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PlaidCTF 2020 - MPKC (Crypto 350)
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| from sage.all import * | |
| import sys | |
| q,n,a,s = (3,59,10,25) | |
| m = n+1-a+s | |
| FF = GF(q) | |
| R = PolynomialRing(FF, ["x{}".format(i) for i in range(n)]) | |
| xs = R.gens() | |
| pk, ct = open("output").readlines() | |
| ct = eval(ct) | |
| try: | |
| pk = load("pub") | |
| print("load ok") | |
| except IOError: | |
| pk = eval(pk.replace("^", "**"), {}, {"x%d" % i: x for i, x in enumerate(xs)}) | |
| save(pk, "pub") | |
| from itertools import * | |
| # 1. find linear combinations of outputs which have no quadratic terms | |
| order = [prod(c) for c in combinations_with_replacement(xs, 2)] | |
| mono2i = {mono: i for i, mono in enumerate(order)} | |
| m = matrix(FF, len(pk), len(order)) | |
| for y, poly in enumerate(pk): | |
| for coef, mono in list(poly): | |
| if mono.degree() == 2: | |
| m[y,mono2i[mono]] = coef | |
| # matrix to obtain linear functions | |
| mdec = m.left_kernel().matrix() | |
| # 2. convert affine polys to a matrix | |
| mono2i = {x: i for i, x in enumerate(xs)} | |
| polys = mdec * vector(R, pk) | |
| m = matrix(FF, len(polys), n) | |
| t = vector(FF, len(polys)) | |
| for y, poly in enumerate(polys): | |
| for coef, mono in list(poly): | |
| if mono.degree() == 1: | |
| m[y,mono2i[mono]] = coef | |
| elif mono.degree() == 0: | |
| t[y] = coef | |
| # generate kernel to exhaust solutions | |
| zs = list(m.right_kernel()) | |
| print("kernel size", len(zs)) | |
| presol = [] | |
| for I, block0 in enumerate(ct[::-1]): | |
| print("Block", I) | |
| block = mdec * vector(FF, block0) | |
| sol0 = m.solve_right(block - t) | |
| for z in zs: | |
| sol = sol0 + z | |
| full_sol = list(presol) + list(sol[::-1]) | |
| s = "".join(map(str, full_sol)) | |
| s = int(s, 3) * 3**(n*(5-I)) | |
| # some hand calculations of sizes | |
| if s >= 256**70//2: continue | |
| test = s.to_bytes(70, "big")[:11*(I+1)].strip(b"\x00") | |
| if sum((32 <= c < 127) for c in test) >= len(test): | |
| full = s.to_bytes(70, "big").strip(b"\x00") | |
| print("maybe", full) | |
| for p, c in zip(pk[:10], block0): | |
| if p(*sol) != c: | |
| break | |
| else: | |
| presol += list(sol[::-1]) | |
| print("verified!") | |
| break | |
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| # Jiahui Chen et al. cryptosystem, 80-bit security | |
| # WARNING: very slow implementation. | |
| import sys | |
| q,n,a,s = (3,59,10,25) | |
| m = n+1-a+s | |
| FF = GF(q) | |
| R = PolynomialRing(FF, ["x{}".format(i) for i in range(n)]) | |
| xs = R.gens() | |
| def keygen(): | |
| while True: | |
| C = random_matrix(FF, n+1, n) | |
| if matrix(FF, [2*C[i]-2*C[i+1] for i in range(n)]).is_invertible(): | |
| break | |
| FC = [] | |
| for i in range(n+1): | |
| p = 0 | |
| for j in range(n): | |
| p += (xs[j] - C[i][j])^2 | |
| FC.append(p) | |
| while True: | |
| S_lin = random_matrix(FF, n, n) | |
| if S_lin.is_invertible(): | |
| break | |
| S_trans = (FF^n).random_element() | |
| S = (S_lin, S_trans) | |
| while True: | |
| T_lin = random_matrix(FF, m, m) | |
| if T_lin.is_invertible(): | |
| break | |
| T_trans = (FF^m).random_element() | |
