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pbctf 2020: Jiang Ying's Disasssembler author's writeup
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// TLDR: | |
// Whitebox 128-bit rsa with e=17. Input is multiplied by a constant before the RSA | |
#include <Windows.h> | |
#include <stdio.h> | |
#include <stdint.h> | |
extern "C" void __fastcall rsa_encrypt (uint8_t* in, uint8_t* out); | |
// 1. Func is ~90kb, and control flow is simple. Should be decompilable just extremely SLOW. | |
// It also seems like it only uses a handful of instructions, a lot of imul add etc. Very uniform | |
// So it's probably some big and autogenerated shit, we should try to see if we can see some repeated patterns | |
// Then we can try to figure out what each repeated block does. | |
// But assembly code is too low level to get an idea of what's going on. | |
// We want something that will at least give us value numbering; either custom lifter or some decompiler | |
// | |
// Try a bunch of random decompilers, hexrays, snowman, binja, retdec | |
// Retdec gives output with incorrect parameters but at least the code is extremely uniform | |
// See: fuck5.c | |
// Idiot strategy: look for statements that stand out, this could indicate some kind of boundaries within this huge block of code | |
// Observation: most lines are quite short but there are a handful of very LONG lines. | |
// So look for really LONG lines, and break up the code at these spots | |
// | |
// Result: Breaking up the code by the longest length lines, we found that there's only a few chunks. Like 5 or 6 or so | |
// See: one.c, two.c | |
// 5 of the chunks have the EXACT SAME CODE, other than variable names!! | |
// If we can understand one of the chunks, should be a good step to solve the challenge | |
// | |
// There is also 1 chunk at the top that isn't the same as the other repeated chunks. | |
// | |
// Other observations: | |
// 128-bit input and output. | |
// A lot of 0x10000 and 0xffff, so maybe this is kind of bignum implementation based on int16 (??) | |
// | |
// Huge repeated chunks that are identical except for variables. | |
// Might be due to aggressive inlining. | |
// We say each huge repeated chunk is a "round". From counting, there's 5 rounds? | |
// | |
// The only interesting constants are found in imul instructions as immediates. | |
// If we extract all of the imul constants, there are actually only 32 unique ones. | |
// The first 8 are used at the start only, but not in the 5 rounds. | |
// The other 24 are used in each of the 5 rounds. | |
// | |
// // Constants that don't seem repeated | |
// 1A3D | |
// 061C | |
// D64E | |
// EB7F | |
// 5C62 | |
// 2797 | |
// 7287 | |
// 4724 | |
// // Constants that are repeated in rounds | |
// 946C | |
// B05B | |
// 052C | |
// F508 | |
// 45C1 | |
// B5D3 | |
// 7988 | |
// A4BA | |
// A71B | |
// 268F | |
// 5EFB | |
// 7430 | |
// 0FF7 | |
// 2D29 | |
// 557C | |
// 8FB2 | |
// 43F7 | |
// 84E1 | |
// 1EFF | |
// F8AF | |
// 047A | |
// AA2B | |
// 3681 | |
// E409 | |
int main() { | |
// Ok fuck it let's try black boxing this shit | |
HMODULE fuck = LoadLibraryA("licenseChecker.dll"); | |
void (*rsa_encrypt)(uint8_t*, uint8_t*) = (void(*)(uint8_t*, uint8_t*))((char*)fuck+0x1010); | |
printf("%p\n", fuck); | |
printf("%p\n", rsa_encrypt); | |
uint8_t in[16]; | |
uint8_t out[16]; | |
memset(in,0,16); | |
memset(out,0,16); | |
for ( uint32_t i = 0; i < 100; i++) { | |
*(uint32_t*)in = i; | |
