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BRICS+ CTF 2024 - xoshiro256++ (works with 4500 outputs)
Raw
a.jl
flag = read("flag.txt") # brics+{...}
for _ in 1:1500
println(bytes2hex(flag .⊻ rand(UInt8, length(flag))))
end
Raw
gen_rels.cpp
#include <m4ri/m4ri.h>
#include <pthread.h>
#include <cinttypes>
#include <random>
#include <vector>
using std::size_t;
pthread_mutex_t print_mutex;
constexpr int N_BINS = 256;
constexpr int MASK = N_BINS - 1;
uint64_t rotl(uint64_t x, int k) {
return (x << k) | (x >> (64 - k));
}
uint64_t f(uint64_t x, uint64_t y) {
return rotl(x + y, 23) + x;
}
void process(uint64_t tgt) {
fprintf(stderr, "tgt: %lu\n", tgt);
std::mt19937_64 mt;
size_t n_cols = 1;
n_cols += 128;
n_cols += 128 * 127 / 2;
fprintf(stderr, "%zu monomials\n", n_cols);
mzd_t *A = mzd_init(40000, n_cols);
// mzd_t *B = mzd_init(20000, 64);
for (size_t ri = 0; ri < A->nrows; ri++) {
uint64_t x = 0, y = 0;
while (1) {
x = mt();
y = mt();
if ((f(x, y) & MASK) == tgt)
break;
}
__uint128_t t = (((__uint128_t)x) << 64) | (__uint128_t)y;
size_t mi = 0;
mzd_write_bit(A, ri, mi++, 1);
for (size_t i = 0; i < 128; i++)
mzd_write_bit(A, ri, mi++, (t >> i) & 1);
for (size_t i = 0; i < 128; i++)
for (size_t j = 0; j < i; j++)
mzd_write_bit(A, ri, mi++, (t >> i) & (t >> j) & 1);
assert(mi == n_cols);
}
mzd_t *ker = mzd_kernel_left_pluq(A, 0);
fprintf(stderr, "mat dim: %zu rows, %zu cols\n", A->nrows, A->ncols);
if (ker == nullptr) {
fprintf(stderr, "ker is null\n");
mzd_free(A);
return;
}
fprintf(stderr, "ker dim: %zu rows, %zu cols\n", ker->nrows, ker->ncols);
mzd_t *tker = mzd_transpose(nullptr, ker);
fprintf(stderr, "tker dim: %zu rows, %zu cols\n", tker->nrows, tker->ncols);
mzd_free(A);
mzd_free(ker);
// check again that the relations are certain (not very fast)
// for (size_t ri = 0; ri < tker->nrows; ri++) {
// for (size_t _ = 0; _ < 10; _++) {
// uint64_t x = 0, y = 0;
// do {
// x = mt();
// y = mt();
// } while (((f(x, y) >> shift) & 1) != bit);
// __uint128_t t = (((__uint128_t)x) << 64) | (__uint128_t)y;
// size_t nm = 0;
// size_t mi = 0;
// nm ^= mzd_read_bit(tker, ri, mi++);
// for (size_t i = 0; i < 128; i++)
// nm ^= mzd_read_bit(tker, ri, mi++) & (t >> i) & 1;
// for (size_t i = 0; i < 128; i++)
// for (size_t j = 0; j < i; j++)
// nm ^=
// mzd_read_bit(tker, ri, mi++) & (t >> i) & (t >> j) & 1;
// //assert(mi == n_cols);
// assert(nm == 0);
// }
// }
pthread_mutex_lock(&print_mutex);
for (size_t ri = 0; ri < tker->nrows; ri++) {
printf("%lu ", tgt);
for (size_t ci = 0; ci < tker->ncols; ci++)
printf("%d", (int)mzd_read_bit(tker, ri, ci));
printf("\n");
}
pthread_mutex_unlock(&print_mutex);
mzd_free(tker);
}
constexpr int N_THREADS = 8;
int main() {
// for (int i = 0; i < N_BINS; i++)
// process(i);
pthread_mutex_init(&print_mutex, nullptr);
pthread_t threads[N_THREADS];
for (int i = 0; i < N_THREADS; i++)
pthread_create(
&threads[i], nullptr,
[](void *arg) -> void * {
for (int i = 0; i < N_BINS && (i + (size_t)arg) < N_BINS;
i += N_THREADS)
process(i + (size_t)arg);
return nullptr;
},
(void *)i);
for (int i = 0; i < N_THREADS; i++)
pthread_join(threads[i], nullptr);
pthread_mutex_destroy(&print_mutex);
return 0;
}
Raw
gen_test.py
from hashlib import sha256
MASK32 = 0xFFFFFFFF
MASK64 = 0xFFFFFFFFFFFFFFFF
def rotl64(x, k):
return ((x << k) | (x >> (64 - k))) & MASK64
class JuliaXoshiro:
def __init__(self, s0, s1, s2, s3):
self.s0 = s0
self.s1 = s1
