Tokyo Westerns CTF 2020 - writeups.
[Rev] Reversing iS Amazing
It is a warmup chall, Given a rsa file, a 64 bit executable.Decompiled the executable with ghidra.
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| undefined8 FUN_00100a6a(int param_1,long param_2) | |
| { | |
| int iVar1; | |
| undefined8 uVar2; | |
| size_t sVar3; | |
| long lVar4; | |
| undefined8 *puVar5; | |
| undefined8 *puVar6; | |
| long in_FS_OFFSET; | |
| EVP_PKEY *local_b10; | |
| rsa_st *local_b08; | |
| BIO *local_b00; | |
| undefined local_af8; | |
| undefined local_af7; | |
| undefined local_af6; | |
| undefined local_af5; | |
| undefined local_af4; | |
| undefined local_af3; | |
| undefined local_af2; | |
| undefined local_af1; | |
| undefined local_af0; | |
| undefined local_aef; | |
| undefined local_aee; | |
| undefined local_aed; | |
| undefined local_aec; | |
| undefined local_aeb; | |
| undefined local_aea; | |
| undefined local_ae9; | |
| undefined local_ae8; | |
| undefined local_ae7; | |
| undefined local_ae6; | |
| undefined local_ae5; | |
| undefined local_ae4; | |
| undefined local_ae3; | |
| undefined local_ae2; | |
| undefined local_ae1; | |
| undefined local_ae0; | |
| undefined local_adf; | |
| undefined local_ade; | |
| undefined local_add; | |
| undefined local_adc; | |
| undefined local_adb; | |
| undefined local_ada; | |
| undefined local_ad9; | |
| undefined local_ad8; | |
| undefined local_ad7; | |
| undefined local_ad6; | |
| undefined local_ad5; | |
| undefined local_ad4; | |
| undefined local_ad3; | |
| undefined local_ad2; | |
| undefined local_ad1; | |
| undefined local_ad0; | |
| undefined local_acf; | |
| undefined local_ace; | |
| undefined local_acd; | |
| undefined local_acc; | |
| undefined local_acb; | |
| undefined local_aca; | |
| undefined local_ac9; | |
| undefined local_ac8; | |
| undefined local_ac7; | |
| undefined local_ac6; | |
| undefined local_ac5; | |
| undefined local_ac4; | |
| undefined local_ac3; | |
| undefined local_ac2; | |
| undefined local_ac1; | |
| undefined local_ac0; | |
| undefined local_abf; | |
| undefined local_abe; | |
| undefined local_abd; | |
| undefined local_abc; | |
| undefined local_abb; | |
| undefined local_aba; | |
| undefined local_ab9; | |
| undefined local_ab8; | |
| undefined local_ab7; | |
| undefined local_ab6; | |
| undefined local_ab5; | |
| undefined local_ab4; | |
| undefined local_ab3; | |
| undefined local_ab2; | |
| undefined local_ab1; | |
| undefined local_ab0; | |
| undefined local_aaf; | |
| undefined local_aae; | |
| undefined local_aad; | |
| undefined local_aac; | |
| undefined local_aab; | |
| undefined local_aaa; | |
| undefined local_aa9; | |
| undefined local_aa8; | |
| undefined local_aa7; | |
| undefined local_aa6; | |
| undefined local_aa5; | |
| undefined local_aa4; | |
| undefined local_aa3; | |
| undefined local_aa2; | |
| undefined local_aa1; | |
| undefined local_aa0; | |
| undefined local_a9f; | |
| undefined local_a9e; | |
| undefined local_a9d; | |
| undefined local_a9c; | |
| undefined local_a9b; | |
| undefined local_a9a; | |
| undefined local_a99; | |
| undefined local_a98; | |
| undefined local_a97; | |
| undefined local_a96; | |
| undefined local_a95; | |
| undefined local_a94; | |
| undefined local_a93; | |
| undefined local_a92; | |
| undefined local_a91; | |
| undefined local_a90; | |
| undefined local_a8f; | |
| undefined local_a8e; | |
| undefined local_a8d; | |
| undefined local_a8c; | |
| undefined local_a8b; | |
| undefined local_a8a; | |
| undefined local_a89; | |