rsa_encrypt(in,out); | |
printf("0x%016llx%016llx\n", *(uint64_t*)(out+8), *(uint64_t*)out); | |
} | |
// Observations: f(0) = 0 | |
// 128-bit little endian | |
// f(1,2,3,4...) = junk | |
// When we plot the outputs (outputs.py), we notice that: | |
// -> output isn't full range from 0000..ffff. There seems to be a maximum(!) | |
// Try to approximate output upper bound (modulus?) | |
uint64_t max = 0; | |
for ( uint32_t i = 0; i < 1000000000; i++) { | |
*(uint32_t*)in = i; | |
rsa_encrypt(in,out); | |
// printf("0x%016llx%016llx\n", *(uint64_t*)(out+8), *(uint64_t*)out); | |
uint64_t hi = *(uint64_t*)(out+8); | |
if (hi > max) { | |
printf("0x%016llx\n", hi); | |
max=hi; | |
} | |
} | |
// max = 0xe4093660f9061aac => e409 3681 | |
printf("\n\n0x%016llx0000000000000000\n", max); | |
// These constants are repeated in rounds! And there are roughly 5 rounds | |
// If we don't know, we can also brute force the combinations and see if any of the resulting 128-bit numbers are interesting. | |
// Anyways, seems like the constants form 128-bit integers. | |
// And coincidentally the compiler uses them in MSB to LSB order in the code. | |
// 43F7 7 | |
// 84E1 6 | |
// 1EFF 5 | |
// F8AF 4 | |
// 047A 3 | |
// AA2B 2 | |
// 3681 1 | |
// E409 0 | |
// N = 0xe4093681aa2b047af8af1eff84e143f7 ? | |
// N is small, so we can factor it. | |
// p = 17260683863472602563 | |
// q = 17560823292485810621 | |
// p and q are prime! => This must be based on RSA! | |
// Makes sense because RSA is commonly used for signing software licenses. | |
// But what's e?? | |
// 5 rounds, so e could be 17. But using e=17 doesn't give the same output. | |
// So what's e? | |
// OK don't know what the fuck is going on in this whitebox shit | |
// So lets whip out the dIfFeReNTiAL fAuLT aNaLySis. | |
// We have 32 16-bit constants, grouped into 4 128-bit constants. | |
// Let's call them O1-O4. We discovered earlier that O4 is our modulus. | |
/* | |
// This are only used at the start. | |
// Call this constant "O1". | |
'1A3Dh':, | |
'61Ch', | |
'0D64Eh', | |
'0EB7Fh', | |
'5C62h', | |
'2797h', | |
'7287h', | |
'4724h', | |
// These are used in each round but we don't what they are | |
// Call this constant "O2" | |
'946Ch', | |
'0B05Bh', | |
'52Ch', | |
'0F508h', | |
'45C1h', | |
'0B5D3h', | |
'7988h', | |
'0A4BAh', | |
// Call this constant "O3" | |
'0A71Bh', | |
'268Fh', | |
'5EFBh', | |
'7430h', | |
'0FF7h', | |
'2D29h', | |
'557Ch', | |
'8FB2h', | |
// Call this constant "O4" | |
// This is the modulus N | |
'43F7h', | |
'84E1h', | |
'1EFFh', | |
'0F8AFh', | |
'47Ah', | |
'0AA2Bh', | |
'3681h', | |
'0E409h' | |
*/ | |
// Lets try fucking up the constants and see what happens to the functions behavior | |
//python3 dickit.py && nasm -f win64 lol.asm -o lol.obj && cl /MDd cheese.cpp lol.obj && cheese | |
for ( uint32_t i = 0; i < 1000; i++) { | |
*(uint32_t*)in = i; | |
rsa_encrypt(in,out); | |
printf("0x%016llx%016llx\n", *(uint64_t*)(out+8), *(uint64_t*)out); | |
} | |
// Observations: | |
// O1=0 gives all 0s (mask / multiplier?) | |
// O2=0, output can be greater than modulus (!) | |
// O3=0 gives junk | |
// O4=0 gives junk, obviously (since O4 is our modulus) | |
// If O1=0, other stuff doesn't matter, it always gives 0s | |
// -> So O1 must be used first before any of the RSA | |
// -> O2,O3 is probably part of exponentiation in RSA (??) | |
// Our hypothesized cipher: | |
// g(x) = something we don't know that uses O1 | |
