pbctf 2020: Jiang Ying's Disasssembler author's writeup

cheese.cpp

// 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;
}

dickit.py

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))

outputs.py

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,
0xcf0bd20272159fc4c54ff6f3720cba7e,
0xcb946b8249e3bfc56615b344fb1f88ea,
0x2bea99d69a9a874ebf9231c6be9d94da,
0xdc9e2b9a44710f75171f85f890240b85,
0x13d7cb668a96be50d1a37749c6a64ce6,
0x4a679f0cb50a8f537ec7319ae2890df2,
0x25482f194ec4f1c70f61b94802942429,
0x013e130852681cd240eeb0cec00f2b16,
0x13b0e8dd052ef83a6f3a365987edc2eb,
0x244724320b61e595645311fe5cb9f6a7,
0xd7837e1048713de36a41f2c14334b4f7,
0x78aacf36c0ef203f27b96d9513e17c3a,
0xb76a3348f724599feb8a145eef85c0e7,
0x1cf055c0b19f64ab93c1ec8fbda660e3,
0x24c1e16df2783b3335cbb5fc88abe3ce,
0xa5d745110305208fafa082c94e49628a,
0x0e54298a7e48d28fbf343649dfdcb169,
0x07c90dc2480424ab554e7b6c8fd360ec,
0xcac9508e1d2e021b23c0d1d8ef97f315,
0x43d0a0395013c7759d7371f26e995b7c,
0x58875552e693ad3c5c60ebb41bf0567c,
0x961ec97456fe547f04d51050e2ee130d,
0x95084e7e2fe76ad71bc951ac7d63687d,
0x1cfeb213c6f35d9007b6ff7a2b769cb9,
0x5aa5c0bd5d00118ab4c3df59736e3a20,
0xbd64271efff5439966eccdc417d15b8f,
0x1280fcc8840d303cb417ef5b438f0def,
0x000389a264cf7823561840ed206fc398,
0x40b7c7264ca58c9831a0e7d29617c524,
0x4eb7865db0ef6ddbc00f1ac55df689f4,
0xd9e47b28ade93ffa790b7ed51ede957f,
0x9466e6e68841b4e0ec3575e795bcb5de,
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0x11219404aa368b6f1cb93df1e2cf3a85,
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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()

rsa.py

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)))