| undefined local_a88; | |
| undefined local_a87; | |
| undefined local_a86; | |
| undefined local_a85; | |
| undefined local_a84; | |
| undefined local_a83; | |
| undefined local_a82; | |
| undefined local_a81; | |
| undefined local_a80; | |
| undefined local_a7f; | |
| undefined local_a7e; | |
| undefined local_a7d; | |
| undefined local_a7c; | |
| undefined local_a7b; | |
| undefined local_a7a; | |
| undefined local_a79; | |
| undefined8 local_a78 [76]; | |
| uchar local_818 [1024]; | |
| uchar local_418 [1032]; | |
| long local_10; | |
| local_10 = *(long *)(in_FS_OFFSET + 0x28); | |
| local_af8 = 0x6f; | |
| local_af7 = 0x86; | |
| local_af6 = 0xe4; | |
| local_af5 = 0x96; | |
| local_af4 = 0x29; | |
| local_af3 = 0xbe; | |
| local_af2 = 0x8a; | |
| local_af1 = 0x5e; | |
| local_af0 = 0x21; | |
| local_aef = 0xe2; | |
| local_aee = 0xc0; | |
| local_aed = 0xda; | |
| local_aec = 0x25; | |
| local_aeb = 0xb7; | |
| local_aea = 0x95; | |
| local_ae9 = 0xe0; | |
| local_ae8 = 0x5f; | |
| local_ae7 = 10; | |
| local_ae6 = 0x6c; | |
| local_ae5 = 0xe9; | |
| local_ae4 = 0x44; | |
| local_ae3 = 0xdb; | |
| local_ae2 = 0x12; | |
| local_ae1 = 0x4c; | |
| local_ae0 = 0x3a; | |
| local_adf = 0x6c; | |
| local_ade = 0x14; | |
| local_add = 0x87; | |
| local_adc = 0xc6; | |
| local_adb = 0x36; | |
| local_ada = 0x6b; | |
| local_ad9 = 0x6d; | |
| local_ad8 = 0x95; | |
| local_ad7 = 6; | |
| local_ad6 = 0x1c; | |
| local_ad5 = 0x2d; | |
| local_ad4 = 0x11; | |
| local_ad3 = 0x9e; | |
| local_ad2 = 0xf8; | |
| local_ad1 = 0x72; | |
| local_ad0 = 0xcc; | |
| local_acf = 0x9b; | |
| local_ace = 0x74; | |
| local_acd = 0x87; | |
| local_acc = 0x73; | |
| local_acb = 0xa7; | |
| local_aca = 0x52; | |
| local_ac9 = 0x72; | |
| local_ac8 = 0xc; | |
| local_ac7 = 0x5b; | |
| local_ac6 = 0x92; | |
| local_ac5 = 0x8d; | |
| local_ac4 = 0x7c; | |
| local_ac3 = 0xa9; | |
| local_ac2 = 0x35; | |
| local_ac1 = 0xeb; | |
| local_ac0 = 0xc5; | |
| local_abf = 0xd6; | |
| local_abe = 0x1e; | |
| local_abd = 0x1c; | |
| local_abc = 0x9e; | |
| local_abb = 0x7e; | |
| local_aba = 0xd3; | |
| local_ab9 = 0x6e; | |
| local_ab8 = 0x43; | |
| local_ab7 = 0x35; | |
| local_ab6 = 0x93; | |
| local_ab5 = 0xd0; | |
| local_ab4 = 0x6c; | |
| local_ab3 = 0x26; | |
| local_ab2 = 0xb4; | |
| local_ab1 = 0x95; | |
| local_ab0 = 0xe5; | |
| local_aaf = 0x99; | |
| local_aae = 0x28; | |
| local_aad = 99; | |
| local_aac = 0x5e; | |
| local_aab = 0xeb; | |
| local_aaa = 0xad; | |
| local_aa9 = 0x40; | |
| local_aa8 = 0xce; | |
| local_aa7 = 0x26; | |
| local_aa6 = 0x67; | |
| local_aa5 = 0xf7; | |
| local_aa4 = 0x32; | |
| local_aa3 = 0xb2; | |
| local_aa2 = 3; | |
| local_aa1 = 0xd; | |
| local_aa0 = 0x30; | |
| local_a9f = 0x24; | |
| local_a9e = 0x93; | |
| local_a9d = 0x84; | |
| local_a9c = 0x3a; | |
| local_a9b = 0x19; | |
| local_a9a = 0xac; | |
| local_a99 = 0x6f; | |
| local_a98 = 0x11; | |
| local_a97 = 0xbb; | |
| local_a96 = 0xb; | |
| local_a95 = 0x5b; | |
| local_a94 = 0x41; | |
| local_a93 = 0x8d; | |
| local_a92 = 0x9d; | |
| local_a91 = 0x49; | |
| local_a90 = 0x1a; | |
| local_a8f = 0xb1; | |
| local_a8e = 0x21; | |
| local_a8d = 0xd9; | |
| local_a8c = 0x79; | |
| local_a8b = 0x43; | |
| local_a8a = 0xbc; | |
| local_a89 = 0x83; | |
| local_a88 = 0x1c; | |
| local_a87 = 0x36; | |
| local_a86 = 0x98; | |
| local_a85 = 0xb9; | |
| local_a84 = 0x5a; | |
| local_a83 = 0x53; | |
| local_a82 = 0xd9; | |
| local_a81 = 0xf4; | |
| local_a80 = 0xa3; | |
| local_a7f = 0x99; | |
| local_a7e = 0x34; | |