// f(x) = something related to RSA that uses O2,O3,O4 | |
// Overall func = f(g(x)) | |
// Since g(x) seems to take priority, let's first focus on attacking g(x) | |
// Set O1=1 and don't touch rest. This is our new weakened function: | |
/* | |
1 0x00000000000000000000000000000000 | |
2 0x00000000000000000000000000000001 | |
3 0x00000000000000000000000000020000 | |
4 0x00000000000000000000000007b285c3 | |
5 0x00000000000000000000000400000000 | |
6 0x0000000000000000000000b1a2bc2ec5 | |
7 0x000000000000000000000f650b860000 | |
8 0x00000000000000000000d39383266e87 | |
9 0x00000000000000000008000000000000 | |
10 0x0000000000000000003b3fcef3103289 | |
11 0x0000000000000000016345785d8a0000 | |
12 0x00000000000000000703b564fa7a264b | |
13 0x00000000000000001eca170c00000000 | |
14 0x0000000000000000780c7372621bd74d | |
15 0x0000000000000001a727064cdd0e0000 | |
16 0x000000000000000557531cfaa19df90f | |
17 0x00000000000000100000000000000000 | |
18 0x000000000000002cd843cb4764370911 | |
19 0x00000000000000767f9de62065120000 | |
20 0x000000000000012917a55ad23e5a92d3 | |
... | |
*/ | |
// Wow! This is (x^17 % N)! | |
// So we know that f(x) must just be the RSA encryption | |
// So we know for sure e = 17. | |
// But what is g(x) ?? | |
// Seems like when O1=0, g(x) = 0. O1=1, then g(x) = 1. | |
// Maybe some linear function? | |
// e=17 and we know p,q so we can compute d=0x283ddc713c25b57ec78c48b7a8a227d9 | |
// In that case we can make f^-1(x) as just RSA decryption. | |
// We can take a bunch of output from f(g(x)), and apply f^-1 to get g(x) | |
// Then we can take a stab at what g(x) is doing. | |
/* | |
1 0x00000000000000000000000000000000 | |
2 0x7287472427975c62eb7fd64e061c1a3d | |
3 0x010557c6a503b44ade508d9c8756f083 | |
4 0x5795d56c76c61528c27f82ea12544eb7 | |
5 0xca1d1c909e5d718badff5938187068f4 | |
6 0x3ca463b4c5f4cdee997f2f861e8c8331 | |
7 0xaf2baad8ed8c2a5184ff05d424a89d6e | |
8 0x21b2f1fd152386b4707edc222ac4b7ab | |
9 0x943a39213cbae3175bfeb27030e0d1e8 | |
10 0x06c1804564523f7a477e88be36fcec25 | |
11 0x7948c7698be99bdd32fe5f0c3d190662 | |
12 0x07c6d80c0955f3c525cf165abe53dca8 | |
13 0x5e5755b1db1854a309fe0ba849513adc | |
14 0xd0de9cd602afb105f57de1f64f6d5519 | |
15 0x4365e3fa2a470d68e0fdb84455896f56 | |
16 0xb5ed2b1e51de69cbcc7d8e925ba58993 | |
17 0x287472427975c62eb7fd64e061c1a3d0 | |
18 0x9afbb966a10d2291a37d3b2e67ddbe0d | |
19 0x0d83008ac8a47ef48efd117c6df9d84a | |
20 0x800a47aef03bdb577a7ce7ca7415f287 | |
*/ | |
// ^ this output will obviously be mod(N) because it's the result from RSA decryption | |
// So indeed g(x) seems to be doing 0x7287472427975c62eb7fd64e061c1a3d * x | |
// So overall our function is pow(x*0x7287472427975c62eb7fd64e061c1a3d,e,N) | |
// We can invert this to sign our own licenses! | |
// Modular inverse of 0x7287472427975c62eb7fd64e061c1a3d is 123456789 ... lol | |
// So to sign license: | |
// x = sha256(license[16:]) | |
// x *= 123456789 | |
// d = 0x283ddc713c25b57ec78c48b7a8a227d9 | |
// N = 0xe4093681aa2b047af8af1eff84e143f7 | |
// x = pow(x,d,N) | |
return 0; | |
} |
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lines = open('lol_orig.asm','r').readlines() | |
consts = { | |
