1 )=0</span>
<span style="font-family: Lucida Console,Monaco,monospace;">t=t+1</span>
<span style="font-family: Lucida Console,Monaco,monospace;">q=int(q/2)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">wend</span>
<span style="font-family: Lucida Console,Monaco,monospace;">r=FastExp(b, q, n)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if ( r <> 1 ) then</span>
<span style="font-family: Lucida Console,Monaco,monospace;">e=0</span>
<span style="font-family: Lucida Console,Monaco,monospace;">while ( e < (t-1) )</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if ( r <> (n-1) ) then</span>
<span style="font-family: Lucida Console,Monaco,monospace;">r=FastExp(r, r, n)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">else</span>
<span style="font-family: Lucida Console,Monaco,monospace;">Exit While</span>
<span style="font-family: Lucida Console,Monaco,monospace;">end if</span>
<span style="font-family: Lucida Console,Monaco,monospace;">e=e+1</span>
<span style="font-family: Lucida Console,Monaco,monospace;">wend</span>
<span style="font-family: Lucida Console,Monaco,monospace;">[ExitLoop]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">end if</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if ( (r=1) OR (r=(n-1)) ) then</span>
<span style="font-family: Lucida Console,Monaco,monospace;">MillerRabin=0</span>
<span style="font-family: Lucida Console,Monaco,monospace;">else</span>
<span style="font-family: Lucida Console,Monaco,monospace;">MillerRabin=1</span>
<span style="font-family: Lucida Console,Monaco,monospace;">end if</span>
<span style="font-family: Lucida Console,Monaco,monospace;">[ExtFn]</span>
<span style="font-family: Lucida Console,Monaco,monospace;">End Function</span>
<span style="font-family: Lucida Console,Monaco,monospace;">Function Random( Digits )</span>
<span style="font-family: Lucida Console,Monaco,monospace;">' x=INT(RND(1)*TIME$("ms")*9912812828239112219) * INT(RND(1)*9912166437771297131373) * INT(RND(1)*71777126181142123) * INT(RND(1)*7119119672435637981) * INT(RND(1)*991216643912127789) * INT(RND(1)*79126181142123) * INT(RND(1)*711911128376332417) * INT(RND(1)*991216643123129) * INT(RND(1)*79126181142123) * INT(RND(1)*6661912727312317)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">' Random=INT(VAL(RIGHT$(STR$(x,1)))</span>
<span style="font-family: Lucida Console,Monaco,monospace;">x=INT(RND(1)*TIME$("ms")*9912812828239112219) * INT(RND(1)*9912166437771297131373) * INT(RND(1)*71777126181142123) * INT(RND(1)*7119119672435637981) * INT(RND(1)*991216643912127789) * INT(RND(1)*79126181142123) * INT(RND(1)*711911128376332417)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">x=x*x+x+41</span>
<span style="font-family: Lucida Console,Monaco,monospace;">y$=mid$(str$(x),INT(rnd(1)*30+1),Digits )</span>
<span style="font-family: Lucida Console,Monaco,monospace;">ldg=val(right$(y$,1))</span>
<span style="font-family: Lucida Console,Monaco,monospace;">z=0</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if ldg=0 then z=1</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if ldg=2 then z=1</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if ldg=4 then z=1</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if ldg=6 then z=1</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if ldg=8 then z=1</span>
<span style="font-family: Lucida Console,Monaco,monospace;">Random=val(y$)+z</span>
<span style="font-family: Lucida Console,Monaco,monospace;">End Function</span>
<span style="font-family: Lucida Console,Monaco,monospace;">FUNCTION TEXT2DEC( x$ )</span>
<span style="font-family: Lucida Console,Monaco,monospace;">a$=UPPER$(x$)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">y$=""</span>
<span style="font-family: Lucida Console,Monaco,monospace;">FOR i=1 TO LEN(a$)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">y$=y$+STR$(ASC(MID$(a$,i,1)))</span>
<span style="font-family: Lucida Console,Monaco,monospace;">NEXT</span>
<span style="font-family: Lucida Console,Monaco,monospace;">TEXT2DEC=VAL(y$)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">END FUNCTION</span>
<span style="font-family: Lucida Console,Monaco,monospace;">FUNCTION DEC2TEXT$( n )</span>
<span style="font-family: Lucida Console,Monaco,monospace;">a$=STR$(n)</span>
<span style="font-family: Lucida Console,Monaco,monospace;">y$=""</span>
<span style="font-family: Lucida Console,Monaco,monospace;">FOR i=1 TO LEN(a$)-1 STEP 2</span>
<span style="font-family: Lucida Console,Monaco,monospace;">m=VAL(MID$(a$,i,2))</span>
<span style="font-family: Lucida Console,Monaco,monospace;">if m>30 and m<99 then y$=y$+CHR$(m) else y$=y$+"."</span>
<span style="font-family: Lucida Console,Monaco,monospace;">NEXT</span>
<span style="font-family: Lucida Console,Monaco,monospace;">DEC2TEXT$=y$</span>
<span style="font-family: Lucida Console,Monaco,monospace;">END FUNCTION</span>
<span style="font-size: 12px;"> </span> ||
[[code]]
[[code]]
</span>