| local_a7d = 0x67; | |
| local_a7c = 0xa2; | |
| local_a7b = 0x8b; | |
| local_a7a = 0xce; | |
| local_a79 = 6; | |
| lVar4 = 0x4c; | |
| puVar5 = &DAT_00101100; | |
| puVar6 = local_a78; | |
| while (lVar4 != 0) { | |
| lVar4 = lVar4 + -1; | |
| *puVar6 = *puVar5; | |
| puVar5 = puVar5 + 1; | |
| puVar6 = puVar6 + 1; | |
| } | |
| if (param_1 == 2) { | |
| sVar3 = strlen(*(char **)(param_2 + 8)); | |
| memcpy(local_418,*(void **)(param_2 + 8),(long)(int)sVar3); | |
| local_b08 = (rsa_st *)0x0; | |
| local_b10 = (EVP_PKEY *)0x0; | |
| local_b00 = (BIO *)0x0; | |
| local_b00 = BIO_new_mem_buf(local_a78,0x260); | |
| if (local_b00 == (BIO *)0x0) { | |
| uVar2 = 1; | |
| } | |
| else { | |
| local_b10 = d2i_PrivateKey_bio(local_b00,&local_b10); | |
| if (local_b10 == (EVP_PKEY *)0x0) { | |
| uVar2 = 1; | |
| } | |
| else { | |
| local_b08 = EVP_PKEY_get1_RSA(local_b10); | |
| if (local_b08 == (rsa_st *)0x0) { | |
| uVar2 = 1; | |
| } | |
| else { | |
| iVar1 = RSA_private_encrypt((int)sVar3,local_418,local_818,(RSA *)local_b08,1); | |
| if (iVar1 < 0) { | |
| uVar2 = 1; | |
| } | |
| else { | |
| iVar1 = memcmp(local_818,&local_af8,(long)iVar1); | |
| if (iVar1 == 0) { | |
| puts("Correct!"); | |
| } | |
| else { | |
| puts("Incorrect!"); | |
| } | |
| RSA_free((RSA *)local_b08); | |
| EVP_PKEY_free(local_b10); | |
| BIO_free_all(local_b00); | |
| uVar2 = 0; | |
| } | |
| } | |
| } | |
| } | |
| } | |
| else { | |
| printf("./rsa TWCTF{*****************************}"); | |
| uVar2 = 1; | |
| } | |
| if (local_10 != *(long *)(in_FS_OFFSET + 0x28)) { | |
| /* WARNING: Subroutine does not return */ | |
| __stack_chk_fail(); | |
| } | |
| return uVar2; | |
| } |
Those are openssl library API calls, by going through the documentation and code.
in the binary it has an EVP key, Cipher text.
The binary is creating a RSA private key from EVP Key , then encrypting our input and checking with cipher text.
Dumped the EVP Key, Cipher text from the binary. Written a decrypting code with same api calls (as we have private key).
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| #include <stdio.h> | |
| #include <string.h> | |
| #include <openssl/x509v3.h> | |
| #include <openssl/objects.h> | |
| #include <openssl/pem.h> | |
| #include <openssl/evp.h> | |
| int main(int argc, char const *argv[]) { | |
| char chunk[609] = {48, 130, 2, 92, 2, 1, 0, 2, 129, 129, 0, 174, 104, 97, 212, 115, 166, 51, 49, 51, 194, 26, 94, 190, 245, 236, 144, 234, 133, 119, 234, 194, 219, 98, 115, 181, 41, 93, 194, 187, 58, 60, 209, 80, 187, 212, 212, 158, 238, 51, 221, 59, 48, 69, 60, 235, 190, 241, 31, 103, 228, 5, 92, 139, 156, 111, 58, 86, 186, 226, 186, 236, 154, 167, 208, 67, 237, 188, 39, 80, 70, 200, 64, 146, 46, 135, 182, 36, 227, 244, 195, 27, 214, 189, 173, 85, 164, 81, 100, 35, 16, 209, 108, 20, 253, 53, 168, 24, 161, 159, 171, 51, 20, 249, 62, 80, 52, 196, 60, 40, 182, 16, 210, 252, 144, 155, 151, 96, 213, 154, 19, 229, 62, 191, 56, 208, 82, 102, 125, 2, 3, 1, 0, 1, 2, 129, 128, 3, 126, 129, 223, 64, 197, 230, 166, 168, 179, 205, 213, 114, 27, 249, 54, 90, 12, 124, 127, 142, 145, 216, 162, 26, 210, 14, 87, 213, 106, 112, 71, 125, 71, 150, 23, 0, 108, 35, 75, 222, 96, 180, 50, 105, 66, 181, 15, 253, 3, 219, 123, 164, 44, 105, 42, 17, 12, 195, 120, 29, 63, 103, 247, 66, 188, 186, 56, 174, 204, 38, 219, 202, 129, 30, 73, 253, 250, 6, 189, 50, 131, 59, 158, 102, 30, 155, 139, 79, 245, 4, 94, 129, 218, 105, 219, 145, 126, 15, 150, 105, 161, 81, 147, 179, 80, 244, 132, 16, 216, 73, 36, 198, 176, 81, 43, 188, 122, 