# O1 | |
# '1A3Dh':'1h', | |
# '61Ch':'0h', | |
# '0D64Eh':'0h', | |
# '0EB7Fh':'0h', | |
# '5C62h':'0h', | |
# '2797h':'0h', | |
# '7287h':'0h', | |
# '4724h':'0h', | |
# O2 | |
# '946Ch':'0h', | |
# '0B05Bh':'0h', | |
# '52Ch':'0h', | |
# '0F508h':'0h', | |
# '45C1h':'0h', | |
# '0B5D3h':'0h', | |
# '7988h':'0h', | |
# '0A4BAh':'0h', | |
# O3 | |
# '0A71Bh':'0h', | |
# '268Fh':'0h', | |
# '5EFBh':'0h', | |
# '7430h':'0h', | |
# '0FF7h':'0h', | |
# '2D29h':'0h', | |
# '557Ch':'0h', | |
# '8FB2h':'0h', | |
# dont mess up modulus | |
# O4=N | |
# '43F7h':'0h', | |
# '84E1h':'0h', | |
# '1EFFh':'0h', | |
# '0F8AFh':'0h', | |
# '47Ah':'0h', | |
# '0AA2Bh':'0h', | |
# '3681h':'0h', | |
# '0E409h':'0h' | |
} | |
result = [] | |
for l in lines: | |
for c,replace in consts.items(): | |
l = l.replace(c, replace) | |
result.append(l) | |
open('lol.asm','w').write(''.join(result)) |
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ys = [ | |
0x00000000000000000000000000000000, | |
0x00cc5b325b06d6f3c93e9c36ee9546ab, | |
0xbde932133cf18e7c4f206806d252681a, | |
0x89acaf80eea2e9513d7f10af9a9bdfbe, | |
0x8dee2e886c276366e0258dd762ab0ab2, | |
0xb2b4f816772a1f6af0d9435ca3a1dbfd, | |
0x6b2c2e2f9f5a8ae4951e46e1caee2a05, | |
0x8ad233346d98cba40ff202e72df53eae, | |
0xcc97c682cc56b3ca25ab1e8476c06631, | |
0x988b3b37afe97a8910abc10dce87db17, | |
0x47909f5fa6662c5ffcc1863cadf5a32e, | |
0x5f172ad8ecbc83b7a28ac3ff1484f984, | |
0x9937592ab41d0535e497c4de1786f01a, | |
0x021b86d2332e4b43d20ebd0844464e80, | |
0x6edbdc525743a73c4ec0a1d178ec3530, | |
0x8f567789c5562c1991cc2b0ba48778fd, | |
0xc01078eb052fae49a3487020ec8768b4, | |
0x15c5bd3f52d4f536589466b3c30e42fe, | |
0x2302e5a867939ba13722c1c854c00a80, | |
0x274892f7f70317714306d780485d9b20, | |
0x7e6b364fccb61280921297322ac56e1e, | |
0xcf41be0729449e2948fee402344e87e6, | |
0xb565f70aeb629122ab790add25543d5d, | |
0x86b506e113e7eab4adf2318b8dd4c2ec, | |
0x8904be8ce810820e46b69680231d9012, | |
0x37fea4140184ef0817244392f8509783, | |
0x157ac9b80cebafe3d462a86b59cf8ccc, | |
0xdc317a566604d3c5fe54f1eff85ce29e, | |
0x237dac2b6b256d263ee7518dc4632028, | |
0xd68b29d60577395d45a280b07efde928, | |
0x71aecbdf0870861a5d4d807bff9f403a, | |
0xcffc24b38fed9e566b6de503806fbbf5, | |
0xe0f22cfeb81e358abab58373f0107d13, | |
0xd1da47c20e3a7c0b42e6b862bc62dca9, | |
0x76854afe376c623e6d2c6f2db81e786d, | |
0x15e35d18c79ae241e15cbfd1aa4f32ee, | |
0x0718164a69ae3b909d67eb4e7905537c, | |
0x8b33279bef66ce2a18f5c6540a31de0f, | |
0x5801acd999271becb5e2479767ffd97b, | |
0xa94f880fb3cb7fb7ccfa68f46aa14a36, | |
0x2741cfa39d8575953f1cb53789a280db, | |
0xb7f73b743347db543eb9e96ac01720d7, | |
0x5ce20fde9a65aa023483a06a35e8fc18, | |
0x577e77f04aced4792f7344d082c8bfe6, | |
0x0f84a54805f9c7ebbb9f1d14107e9159, | |
0xb412ad8ca822b8047120de7afe842dea, | |
0xbf51b4d1a4cd474815dac01f1679160b, | |
0x7709608a617abe1dab1aa7c5fea39d07, | |
0xde4de0ec8b94464c5d6f790eeb1ccb4b, | |
0x6e23a97536681c3cea48dc9cd0399a9d, | |
0xe1eb85c08df4ea784724e517aeed8b78, | |
0x6fdccde799d25db4ad9c3ac5f9764ca2, | |
0x11ad37eac319f6dc8b983bb55acdf8f8, | |
0x70ee127fb0072851998f40dd9f478d62, | |
0x19e54b042c18f0bed1a6c27f2c16d184, | |
0x106782a7ee2778d79dfb474b8d8485fa, | |
0xb2a548a08ad499aa32383a03fffe9206, | |
0x7857c0e5779b467466487189e53301e6, | |
0x0aea935626af6305ca9060259e6c9470, | |
0xbaf4f0961848de2debdb784000a53922, | |
0x4c2e7e77522822a15dfed9006a513d37, | |
0x3ae08085c5da3aaac865844b9e4cacae, | |
0xbd3802666379046284c1cd569dca74a7, | |
0x6a126cd4bd342d266f3e62b8798d6684, | |
0xd0ed75f496b99da5007f0207d1e0c587, | |
0xa180deabf9e03a9459439e2d6d49cc33, | |
0x0c288238067b5f4789843f8df84c3577, | |
0xb5f53521530c93198bd3ad0c99853a0b, | |
0x1257bdd97520967fb4fe8c385797eafc, | |
0x9c272b83c29470eb178f1b27b3e75245, | |
0x03ce1bd27dbcb78f559b09e7deb9f70b, | |
0xe17bcebd1ff045a74d7e8c2260ba098e, | |