self.s2 = s2
self.s3 = s3
self.buf = b""
def next(self):
s0, s1, s2, s3 = self.s0, self.s1, self.s2, self.s3
ret = (rotl64((s0 + s3) & MASK64, 23) + s0) & MASK64
t = (s1 << 17) & MASK64
s2 ^= s0
s3 ^= s1
s1 ^= s2
s0 ^= s3
s2 ^= t
s3 = rotl64(s3, 45)
self.s0, self.s1, self.s2, self.s3 = s0, s1, s2, s3
return ret
def bytes(self):
while True:
if not self.buf:
self.buf = self.next().to_bytes(8, "little")
b = self.buf[0]
self.buf = self.buf[1:]
yield b
@staticmethod
def from_seed(seed):
bs = b""
while seed:
bs += (seed & MASK32).to_bytes(4, "little")
seed >>= 32
h = sha256(bs).digest()
s0 = int.from_bytes(h[:8], "little")
s1 = int.from_bytes(h[8:16], "little")
s2 = int.from_bytes(h[16:24], "little")
s3 = int.from_bytes(h[24:32], "little")
return JuliaXoshiro(s0, s1, s2, s3)
def xor(a, b):
return bytes(x ^ y for x, y in zip(a, b))
flag = b"brics+{" + b"q" * (41 - 7 - 1) + b"}"
assert len(flag) == 41
rand = JuliaXoshiro.from_seed(48763)
for _ in range(1500 * 3):
print(xor(flag, rand.bytes()).hex())
Raw
hax.cpp
#include <m4ri/m4ri.h>
#include <array>
#include <bitset>
#include <random>
#include <vector>
using std::size_t;
uint64_t rotl(uint64_t x, int k) {
return (x << k) | (x >> (64 - k));
}
uint64_t func(uint64_t x, uint64_t y) {
return rotl(x + y, 23) + x;
}
constexpr size_t N_MONO = 1 + 256 + 256 * 255 / 2;
using deg2_rel = std::bitset<1 + 256 + 256 * 255 / 2>;
using deg2_rel128 = std::bitset<1 + 128 + 128 * 127 / 2>;
using lin_rel = std::bitset<256>;
struct sym_u64 {
lin_rel st[64]{};
sym_u64 &operator^=(const sym_u64 &rhs) {
for (size_t i = 0; i < 64; i++)
st[i] ^= rhs.st[i];
return *this;
}
sym_u64 operator^(const sym_u64 &rhs) const {
sym_u64 ret = *this;
ret ^= rhs;
return ret;
}
sym_u64 operator<<(int by) const {
sym_u64 ret{};
for (size_t i = 0; i < 64 - by; i++)
ret.st[i + by] = st[i];
return ret;
}
sym_u64 operator>>(int by) const {
sym_u64 ret{};
for (size_t i = 0; i < 64 - by; i++)
ret.st[i] = st[i + by];
return ret;
}
sym_u64 rotl(int by) const {
sym_u64 ret{};
for (size_t i = 0; i < 64; i++)
ret.st[(i + by) % 64] = st[i];
return ret;
}
};
struct sym_u128_st {
sym_u64 x, y;
lin_rel &operator[](size_t i) {
if (i < 64)
return y.st[i];
else
return x.st[i - 64];
}
};
struct sym_xs256 {
sym_u64 s0, s1, s2, s3;
sym_xs256() {
for (size_t i = 0; i < 64; i++) {
s0.st[i][i] = true;
s1.st[i][i + 64] = true;
s2.st[i][i + 128] = true;
s3.st[i][i + 192] = true;
}
}
sym_u128_st step() {
sym_u128_st ret{s0, s3};
sym_u64 t = s1 << 17;
s2 ^= s0;
s3 ^= s1;
s1 ^= s2;
s0 ^= s3;
s2 ^= t;
s3 = s3.rotl(45);
return ret;
}
};
constexpr int N_BINS = 256;
constexpr int MASK = N_BINS - 1;
std::array<std::vector<deg2_rel128>, N_BINS> krels;
deg2_rel to_deg2(lin_rel lhs) {
deg2_rel ret{};
for (size_t i = 0; i < 256; i++)
ret[i + 1] = lhs[i]; // 0 is the constant term
return ret;
}
deg2_rel mul(lin_rel lhs, lin_rel rhs) {
deg2_rel ret{}; // compute the product coefficients directly
size_t mi = 1;
for (size_t i = 0; i < 256; i++) {
ret[mi] = ret[mi] ^ (lhs[i] & rhs[i]);
mi++;
}
for (size_t i = 0; i < 256; i++)
for (size_t j = 0; j < i; j++) {
ret[mi] = ret[mi] ^ (lhs[i] & rhs[j]);
ret[mi] = ret[mi] ^ (lhs[j] & rhs[i]);
mi++;
}
return ret;
}
void assert_rel(std::vector<deg2_rel> &vec, int b, int v) {
// assert tht b-th bit is v (0 or 1)
// bits[b] == v
deg2_rel r{};
r[0] = v;
r[1 + b] = 1;
vec.push_back(std::move(r));
// v == 0: bits[b] * bits[?] = 0
// v == 1: bits[b] * bits[?] = bits[?]