224, 38, 223, 66, 239, 187, 155, 87, 226, 221, 2, 65, 0, 217, 139, 131, 169, 246, 189, 148, 204, 239, 147, 52, 90, 53, 238, 139, 179, 78, 50, 65, 124, 198, 156, 42, 94, 240, 151, 194, 69, 61, 143, 104, 30, 52, 183, 176, 95, 175, 94, 158, 253, 65, 184, 238, 92, 139, 90, 202, 78, 183, 81, 122, 222, 87, 33, 55, 170, 64, 158, 35, 10, 81, 29, 237, 107, 2, 65, 0, 205, 60, 203, 57, 126, 206, 223, 159, 210, 200, 103, 157, 100, 134, 34, 211, 229, 188, 63, 10, 51, 50, 184, 224, 63, 220, 160, 127, 230, 166, 252, 135, 223, 78, 134, 128, 129, 58, 228, 224, 94, 225, 65, 26, 208, 244, 184, 194, 78, 0, 145, 154, 26, 240, 30, 56, 159, 202, 85, 226, 163, 45, 205, 183, 2, 65, 0, 129, 41, 123, 119, 235, 94, 174, 61, 107, 53, 12, 77, 79, 94, 29, 165, 205, 20, 187, 155, 24, 212, 217, 183, 90, 195, 207, 253, 138, 74, 93, 248, 41, 54, 178, 202, 108, 246, 18, 17, 173, 246, 221, 215, 38, 138, 54, 57, 188, 79, 237, 82, 155, 138, 198, 97, 24, 82, 139, 221, 113, 66, 2, 151, 2, 64, 18, 173, 81, 161, 45, 213, 13, 172, 177, 181, 227, 24, 3, 169, 225, 73, 127, 66, 158, 74, 3, 86, 190, 84, 73, 251, 125, 239, 165, 193, 212, 129, 88, 229, 0, 128, 121, 66, 46, 201, 236, 88, 123, 96, 65, 91, 195, 228, 138, 204, 170, 115, 103, 184, 42, 71, 228, 226, 184, 230, 35, 11, 108, 9, 2, 64, 62, 118, 100, 99, 212, 131, 176, 14, 98, 70, 184, 31, 13, 227, 48, 62, 233, 22, 64, 121, 143, 138, 119, 48, 102, 174, 37, 230, 195, 59, 117, 126, 171, 126, 255, 74, 9, 224, 56, 236, 182, 93, 235, 179, 133, 89, 192, 109, 85, 78, 168, 5, 195, 113, 239, 96, 24, 219, 43, 109, 204, 30, 146, 252}; | |
| BIO *key ; | |
| EVP_PKEY *pkey; | |
| RSA *rsakey; | |
| unsigned char encrypted[4098]={ 111, 134, 228, 150, 41, 190, 138, 94, 33, 226, 192, 218, 37, 183, 149, 224, 95, 10, 108, 233, 68, 219, 18, 76, 58, 108, 20, 135, 198, 54, 107, 109, 149, 6, 28, 45, 17, 158, 248, 114, 204, 155, 116, 135, 115, 167, 82, 114, 12, 91, 146, 141, 124, 169, 53, 235, 197, 214, 30, 28, 158, 126, 211, 110, 67, 53, 147, 208, 108, 38, 180, 149, 229, 153, 40, 99, 94, 235, 173, 64, 206, 38, 103, 247, 50, 178, 3, 13, 48, 36, 147, 132, 58, 25, 172, 111, 17, 187, 11, 91, 65, 141, 157, 73, 26, 177, 33, 217, 121, 67, 188, 131, 28, 54, 152, 185, 90, 83, 217, 244, 163, 153, 52, 103, 162, 139, 206, 6 }; | |
| int enc_len = strlen(encrypted); | |
| unsigned char decrypted[4098]={}; | |
| int dec_len; | |
| key = BIO_new_mem_buf(chunk, 609); | |
| if (key) { | |
| pkey = d2i_PrivateKey_bio(key, &pkey); | |
| if (pkey){ | |
| rsakey = EVP_PKEY_get1_RSA(pkey); | |
| if (rsakey){ | |
| if(RSA_check_key(rsakey)) { | |
| PEM_write_PrivateKey(stdout,pkey,NULL,NULL,0,0,NULL); | |
| printf("\n[+] Trying to decrypt !...\n"); | |
| dec_len = RSA_public_decrypt(enc_len, encrypted, decrypted, rsakey, 1); | |
| if(dec_len == -1) { | |
| printf("[-] Failed to decrypt the data.\n"); | |
| } else { | |
| printf("\n[+] Data decrypted\n"); | |
| printf("[+] Data Length = %d\n",dec_len); | |
| printf("[+] Data = %s\n",decrypted); | |
| } | |
| RSA_free(rsakey); | |
| EVP_PKEY_free(pkey); | |
| BIO_free_all(key); | |
| } else { | |
| printf("[+] RSA key is invalid. :(\n"); | |
| } | |
| } else { | |
| printf("[-] Failed to RSA key from pkey\n"); | |
| } | |
| } else { | |
| printf("[-] Failed to load pkey from bio\n"); | |
| } | |
| } else { | |
| printf("[-] Failed to create key BIO\n"); | |
| } | |
| return 0; | |
| } |
[Rev] Tamarin
Given an apk file. by unpacking it going through files found libmonodroid_bundle_app.so(lib file).a Xamarin/Monodroid application bundle from which we can unbundle it get DLL files.