0x85dbc459680ae06559ac46b36f709b55, | |
0xd6365428b392a3a788e48cf61bb83e32, | |
0x4ac74a7590b9cfb2c75cdb5a3d48d9e3, | |
0x43b500e3b2ef344d616805b632b4c269, | |
0xdd490d5e13dc21622459c70773e89258, | |
0x8d1de388ca8b8951856eaa0ee845a733, | |
0x6de20e418c916b0aee961115fefa894d, | |
0x7dca5b33940884d68bd457cd200969b3, | |
0x4fc72c051a0cd928ca3883172ee7a466, | |
0x2383cb9f82b1d658a7c008772667c39f, | |
0x05817272ac3ee002aceeb3d517981175, | |
0x29af9f686da3c54f6bd15b8c90864bd9, | |
0x0d68d1b184d6411da37434976b582f28, | |
0xcf76dd1b050fa71ef46d84a50b34a8ce, | |
0x560b0996f25c39bdb7e9960bdb72a002, | |
0x4ff457b088c19a876ee1af3410a2dfcb, | |
0x3cab6057af83603ff1162eed676ea519, | |
0xc392bcc7ed32ea28d6648016de89dddf, | |
0x723cddb609b06fdaa2002e7adb0e3ac7, | |
0x29babf03c2aa16339c6bcc24515967c9, | |
0x14297bc7b0f943634ab7e094929e37b8, | |
0xb76e66631692389547edbb3fc024541c, | |
0x92c90c096b21e42c9bb341d0fc555564, | |
0x569a65b99175c71ded8037b909a19101, | |
0x676a51bfc35174478a1ec7465e11c829, | |
0x0c2a2d16dbba722d84df47331992abae, | |
0x4ae0d8a676e09aa67ed708afaa9a3e93, | |
0xc7d76ec5a851b258b60121824ac3fd5e, | |
0xae49e5fdc27ae983c4b2b0cf41e61937, | |
0xd7f59b0afa176644d74ee2da9e032ddc, | |
0xc7c595e4ad277ac781a46ad9596fa417, | |
0x483d9744f3d84ac15f82d891f3e10729, | |
0x42324c22627746c2d14c78b245b6a530, | |
0x1afdf64951a6cedd28a2d5d197ce3ffc, | |
0x91e0a4d081c61d85c8468c75822e3fdc, | |
0x248471cca42ea0508ea3a71f9a3eb4b3, | |
0x6e634d68346d25aadf581823e9f47b44, | |
0x2ffae42602be95d2b50b6cc38cad9f09, | |
0x41f181487698c2810e815413b4e42f55, | |
0x57e7eb185ed6e0408029a2767a271e1a, | |
0x15e73a6edec64bedea017be544d3edf3, | |
0x62e78e73acfa0a73ee3efb96ef865b9e, | |
0x4c2be9a4a907af46f21412a87c0d6a7c, | |
0x0ee0619f2e743f711ab2decb8a6d54b2, | |
0x69e22d2aafe71d50fc1a380523732f8e, | |
0x9786f243c883e890a6a1a9db5438a24f, | |
0x35e83bc70b172489eab00f2c038eb1e4, | |
0x2de3061a0a49d62cac99c9b794ba928f, | |
0x8f08de20195d1c4efcae0041e48b15f0, | |
0x87c5bbeeea360ad4a07bc51f2e49fc03, | |
0x9b2d4124b4ca4d0723168d2cc332a1b9, | |
0x16c6be1d14ad62ab4065c54948e5a132, | |
0x69c8455432c87a1f599a34d81946e64b, | |
0x3fd3a63e1c3672bbd9fb743128efb0ad, | |
0xa78c69f1c569d8131b428da49ca5bf68, | |
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0x36614094fe3f2090d0e110a5148bb548, | |
0xaa716e1f8e7b52e6f8c0c633ba60bcba, | |
0xa8a15cd54e5c56931fd5da8bb6c1a5f7, | |
0x94fa5108e4f0384a8f4764f460476556, | |
0x43bc7df8a99053ad899c3024f6ac8e07, | |
0x33a99365d10f4b9b6f93940eb60c9fc4, | |
0xcb13954e55f03c4230d76d2ef52472f3, | |
0x8249133874ea08f5a670b7ed41b96c59, | |
0xd864a9137076ff389943b5dd5234e7bd, | |
0x4d98296c620d908b210622c69ef71103, | |
0xe4069c6c8b7dc2ed4a1596e2ccbfe89c, | |
0x9e91dd6ad19b64498137047da86abfa0, | |
0xa369155b4fe166713e97e8c388e431c7, | |
0x7861fd5b6d89e94b118931bcd0be025a, | |
0xe18d8b367264882da6beff2ebcace471, | |
0x944622ade029cc2e668e8d2a1191ad44, | |
0xc63f36b7eed97e2250428227ce8a17fa, | |
0xe3ce807f08bdf5dc9dce82921fbc023c, | |
0x09387f0fc71e0148d8a1ded9978e3a9c, | |
0x8230b74b336bdccb88bbd5b754af6d10, | |
0x1d940967db3ce5c78455a5726b94bfd0, | |
0x61297ecbb563eedee4ddc441e04f0e09, | |
0x4219bb3d7ad801a332fb09903ffd6de2, | |
0xa301b56d89a403bc5e8cd35222ec0d38, | |
0x1d75bc128e327380905a79cbeea6c528, | |
0x05882fe4b9ed055fca0c4f1619696c9b, | |
0x1133245b0de1d40702d647601626b7a4, | |
0x54e6d04a1a46b3a2b81e0db7dbde816a, | |
0x735a27d1e0aab8873aaeb05c334ffd1b, | |
0x3f561dd0bc0d5900432961eb4c87ee28, | |
0xcaca7a36ea29241774e34e7f3b8c0d2d, | |