lin_rel base{};
base[b] = 1;
for (int i = 0; i < 256; i++) {
if (b == i)
continue;
lin_rel other{};
other[i] = 1;
deg2_rel r = mul(base, other);
if (v == 0) {
r[0] = 0;
} else {
r[1 + i] = 1;
}
vec.push_back(std::move(r));
}
}
int main() {
FILE *f = fopen("rels256.txt", "r");
while (true) {
char buf[9000];
uint64_t res = 0;
int ok = fscanf(f, "%lu %s", &res, buf);
if (ok < 2)
break;
res &= MASK;
deg2_rel128 rel{};
for (size_t i = 0; i < rel.size(); i++)
rel[i] = buf[i] - '0';
krels[res].push_back(std::move(rel));
}
fclose(f);
// for (int res = 0; res < N_BINS; res++) {
// fprintf(stderr, "res=%d, sz=%zu\n", res, krels[res].size());
// }
// return 0;
constexpr int FLAG_LEN = 41;
f = fopen("local_out.bin", "rb"); // decoded to binary using `xxd -r -p`
uint8_t encflag[FLAG_LEN];
for (size_t i = 0; i < FLAG_LEN; i++) {
encflag[i] = fgetc(f);
}
fseek(f, 0, SEEK_SET);
sym_xs256 rng{};
uint8_t known_flag[FLAG_LEN] = "brics+{";
known_flag[FLAG_LEN - 1] = '}';
std::vector<deg2_rel> all_rels;
for (size_t i = 0;; i += 8) {
uint64_t v;
if (fread(&v, 8, 1, f) != 1) {
fprintf(stderr, "EOF\n");
break;
}
sym_u128_st s0s3 = rng.step();
if ((i % FLAG_LEN) != 0 && (i % FLAG_LEN) != 1 && (i % FLAG_LEN) != 2 &&
(i % FLAG_LEN) != 3 && (i % FLAG_LEN) != 4 && (i % FLAG_LEN) != 5 &&
(i % FLAG_LEN) != 6 && (i % FLAG_LEN) != 40)
continue;
// printf("%d\n", i / 8);
uint64_t outb = (v & 0xff) ^ known_flag[i % FLAG_LEN];
outb &= MASK;
for (const deg2_rel128 &big_rel : krels[outb]) {
deg2_rel res{};
size_t mi = 1;
if (big_rel[0])
res[0] = res[0] ^ 1;
for (size_t i = 0; i < 128; i++) {
if (big_rel[mi])
res ^= to_deg2(s0s3[i]);
mi++;
}
for (size_t i = 0; i < 128; i++)
for (size_t j = 0; j < i; j++) {
if (big_rel[mi])
res ^= mul(s0s3[i], s0s3[j]);
mi++;
}
assert(mi == 1 + 128 + 128 * 127 / 2);
all_rels.push_back(res);
}
}
fclose(f);
// if some bits are known, assert them
// uint64_t S0 = 0x24eb761d3f927390;
// uint64_t S1 = 0x26c7b27ded480a51;
// for (int i = 0; i < 64; i++) {
// assert_rel(all_rels, i, (S0 >> i) & 1);
// assert_rel(all_rels, i + 64, (S1 >> i) & 1);
// }
fprintf(stderr, "%zu\n", all_rels.size());
mzd_t *A = mzd_init(all_rels.size(), N_MONO);
for (size_t i = 0; i < all_rels.size(); i++) {
for (size_t j = 0; j < N_MONO; j++)
mzd_write_bit(A, i, j, all_rels[i][j]);
}
// we solve this system by linearization
fprintf(stderr, "starting solve\n");
fprintf(stderr, "mat dim: %zu rows, %zu cols\n", A->nrows, A->ncols);
mzd_t *ker = mzd_kernel_left_pluq(A, 0);
if (ker == nullptr) {
fprintf(stderr, "ker is null\n");
mzd_free(A);
return 1;
}
mzd_t *tker = mzd_transpose(nullptr, ker);
fprintf(stderr, "tker dim: %zu rows, %zu cols\n", tker->nrows, tker->ncols);
mzd_free(A);
mzd_free(ker);
assert(tker->nrows == 1); // only 1 solution
sym_xs256 rng2{};
// the initial state. dot product with symbolic output equals concrete output
lin_rel ist;
for (size_t j = 0; j < 256; j++)
ist[j] = mzd_read_bit(tker, 0, j + 1);
for (size_t i = 0; i < FLAG_LEN; i += 8) {
sym_u128_st s0s3 = rng2.step();
uint64_t x = 0;
for (size_t j = 0; j < 64; j++)
x |= uint64_t((s0s3.x.st[j] & ist).count() % 2) << j;
uint64_t y = 0;
for (size_t j = 0; j < 64; j++)
y |= uint64_t((s0s3.y.st[j] & ist).count() % 2) << j;
uint64_t out = func(x, y);
uint8_t *outb = (uint8_t *)&out;
for (int j = 0; j < 8 && i + j < FLAG_LEN; j++)
printf("%c", encflag[i + j] ^ outb[j]);
}
printf("\n");
return 0;
}
Raw
rels256.txt
This file has been truncated, but you can view the full file.
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