which i have learned from past `Alles 2020 CTF` Secret Notes chall , I tried a lot, sadly didn't solved it, due to lack of knowledge on this concept.
Used the tool : https://github.com/tjg1/mono_unbundle
Unpacked , and found a Tamarin.dll file. Used dnSpy to decompile and see the dll file
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| using System; | |
| using System.Collections.Concurrent; | |
| using System.Collections.Generic; | |
| using System.Linq; | |
| using System.Security.Cryptography; | |
| using System.Text; | |
| using System.Threading.Tasks; | |
| namespace Core | |
| { | |
| // Token: 0x02000004 RID: 4 | |
| public static class Check | |
| { | |
| // Token: 0x06000007 RID: 7 RVA: 0x00002764 File Offset: 0x00000964 | |
| private static uint Func1(uint x, int n) | |
| { | |
| uint num = 1U; | |
| for (int i = 0; i < n; i++) | |
| { | |
| num *= x; | |
| } | |
| return num; | |
| } | |
| // Token: 0x06000008 RID: 8 RVA: 0x00002784 File Offset: 0x00000984 | |
| private static uint Func2(List<uint> coefficients, uint x, int pos) | |
| { | |
| if (pos == -1) | |
| { | |
| return 0U; | |
| } | |
| uint num = coefficients[pos] * Check.Func1(x, pos); | |
| return num + Check.Func2(coefficients, x, pos - 1); | |
| } | |
| // Token: 0x06000009 RID: 9 RVA: 0x000027B8 File Offset: 0x000009B8 | |
| private static uint Func3() | |
| { | |
| byte[] array = new byte[4]; | |
| using (RNGCryptoServiceProvider rngcryptoServiceProvider = new RNGCryptoServiceProvider()) | |
| { | |
| rngcryptoServiceProvider.GetBytes(array); | |
| } | |
| return BitConverter.ToUInt32(array, 0); | |
| } | |
| // Token: 0x0600000A RID: 10 RVA: 0x000027FC File Offset: 0x000009FC | |
| public static bool Func4(string flag) | |
| { | |
| ParallelOptions parallelOptions = new ParallelOptions | |
| { | |
| MaxDegreeOfParallelism = 4 | |
| }; | |
| byte[] bytes = Encoding.ASCII.GetBytes(flag); | |
| int length = flag.Length; | |
| if ((length & 3) != 0) | |
| { | |
| Array.Resize<byte>(ref bytes, length + (4 - (length & 3))); | |
| } | |
| for (int i = length; i < bytes.Length; i++) | |
| { | |
| bytes[i] = 0; | |
| } | |
| if (bytes.Length != Check.equations_arr.GetLength(0) * 4) | |
| { | |
| return false; | |
| } | |
| object lockObj = new object(); | |
| ConcurrentBag<bool> checkResults = new ConcurrentBag<bool>(); | |
| List<List<uint>> list = new List<List<uint>>(); | |
| for (int j = 0; j < Check.equations_arr.GetLength(0); j++) | |
| { | |
| List<uint> list2 = new List<uint>(); | |
| list2.Add(BitConverter.ToUInt32(bytes, j * 4)); | |
| for (int k = 0; k < Check.equations_arr.GetLength(1); k++) | |
| { | |
| list2.Add(Check.equations_arr[j, k]); | |
| } | |
| list.Add(list2); | |
| } | |
| Parallel.ForEach<List<uint>>(list, parallelOptions, delegate(List<uint> equation) | |
| { | |
| object lockObj = lockObj; | |
| lock (lockObj) | |
| { | |
| uint num = Check.Func3(); | |
| for (int l = 0; l < 10000; l++) | |
| { | |
| num = Check.Func2(equation, num, equation.Count - 2); | |
| } | |
| checkResults.Add(num == equation[equation.Count - 1]); | |
| } | |
| }); | |
| return Enumerable.All<bool>(checkResults.ToArray(), (bool x) => x); | |
| } | |
| // Token: 0x04000001 RID: 1 | |
| private static readonly uint[,] equations_arr = new uint[,] | |
| { | |
| { | |
| 2921822136U, | |
| 1060277104U, | |
| 2035740900U, | |
| 823622198U, | |
| 210968592U, | |
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| } | |
| } |
The code has 4 functions namely, Func1, Func2, Func3, Func4.