0x7d7a6a03c34a141b43f209e66fb1947e, | |
0xdd02d454ab989892c27b011a46296631, | |
0x0c4bf5d2a66f493993dd3c358a186772, | |
0x94fa339d12424559c3c10dc21ed7f253, | |
0xb88498ed2b4a0c19111f79b9a696fa62, | |
0xe06c7a7d9a60043f9991ee9aaf1e00f6, | |
0x821cbef8d3366d0b925843dc6d08ad84, | |
0xd71b2c525ceca7dec7c28ee3994690c2, | |
0x6d73e9a4239693eec49f523965d01c44, | |
0x8250ecc0f9b6fb4b73cf97b08d86c8bb, | |
0x63fcff3e37f7fdbc1edaa06ef356bb3a, | |
0x54f2adea4edd26129761e979a20cc67d, | |
0x5bddf30f9d4a657eec56a9ec42bcf4a5, | |
0x15902a06e89df5eddceff8b7847ef095, | |
0x63c4e72ebd91a7eba0a93d6f47a4d67b, | |
0x216069af6574ab1290d044ba2ce6e4d8, | |
0xb01f1b9d9107bed2a4c45ec08a2bc8f7, | |
0x998a9816b824c0b1bbd9dd55dbfa907e, | |
0x018c01906ce4337fc0d2d30a49b25a5f, | |
0x1eaa7bbc18e1d9688f849d96e2c6dfbf, | |
0xb1d1fee869301a90d224f50ed5b9339c, | |
0x0dace3b81fbecac316079740712c5d0a, | |
0x73c8906aea5c7fa6eb4aa844f583b300, | |
0x29b6c4183653e6b1c6a7511e420957ce, | |
0x9f7d3e82e0f95ff0639d0ec2273fd3c7, | |
0x034f3f2d09644ac25aa97e648eeae36e, | |
0x78b17b096c0539069b6e56855294f439, | |
0x64282c270ccb7fc7fa6e14ccbecd36fb, | |
0x28d9f8be17db6f9be431330e4dfd42db, | |
0x45f2e5a602979c80fe679e89101f3b2b, | |
0x776f0826f219cd22cb2286acd58a9b02, | |
0x656d7b25ce7b4fe77d2b176d54e44791, | |
0xaf76c46059870d8e434adb5c1ad2173c, | |
0x7e5ef79482d990dcfdbdd629d633c81e, | |
0x14dd7703013bc9d43e829f689a9229d7, | |
0x673f248274ab6661ea9859ffe831cf46, | |
0x48ddad43bf8eaf30285d9917999acfbb, | |
0x0e2833511a7ea6d03cf978bd33b447ff, | |
0x002d5e4e3fbe771e6004f54a2e101a3b, | |
0x4bd2de19bd26f057b6cf7e66eb717614, | |
0x86dcdc27614452acc7f5cdba4bca45e0, | |
0x159733dc6522560757fcc27ec0bfe991, | |
0x802c6662164e30e87fa061f507a441b6, | |
0xdd4e5a49d3d5faf27269214c3c9f2cc6, | |
0x3b12647ede77061a62a298f8947c1270, | |
0xc6f5a94809ae0c7f8e5b56aefb571492, | |
0x233984f11def1debab1433ab73fafdc7, | |
0xa43da0872d7a42f507f441c9eed3b448, | |
0x94cffdacf89354d39977e0cb87f227e7, | |
0xd13952c386cee720e828e8d9eadd0e72, | |
0xc9223e0d4660253a4a3b96e936f6b3c0, | |
0x465120e4c38373569064ef86162cd2d6, | |
0xce7350d23ba8c01c2159ab6eaa9c884b, | |
0xb038de8206a23f6d32dd59ef593944a1, | |
0x8065e654ec36b412b3926eaee1ab95b0, | |
0x76fefab7fd4f5fe70e133ccf317b9fd8, | |
0x331bf47a6ab7870fd83a74eabce7af57, | |
0x901f9ce2da25cec268b13caf4686778e, | |
0xd95f556deccc1b5e4d3477afd6b428be, | |
0x98f1ef7246461036576689c25efb8fe9, | |
0x889538cb18d3115a01f07e88b2ee8cc9, | |
0xb6f83c21813c7a58222fab092cc82e97, | |
0x3a2714623d54e2756bd7cb3520c7f2db, | |
0x48f12e96cfcaeb64f04d4643d4492a31, | |
0xd256c346049c117db0ab2a1f770dc6c8, | |
0xcc31d692b6377a2115b0921481f47b3b, | |
0xc62c013152300f931630b16767684a57, | |
0x0e13ba6d0cb419caa4277070b86366d7, | |
0x76d7e909ac349f43b7d1996de2c9f8cc, | |
0x28479c65225d6fe7238680167f03f70c, | |
0xdf4d379004ff8510bb6640fd0709d314, | |
0xbec0ab6dcd5db22ef0917ea1f224c126, | |
0xc1ebd280ef4b2d153fad1e6e2a9fbf76, | |
0x6156f85511240f9e0eab1d56e479f9b4, | |
0x391fff449b0f3ddf04ce1174425b9465, | |
0x6baec5710bbac61c2ac6562ed1b766b6, | |
0x9223b3d945818ffdee693b3e12e9d6ea, | |
0xd2163678c3a70d2b7ae986ff03f770a4, | |
0xcd251b13a3f67501a8e2e0ebec03b1ae, | |
0xbe90f71992ca673e74675254666e7d43, | |
0x68afd0a96d672c91ebf04c3ff0c54e0f, | |
0x5cda9406060abc53d8166258fd09f479, | |
0x561c321a03268bdbfcc7b92b4c8a1f3d, | |
0xa839a8deafbdece38bfc4fbc49c2bdcf, | |
0x7d3dc714feba32801f3122bf367c1c7f, | |
0x32cb855e2ecfd687a2ed5e63c71475b9, | |
0xc3c9ce4a08cfdb3fa9107dd2c01215b5, | |
