CTF writeup - Synergistic Hyperscale Interoperable Tokens (PlaidCTF 2022)

solve.log

[1/10] Produce a new secret token for 6535016376403176904
8673357082917415256
[2/10] Produce a new secret token for 2467768788370249308
6321414967796127680
[3/10] Produce a new secret token for 15027414725812929110
11980021394058769251
[4/10] Produce a new secret token for 10702703014918823634
10162230340064657963
[5/10] Produce a new secret token for 9183860382523110997
9455870811549556796
[6/10] Produce a new secret token for 8012324378975699066
10956485569638790932
[7/10] Produce a new secret token for 5586890336573343448
4547398440643275083
[8/10] Produce a new secret token for 13004947060634539310
17761150032074348261
[9/10] Produce a new secret token for 13679116250745902676
18220244222682735531
[10/10] Produce a new secret token for 15455050481726328053
15334363509564988023
Congrats!
PCTF{rust2wasm2rust2wasm2rust_15a0fc7fa673ae85}

solve.py

from pwn import *
import subprocess

context.log_level = 'error'

def main():
    conn = remote('synergistic.chal.pwni.ng', 1337)

    powargv = conn.recvline().decode().split()
    assert powargv[0] == 'hashcash'
    conn.send(subprocess.check_output(powargv))

    for _ in range(10):
        challine = conn.recvline().decode().strip()
        chal = challine.split()[-1]
        token = subprocess.check_output(
            ('sage', 'solve.sage', chal)
        ).decode()

        print(challine)
        print(token)

        conn.sendline(token.encode())

    print(conn.recv().decode().strip())

if __name__ == '__main__':
    main()

solve.sage

import sys

INIT = [
    0xDA17EDC974CBF88B05BA2B30F33009E3,
    0x7C59A1115F898C02BDEF1E03F8A42971,
    0x1D33F3FCE07374372CE572B38B540058,
    0x029C91EB9CAB7C67405943E2C746EF8A,
    0xF4BE5D2A92C9C93C012DA654BC29E00C,
    0x94AEDB33A79ACDE64A901FC9B5E1F7EF,
    0x2FC1C5CAD1DBB6754707916C3F4F882C,
    0x7953163B864ECA9501E948B96DC61489,
    0xA1CE9B3BE90D180288C7AF20A872B40F,
    0xF08D70B3923D15702DEF3A950A3DF2EE,
]

COEFFS = [
    0xaadc352d973570941c4ef5256bf7691f,
    0x3b8efd66d9ab488a4bda5e346cf43679,
    0xba665904d9ce575bf63d4b112d6fd165,
    0x92c103f01e7ddca6d313806dad60830a,
    0x7bb0ffd1d80fb3212868836edee04734,
    0x603ffacc774e09f2895dd3aa6089713e,
    0x468f22365bd9e2ed0ded12b11aa38888,
    0x6154bec0cd734930d005c98621b0a224,
    0xf380c3e496070199646b9980e07fbde6,
    0x654006a05ad681d0ec32ef2ca379f6ef,
]

def calc_token(inp):
    mat = matrix(
        Zmod(1 << 64),
        [
            COEFFS,
        ] + [
            [0] * i + [1] + [0] * (9 - i)
            for i in range(9)
        ]
    )

    vec = vector(
        Zmod(1 << 64),
        INIT[::-1]
    )

    return ((mat ^ inp) * vec)[0]

sys.stdout.write(str(calc_token(int(sys.argv[1]))))