Func1 is simply power function. pow(base, exp); Used in Func2
Func2 is a Polynomial equation evaluator by recursion. Solve(Coefficients, X_value, pos)
Func3 is random number generator function
Func4 is the flag checking function, where it uses Func2, Func3
Func4 function (Some Math part TLDR;)
from basics checks, we can know the length of input string 88 (4**22), 22 is length of 2D Array(22 x 32) namely equations_arr.The 22 * 32 Array is nothing but coefficents of 22 equations.
For each iteration it uses one array from equations_arr and a uint number by combining 4 bytes from our input .
For each iteration
That number constructed from 4 bytes of input is used as the Constant for the equation taken from equations_arr.That constant is our input and a32..a1 are coefficeients given in equation_arr along with final value
Then
At first I cant understand how can it manage to get the final value, in spite of random `X` value and only with the correct constant.
To check it, I written identical code in python and testing it on sample values.
The results are surprising as everytime it merging to same value, eventhough with different X value.
Checked how it is happening
And found that, in those 10,000 iterations, it is coming to a fixed point. `x == f(x)`. so the next iterations cant even effect it.
It keeps on repeat that value.
I didn't get why this(coming to fixed point) is happening, it may be something with the modular math. as we have uint (32 bits) which simply means (% 2**32).
Note : But just by assuming all those `22 final values` are also fixed points ` x = f(x) `.
Now we have everything
Where x is final value, a32..a1 are coefficents. we can get constant in reverse. Boom:)
Lets calculate the constants for all 22 equations.
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| from Crypto.Util.number import long_to_bytes | |
| def Equation(Coeffs, x, pos): | |
| if pos == -1: | |
| return 0 | |
| num = ( Coeffs[pos] * pow(x, pos, MAX) ) % MAX | |
| return ( num + Equation(Coeffs, x, pos-1) ) % MAX | |
| def Get_constant(List, X): | |
| List = [0] + List | |
| val = Equation(List, X, len(List)-2) % MAX | |
| return (List[-1] - val) % MAX | |
| MAX = 2**32 | |
| arr = [ | |
| [ 2921822136, 1060277104, 2035740900, 823622198, 210968592, 3474619224, 3252966626, 1671622480, 1174723606, 3830387194, 2514889364, 3125636774, 896423784, 4164953836, 2838119626, 2523117444, 1385864710, 3157438448, 132542958, 4108218268, 314662132, 432653936, 1147047258, 1802950730, 67411056, 1207641174, 1920298940, 2947533900, 3468512014, 3485949926, 3695085832, 3903653528 ], | |
| [ 463101660, 3469888460, 2006842986, 144738028, 630007230, 3440652086, 2322916652, 2227002010, 1163469256, 23859328, 2322597530, 3716255122, 2876706098, 713374856, 2345958624, 3496771192, 1773957550, 146382778, 1141367704, 1061893394, 994321632, 3407332344, 2240786438, 2218631702, 2906647610, 1919308420, 2136654012, 164975906, 2834189362, 3118478912, 3258673870, 3211411825 ], | |
| [ 2558729100, 1170420958, 2355877954, 3593652986, 2587766164, 2271696650, 1560549496, 132089692, 2893757564, 3469624876, 10109206, 2948199026, 4170042296, 2717317064, 4210960804, 93756380, 2006217436, 2988057920, 2251383150, 226355976, 579516546, 3915017586, 1273838010, 2852178952, 4272774672, 1006507228, 3595131622, 1880597220, 1230996622, 2542910224, 917668128, 1612363977 ], | |
| [ 3637139654, 2593663532, 649194106, 4275630476, 2730487128, 905133820, 2868808700, 1284610026, 1051455306, 272375560, 1219428572, 163965224, 3899483864, 309833108, 1862243284, 1919038730, 3414916994, 3134382762, 2018925234, 3467081876, 4045123308, 4244105094, 4205568254, 1793827648, 257732384, 2092183712, 3517540150, 2641565070, 2181538960, 2670634300, 2070334778, 1995308868 ], | |