0x267ac5426da10bfac58f72a6a5e49fe5, | |
0x0bf5d3df99d1c1e69212f003d754d65e, | |
0x519026b5c5151a44405044d9382c8216, | |
0x12a779432e9e7859cb4784e1c31a5487, | |
0x331a921ab7b0fd8164a5d533c23cbc33, | |
0x77295cc120a937a63f9a4b01cf54cbd0, | |
0xc7ae39e29f7a8904eb13e285ddf28e09, | |
0x744c5875a3bc0e183d7aa7852eac5330, | |
0xc79032a750dfe837507cb4f7058eac2d, | |
0xd2496636c42bb1db7142a154776a50a6, | |
0xdb0b20726921fbb5ab9f2c34d6c18114, | |
0x80f5b5d170178dfd8755a984acfbe463, | |
0xb36e69cd0e1b2aa8afcf9048e564b4ca, | |
0x8310b9ec00ade7a390a4875fdb469bf9, | |
0xc2bb208b8de510b263802d21eb51b996, | |
0x89f26d14014a67bed3d59a674ee50dd1, | |
0xdc7745bb250b5d761803df1a72a3d242, | |
0x17e7a37dd40b12e287faad1e9ea1534b, | |
0x243a671fd29dc3caa99f952c32d33fb3, | |
0x83ae4ebf844e6f4313c6f786c41a4a27, | |
0x95734365251141db71d5e7b292b09c35, | |
0x319970fd981e6e629af61c0ece255635, | |
0x6be72a321c9ec10d694c005f9f5141a7, | |
0x7d933674679d65a97bb7cf8c67c7c1cf, | |
0xd8b92116d344529b6a1774d76489c640, | |
0x2785310fe3484800b82f588493b7620f, | |
0x4924c23fb47b50e38561ba06629265ce, | |
0xb781c5638670b8582fbff8d073272f39, | |
0xbf6a05f4bd76f17f71c8fedb7a03d665, | |
0x0c3c89e28766a67cddf6eb81da6b946f, | |
0x2c07ffdabed67186e32d8bb0b983de2b, | |
0x0904f6a5af8206c12ee03b5e04a886b7, | |
0x141d7304f684a9906c56f99d3179ebf9, | |
0x0afe356a76bf6178c57da23340a9e5f1, | |
0xbdb67f549261f87157bfadcf9b0cb208, | |
0xaf591a4a51fdd3f1000e11b52b6eac56, | |
0x0637f0f1fc14449f20e9504b95e91cd2, | |
0x35a60ba9d5bdb464a2ef8602348b776d, | |
0x6fb1b8f166062212dce1f0aba48e0fa5, | |
0xcb4d042ba9373cd2951a0ffbaa7783d5, | |
0x9572fb97247187dba568bf06fc6b13ed, | |
0xbe84c7dc218244fa4e8845e0526550f5, | |
0x255a21ed3744d97a01d3e26684b25fab, | |
0x892057dec940b4c52cf5e634d9710bea, | |
0x97c28121b2d7dbaac9b3bc6d58e4e24f, | |
0xacf0ee09a629ebf3d53d515b0be5370a, | |
0x7f5d3f7416726febc55d5df182dda893, | |
0x8e53c634eabebd207ec104f4a1ded7e1, | |
0xdbb290a6e21b3a87cee42a20ef30a8f9, | |
0x2bd0099d7e290a4160a7e3d842a0af74, | |
0x4b0de1b4c5afd6290a83fa959ace5b99, | |
0xd00c8655b5e07c15d2cd158e426138a9, | |
0x1fbbc03ed4dfe95247190c3c207c2dff, | |
0xae249a6241ec63d3fdefb918db9b5e6d, | |
0xd5e6859e501c22040796222a517cbd08, | |
0x33ebf8d21617c1d15a2542da252cebbc, | |
0x49f7d17217c1909d02beb76d441f7334, | |
0x18e1a668da0c825010d0090ad8e1ed5d, | |
0x1c1b72f571c71f0ce9d9688f610414b8, | |
0x5dd6b6d0c26f6c6335b54a4f49761752, | |
0x097bfc872489d690a4631feba144159d, | |
0x66bd623c4dad8d3f3767c18e01abc2d0, | |
0xdb18505df5151a75fdff58566a093b6e, | |
0x77418232ad9628dedae7edfb27aa1169, | |
0x2603fa69323657edfc8695ec1916ce40, | |
0x4fb460ff8614e8fa0ed100048fc7853f, | |
0xd65cf6bc4d44ab5ca640d39431ec7eb5, | |
0x4ac05e3ebc33d5f55c54f621f964b5cf, | |
0xba213303079572f70a98604dbd3739a4, | |
0x61a02e05e82d96cb1f55c91fb24899a1, | |
0x736b4643997a0a2c4806c2348bde3e79, | |
0x2b3cc4cd8d63d5905d54633c66ed209c, | |
0x9038ffd68a62473881c14174d1e477f5, | |
0x04a3f52212e92222c1e5567ca72f79ba, | |
0x720f57e7676b39c386db5b9bf10899bf, | |
0xbba2b8e1ce96e7cabc6a62fd51780bc1, | |
0xdd6250e5f6c1722cb44cc9fe0fed4b2f, | |
0x6e8acb51ad1f4d8f1761651330a8f720, | |
0xcf6e494456a9701b4d4c46e7af5aaf46, | |
0xd89d70327f52d7d392e39de7e5ad8d54, | |
0x17cfa1d3e5ffe3b6afb533dae4ab3cb4, | |
0xdecc503ddb87a56cc9c724f3d8f839a6, | |
0x12001b49990358b8a75dd49a0ae31434, | |
0xb34bf0fd04784c93f94df81fc3a028a2, | |
0xb4d756c4b3f9d476c7295bc1754e8dcf, | |
0x402c936e38944a9d8faf1a2a3562fb8a, | |
0x18102abcc1fe04eac023646d60b8d4b1, | |
