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Crypto CTF 2023: Big (last phase only)
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| from sage.all import * | |
| import output | |
| import binascii | |
| p = 7690745050590286968025665448815927548186441771518218204702842288098845344789340509868897149374937793107491606741591691437711395848517107039674900831427939 | |
| q = 9397241380094769307017158485931177341961951476061947013977394739417988689050439874435488908822482074028128151771446818457295188445665208696820950505470967 | |
| def compute_t(F, c, a): | |
| cf = F(c) | |
| af = F(a) | |
| return ZZ((cf + sqrt(cf ^ 2 + 4 * af)) / 2) | |
| N = output.pkey | |
| a, C = output.E | |
| Fp = GF(p) | |
| Fq = GF(q) | |
| b = [] | |
| for c in C: | |
| tp = compute_t(Fp, c, a) | |
| tq = compute_t(Fq, c, a) | |
| t = crt(tp, tq, p, q) | |
| if kronecker(t, N) == 1: | |
| b.append(1) | |
| else: | |
| b.append(0) | |
| print(binascii.unhexlify(hex(ZZ("".join(map(str, b)), 2))[2:])) |
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| Sun Jul 9 16:45:58 JST 2023 ~/Downloads/Big | |
| > time sage solve.sage | |
| b'CCTF{_Cocks_18e_5chEm3}' | |
| real 0m2.153s | |
| user 0m1.999s | |
| sys 0m0.181s |
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Writeup: https://shiho-elliptic.tumblr.com/post/722391959624433664/crypto-ctf-2023-writeup-en