| [ 561434200, 2730097174, 1499965472, 760244614, 1588114416, 521516362, 2963707630, 1896166800, 411250470, 1601999958, 2973942456, 3027806424, 1238337602, 1380721280, 122976200, 788897864, 3589391734, 1987301254, 1085198712, 3553616586, 1994354546, 1684916442, 2788234788, 2641884090, 612801768, 1801824798, 2019943314, 3304068906, 849354132, 44941780, 3473262708, 1444837808 ], | |
| [ 921974086, 404262832, 1353817916, 764855648, 2290476820, 2023815980, 669786172, 791841140, 526348842, 2979022342, 3656325786, 1276970440, 2424614726, 1190814714, 2804417116, 3654263826, 3068580996, 1908493640, 3101330462, 792198672, 1772484794, 4050408722, 611660842, 1610808360, 431629552, 2319897718, 3255085210, 1426503472, 1630566802, 4241881448, 1606014350, 636517450 ], | |
| [ 2906103140, 1116553354, 2279536366, 3011561210, 2641603848, 1646150780, 192124694, 611421916, 3416039786, 4208848404, 474397384, 1491088256, 3177553844, 2042765300, 1653674858, 1365840538, 1595225706, 2705938552, 3180386458, 1723055560, 2280421090, 1241156010, 3807390206, 2595800854, 2890507242, 4068903400, 3923234634, 2613933834, 3927909200, 2149793556, 3589302752, 802516900 ], | |
| [ 171242408, 1411016272, 2890085382, 624162464, 3117870816, 3388454296, 3869111620, 948964384, 1670102044, 3432346180, 1670460686, 3674313702, 4108083090, 915550832, 4249135230, 411447682, 2915987712, 3865207952, 4017666788, 275767786, 2506858524, 3488718446, 1995975410, 566166116, 1590333384, 329205954, 3913164274, 620615436, 1464604756, 269837028, 963851056, 2483789524 ], | |
| [ 4043184956, 3569779124, 3817645374, 4281618348, 4144074366, 3776223584, 2260112022, 2417238210, 4004384546, 1196429850, 1429697170, 3075499898, 2507660230, 1342925724, 3951341456, 229184726, 2762396986, 1612961426, 986238002, 1228690306, 3948701236, 1378190546, 3106898794, 1894874158, 1488049036, 3718233910, 1078939754, 2355898312, 2030934192, 2879370894, 3017715248, 1647621107 ], | |
| [ 3849716376, 3412391848, 420800182, 156925722, 3602232204, 2645326622, 3864083570, 1279782822, 878821008, 1906288878, 1396282244, 1641728726, 2295751090, 290937256, 1958396986, 2115100470, 3706945590, 2885002942, 1935777480, 1483762940, 3589264430, 3791465274, 2553819596, 2050180502, 1381704584, 4640270, 628970046, 774725214, 2575508070, 1330692832, 1250987676, 3756982724 ], | |
| [ 1460953346, 1175847424, 3477700838, 3783709768, 1064663570, 3559971784, 3802954664, 2431960456, 2198986400, 859802318, 3783810034, 1110187920, 4244034440, 1796543058, 902449590, 160031782, 3639253664, 4255746326, 3339514496, 218988706, 4085181614, 2342973726, 1391523108, 1120970708, 2639842372, 156321138, 1587974922, 3686627774, 1648124740, 2095688044, 293533614, 3056924137 ], | |
| [ 1034259104, 4077045412, 789979418, 961028604, 2185949320, 3457364068, 3532291848, 2206594748, 3072062072, 1796530288, 1402389280, 3478769990, 196567236, 3940435298, 2237679842, 668941406, 170819894, 1102049112, 131349762, 2512464482, 4159048294, 2186098090, 123947608, 1742064290, 1711289746, 1449132362, 58078952, 2976574968, 1774398264, 1532589156, 4089484268, 4041979478 ], | |
| [ 3681899832, 4208608358, 1951338724, 3772673566, 3160075610, 1422174080, 2431526454, 529884656, 2722748162, 236192616, 2684139926, 697549902, 3546454434, 1921398338, 1310272304, 1691292498, 4134700116, 720619430, 2592536546, 2188997288, 2461521148, 455077540, 1421274126, 1052585740, 2383754190, 1567602170, 3773864138, 4036579298, 2416620860, 1931099884, 2051263696, 310763286 ], | |