0xb47f9520377b22a7d07c9a531b1d98ae, | |
0xabc706083d960992560f1c03f667b488, | |
0x6d3f6717a67daff94a7d89ec62b07a76, | |
0x4053bfd012ea8bf0b53ef605ddaa8429, | |
0x1a57d8317ea89cc618f999dfbe470d1c, | |
0x1dd29b2c764638e4df6310210a019589, | |
0xa460df868b0e1cba93c6aa12726d3577, | |
0x81916c70a1729c1fb83bf6f853852ca6, | |
0x780a4b91d78709ea95921dbf64f2c0a8, | |
0x64a55d28a27eb8837b8d039f2a9cda50, | |
0x29bad3b456999e9d089b2314e3475b92, | |
0x7720d77bd408c0982ba4d7108fdfb825, | |
0x05bf07b78461c71b348771c90f77c1a6, | |
0x085b2bc5b751258657cd197486e459a9, | |
0x154263f7035551dbc32983abb4c74c10, | |
0xe2fdd31e54b6d4e6252ec3a5901c391b, | |
0x83e23109452e43cd7214a3ad8936912f, | |
0xd4bfd64fddaa00eca9b26a1242684dcf, | |
0x34db0a2637ae912d995b7187b7d30977, | |
0xc1351174fc56ab65b3e988e7f3a0c45c, | |
0xa22bbde03c1c2aec985a3c8a1e40d737, | |
0x0e6d753f64def0b695a8c4d117019118, | |
0x88b6d13c52140b9e4f6f7601e4c5fdea, | |
0x4a913849a8a21f2dedc9f02140bdd2eb, | |
0xb28f5c87a9c75e05c0d208c142d1208b, | |
0x08552af276d31d5fbf37158c45c4c73b, | |
0xa0f6954ba5016cff9d6f75c1701f73ef, | |
0x31520b7082bbaf42bac78582bb171c43, | |
0x8d1f78962d3f9f95d3a43fe062d3a1e2, | |
0x9202f017d5372a63b27c9a3ad614ba0f, | |
0x01d32a5d07c4ea68a1fd37ac3d599a64, | |
0x3e4ea76da0b07e571bf3178e92985920, | |
0xd9f6934f987d2daf1743af807ffa3998, | |
0xad66b50a3f13e6f056c3ed6f83458309, | |
0xcc5081569d34a9a710c7be84e89e573f, | |
0xc914b3a0a51ef48a656c0a3795b8c75c, | |
0x4ffc6d4436628e75c0f3314a342bc7e6, | |
0xabaeeb2b7a62778243d92aa18eba7578, | |
0xa04d46bfb2a828f47c0a223320530b71, | |
0xb0db550d59baab29530996ec84c61497, | |
0x8bc02f23735ba7958f961e81307ed8a2, | |
0xbe480cb28b465663817bb5bcba221929, | |
0xbd539515a1409d9152b13c4a4a37c740, | |
0xb2a5d008527dd8660cd780863c403423, | |
0x79e869412cc3cfa8308713e0bba35eea, | |
0xd6c05afa3757a1c0e1e7f7d43c4e1f16, | |
0xcf7e0e4538763f63152cc0db481a45ac, | |
0xae62b81c79de06a05954e861403d4eab, | |
] | |
xs = list(range(1000)) | |
import matplotlib.pyplot as plt | |
import matplotlib.ticker as ticker | |
plt.plot(xs, ys, 'o', color='black'); | |
axes = plt.gca() | |
def to_hex(x, pos): | |
return '%x' % (int(x)>>64) | |
fmt = ticker.FuncFormatter(to_hex) | |
axes.get_yaxis().set_major_formatter(fmt) | |
plt.show() |
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q = 17560823292485810621 | |
p = 17260683863472602563 | |
n = 303111819233903650638787601663617221623 | |
e = 17 | |
d = 53490321041277114812464604913116260313 | |
vals = [ | |
0x00000000000000000000000000000000, | |
0x00cc5b325b06d6f3c93e9c36ee9546ab, | |
0xbde932133cf18e7c4f206806d252681a, | |
0x89acaf80eea2e9513d7f10af9a9bdfbe, | |
0x8dee2e886c276366e0258dd762ab0ab2, | |
0xb2b4f816772a1f6af0d9435ca3a1dbfd, | |
0x6b2c2e2f9f5a8ae4951e46e1caee2a05, | |
0x8ad233346d98cba40ff202e72df53eae, | |
0xcc97c682cc56b3ca25ab1e8476c06631, | |
0x988b3b37afe97a8910abc10dce87db17, | |
0x47909f5fa6662c5ffcc1863cadf5a32e, | |
0x5f172ad8ecbc83b7a28ac3ff1484f984, | |
0x9937592ab41d0535e497c4de1786f01a, | |
0x021b86d2332e4b43d20ebd0844464e80, | |
0x6edbdc525743a73c4ec0a1d178ec3530, | |
0x8f567789c5562c1991cc2b0ba48778fd, | |
0xc01078eb052fae49a3487020ec8768b4, | |
0x15c5bd3f52d4f536589466b3c30e42fe, | |
0x2302e5a867939ba13722c1c854c00a80, | |
0x274892f7f70317714306d780485d9b20, | |
0x7e6b364fccb61280921297322ac56e1e, | |
0xcf41be0729449e2948fee402344e87e6, | |
0xb565f70aeb629122ab790add25543d5d, | |
] | |
for v in vals: | |
print ('0x%032x' % (pow(v,d,n))) | |
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