| [ 1461705722, 968835462, 2563821358, 576185928, 1613137824, 940353300, 652295412, 1135005196, 3607866196, 3307698550, 3916080186, 4052934590, 3991167852, 3799175976, 3393348946, 950814766, 2174463160, 2422320256, 959545514, 2820210140, 4284041840, 3082466322, 1257510060, 2676710840, 127465314, 3887977956, 3218198116, 957094088, 1409365960, 2217798938, 277108032, 2579736592 ], | |
| [ 3776055232, 823459706, 1913270776, 1721511850, 633354432, 3901765934, 2089017122, 1103648570, 3791238880, 1686042442, 1567720048, 2924815412, 1695861754, 3641036796, 1208391908, 1593134050, 1674288590, 2322785248, 2472109738, 3572933674, 3828029068, 1641647380, 4116180236, 3884220004, 3146594508, 3587030908, 3451856524, 2965945264, 162291656, 2061732942, 1551591510, 4014200221 ], | |
| [ 3406794856, 3181753846, 2984888850, 1748566984, 1311737108, 3415409722, 2398926736, 2006269026, 3117725174, 2901254050, 2733703362, 1595001962, 106879068, 3933136528, 245096038, 666024082, 134803296, 1657783988, 3429228290, 2120419114, 2879013028, 9653606, 305704628, 3793128986, 369835124, 2274924880, 4233339440, 2224753480, 2427854922, 1808326540, 1833703938, 2391461119 ], | |
| [ 1827597388, 454565514, 1282880792, 561174442, 3610484436, 2327669348, 765794442, 3705161518, 1715916192, 292859360, 183730846, 3298097994, 3535037218, 2904849282, 348832662, 1856773750, 3618335118, 3017093112, 3354956190, 3208811970, 897522204, 2835584374, 3097985334, 2108903166, 3230714490, 2597789348, 1597521406, 1663858876, 94923994, 883872856, 3230397040, 3420763893 ], | |
| [ 4065160224, 2129787468, 3456903512, 2860656238, 2663588170, 3224900102, 2827778318, 2685874320, 2005737334, 586304716, 472376412, 2938324550, 3459137716, 3422216092, 3082124658, 1173945064, 842495374, 2564495050, 357433170, 2050324102, 1138367532, 854845936, 3054001576, 2465772674, 2305389082, 3669610606, 3527889292, 3817664802, 4238531160, 1556372762, 777986002, 1126454981 ], | |
| [ 764733144, 3965849612, 1668893328, 2104626056, 1653642872, 2883395356, 3015268318, 2322404760, 1185726976, 1607036694, 3064704530, 3639372768, 1252489394, 3950622630, 3889240956, 233990458, 2393973872, 3609439896, 2108036182, 152726882, 3730671578, 3038534682, 3388044150, 3128791454, 2499312664, 3396894570, 2872225186, 3048419004, 2864782986, 3169897264, 2890258816, 753842003 ], | |
| [ 2403595118, 2093259638, 2763900156, 3772789760, 3282639530, 2884294140, 3879894514, 2512089226, 318451120, 2464691316, 2179668204, 795049786, 326585310, 1313213364, 3437852224, 4055872768, 1224395344, 1911910472, 983774674, 3804144712, 3208317764, 1534290234, 3243577720, 617743358, 378252266, 3612369740, 1924240610, 961715850, 2058485164, 1460892148, 2613095898, 73199927 ], | |
| [ 3093631524, 2704600210, 3519611266, 5414320, 3358912704, 2462642760, 3764896542, 1253645320, 4034052234, 3137650284, 4083324920, 2667059126, 436316958, 497182460, 404768030, 1122443700, 432434942, 443290780, 3487257114, 2699955512, 4250049274, 3991832458, 1037538700, 3125332984, 1533312690, 1452437348, 1283257518, 3946567854, 716640500, 2417637998, 3063327834, 82885668 ], | |
| [ 1985108, 1694522756, 4205785758, 333118606, 2944637686, 2196892858, 4092971632, 83374602, 4049383084, 2980843496, 1801648602, 2639009750, 1944350566, 3046229260, 2662687100, 2423732014, 4179240348, 1035280058, 1015236846, 3488976898, 1530833166, 3723596058, 4125718292, 1095267878, 3635353922, 2932904358, 2764606674, 45921060, 3107074868, 4198045636, 1923836480, 366302822 ] | |
| ] | |
| Str = '' | |
| for List in arr: | |
| X = List[-1] | |
| Y = Get_constant(List, X) | |
| Str += long_to_bytes(Y)[::-1].decode() | |
| flag = "TWCTF{%s}"%Str | |
| print("[+] Flag : ", flag) |
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