| T = (T_lin, T_trans) | |
| G = [] | |
| for i in range(s): | |
| G.append(R.random_element(degree=2, terms=Infinity)) | |
| F = FC[:n+1-a] + G | |
| P = vector(xs) | |
| P = S[0]*P | |
| P += S[1] | |
| v = [] | |
| for i in range(len(F)): | |
| v.append(F[i](*P)) | |
| print("keygen {}/{}".format(i+1,len(F)), file=sys.stderr) | |
| P = vector(v) | |
| P = T[0]*P | |
| P += T[1] | |
| print("done keygen", file=sys.stderr) | |
| return (P, (C, G, S, T)) | |
| def make_blocks(ss): | |
| x = 0 | |
| for i in ss: | |
| x = x*256+ord(i) | |
| v = [] | |
| while x > 0: | |
| v.append(FF(x%q)) | |
| x = x//q | |
| v += [FF(0) for i in range(n - (len(v) % n))] | |
| blocks = [] | |
| for i in range(0, len(v), n): | |
| blocks.append(vector(v[i:i+n])) | |
| return blocks | |
| def combine_blocks(blocks): | |
| x = 0 | |
| for i in blocks[::-1]: | |
| for j in i[::-1]: | |
| x = x*q+Integer(j) | |
| ss = "" | |
| while x > 0: | |
| ss = chr(x % 256) + ss | |
| x = x//256 | |
| return ss | |
| def encrypt_block(plain, pk): | |
| return pk(*plain) | |
| def encrypt(plain, pk): | |
| blocks = make_blocks(plain) | |
| enc = [] | |
| for i in range(len(blocks)): | |
| print("encrypt {}/{}".format(i+1,len(blocks)), file=sys.stderr) | |
| enc.append(encrypt_block(blocks[i], pk)) | |
| return enc | |
| def decrypt_block(cipher, sk): | |
| C, G, S, T = sk | |
| C2I = matrix(FF, [2*C[i]-2*C[i+1] for i in range(n)]).inverse() | |
| cv = [] | |
| for i in range(n): | |
| cc = 0 | |
| for j in range(n): | |
| cc += C[i+1][j]^2 - C[i][j]^2 | |
| cv.append(cc) | |
| cv = vector(cv) | |
| g1 = T[0].inverse()*(cipher - T[1]) | |
| for g2 in FF^a: | |
| print("decrypt: trying:", g2, file=sys.stderr) | |
| g = vector(list(g1)[:n+1-a]+list(g2)) | |
| g_diff = vector([g[i+1]-g[i] for i in range(len(g)-1)]) | |
| d = C2I * (g_diff-cv) | |
| for i,j in zip(G,g1[n+1-a:]): | |
| if i(*d) != j: | |
| break | |
| else: | |
| return S[0].inverse() * (d - S[1]) | |
| def decrypt(cipher, sk): | |
| dec = [] | |
| for i in range(len(cipher)): | |
| print("decrypt {}/{}".format(i+1,len(cipher)), file=sys.stderr) | |
| dec.append(decrypt_block(cipher[i], sk)) | |
| return combine_blocks(dec) | |
| pk, sk = keygen() | |
| print(pk) | |
| flag = open("flag.txt").read().strip() | |
| print(encrypt(flag, pk)) |
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| (x0^2 - x1^2 - x2^2 - x0*x3 + x1*x3 + x2*x3 - x0*x4 + x1*x4 + x3*x4 - x4^2 - x0*x5 - x2*x5 - x4*x5 + x5^2 - x0*x6 + x1*x6 - x2*x6 - x3*x6 + x5*x6 - x6^2 + x0*x7 + x1*x7 - x2*x7 + x3*x7 + x4*x7 - x5*x7 - x6*x7 + x0*x8 + x1*x8 + x2*x8 + x3*x8 - x5*x8 - x6*x8 - x7*x8 + x1*x9 - x2*x9 - x3*x9 - x5*x9 - x6*x9 - x7*x9 + x9^2 - x2*x10 + x3*x10 + x4*x10 - x5*x10 + x6*x10 - x7*x10 + x10^2 - x1*x11 + x2*x11 - x3*x11 - x5*x11 - x10*x11 - x1*x12 + x2*x12 - x3*x12 - x4*x12 + x5*x12 - x6*x12 - x7*x12 - x8*x12 + x9*x12 - x11*x12 - x1*x13 - x2*x13 - x3*x13 - x4*x13 + x7*x13 - x8*x13 + x11*x13 + x13^2 - x0*x14 - x1*x14 + x2*x14 - x5*x14 + x6*x14 + x11*x14 - x13*x14 + x0*x15 + x1*x15 + x3*x15 - x5*x15 - x10*x15 - x11*x15 - x13*x15 + x14*x15 - x0*x16 - x1*x16 + x3*x16 + x4*x16 + x5*x16 + x6*x16 - x9*x16 - x11*x16 + x12*x16 - x13*x16 + x14*x16 + x16^2 + x0*x17 - x1*x17 - x4*x17 - x6*x17 - x8*x17 + x9*x17 - x10*x17 - x11*x17 - x13*x17 + x14*x17 + x15*x17 + x16*x17 - x0*x18 - x1*x18 - x3*x18 - x5*x18 + x7*x18 - x8*x18 + x12*x18 - x13*x18 - x14*x18 + x15*x18 + x0*x19 - x2*x19 + x6*x19 - x12*x19 - x14*x19 + x15*x19 - x16*x19 + x17*x19 + x18*x19 + x19^2 - x0*x20 - x1*x20 + x2*x20 + x3*x20 + x4*x20 + x6*x20 - x7*x20 - x8*x20 + x10*x20 + x11*x20 - x12*x20 - x14*x20 - x16*x20 - x18*x20 + x20^2 - x1*x21 + x2*x21 - x4*x21 - x5*x21 - x6*x21 + x7*x21 + x8*x21 - x9*x21 + x11*x21 - x13*x21 - x14*x21 + x16*x21 - x18*x21 - x20*x21 - x21^2 - x0*x22 - x1*x22 + x2*x22 - x3*x22 + x4*x22 + x5*x22 + x6*x22 - x7*x22 + x9*x22 + x10*x22 - x12*x22 - x13*x22 + x15*x22 + x17*x22 - x18*x22 - x19*x22 - x20*x22 + x21*x22 - x0*x23 - x1*x23 + x2*x23 - x3*x23 + x5*x23 + x7*x23 + x10*x23 - x11*x23 + x13*x23 + x14*x23 + x17*x23 - x19*x23 + x20*x23 + x21*x23 + x22*x23 + x23^2 + x1*x24 + x2*x24 - x4*x24 + x5*x24 - x7*x24 - x8*x24 + x9*x24 + x10*x24 - x11*x24 + x13*x24 + x15*x24 + x19*x24 + x21*x24 + x22*x24 + x23*x24 + x0*x25 + x1*x25 + x2*x25 - x3*x25 + x5*x25 - x6*x25 + x7*x25 + x8*x25 - x10*x25 + x11*x25 + x12*x25 + x13*x25 - x16*x25 - x17*x25 + x18*x25 - x19*x25 - x20*x25 - x21*x25 - x22*x25 + x24*x25 - x25^2 - x1*x26 + x3*x26 - x5*x26 - x7*x26 + x9*x26 - x17*x26 + x18*x26 + x22*x26 + x23*x26 - x24*x26 - x25*x26 - x3*x27 - x4*x27 + x7*x27 - x8*x27 - x9*x27 - x12*x27 + x14*x27 - x18*x27 + x19*x27 - x21*x27 + x22*x27 - x26*x27 + x1*x28 - x2*x28 + x3*x28 + x4*x28 - x5*x28 - x6*x28 + x7*x28 - x9*x28 + x10*x28 - x12*x28 + x13*x28 - x15*x28 - x16*x28 - x17*x28 + x20*x28 - x21*x28 + x23*x28 + x24*x28 - x26*x28 - x27*x28 - x28^2 - x0*x29 - x1*x29 + x4*x29 - x6*x29 + x7*x29 - x8*x29 - x9*x29 - x12*x29 - x15*x29 + x16*x29 + x17*x29 - x18*x29 - x19*x29 - x20*x29 + x23*x29 + x25*x29 - x26*x29 - x27*x29 - x28*x29 + x1*x30 + x4*x30 + x5*x30 + x7*x30 + x8*x30 - x9*x30 + x12*x30 - x16*x30 - x18*x30 - x19*x30 - x20*x30 + x23*x30 - x24*x30 + x25*x30 + x26*x30 + x30^2 - x0*x31 - x1*x31 - x2*x31 + x4*x31 + x5*x31 + x8*x31 + x12*x31 - x14*x31 + x15*x31 - x16*x31 - x17*x31 - x18*x31 + x20*x31 - x23*x31 + x27*x31 - x28*x31 + x30*x31 + x31^2 + x0*x32 - x1*x32 + x2*x32 + x3*x32 - x5*x32 - x8*x32 - x9*x32 + x11*x32 - x13*x32 - x14*x32 + x15*x32 - x16*x32 - x17*x32 + x18*x32 - x19*x32 + x20*x32 - x21*x32 - x23*x32 + x24*x32 + x26*x32 + x28*x32 - x29*x32 + x31*x32 - x0*x33 + x1*x33 - x3*x33 + x4*x33 - x5*x33 + x6*x33 - x8*x33 - x9*x33 - x11*x33 + x13*x33 - x14*x33 - x15*x33 - x16*x33 - x17*x33 - x18*x33 - x21*x33 - x22*x33 - x23*x33 + x25*x33 + x26*x33 - x27*x33 + x28*x33 - x29*x33 + x30*x33 + x32*x33 + x0*x34 + x2*x34 + x3*x34 + x4*x34 - x5*x34 + x6*x34 + x7*x34 + x8*x34 + x9*x34 - x13*x34 - x14*x34 - x15*x34 + x17*x34 + x19*x34 - x20*x34 + x22*x34 - x29*x34 - x30*x34 + x31*x34 + x32*x34 - x33*x34 - x34^2 + x1*x35 + x2*x35 + x4*x35 + x5*x35 - x6*x35 + x11*x35 + x13*x35 - x14*x35 + x17*x35 - x18*x35 - x24*x35 - x25*x35 + x27*x35 + x29*x35 + x32*x35 + x34*x35 - x35^2 - x0*x36 + x2*x36 + x5*x36 - x7*x36 - x8*x36 - x11*x36 + x12*x36 - x14*x36 + x15*x36 - x16*x36 - x17*x36 - x19*x36 - x20*x36 - x21*x36 + x22*x36 - x24*x36 - x25*x36 + x26*x36 + x28*x36 - 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x26*x40 + x28*x40 - x29*x40 - x32*x40 + x33*x40 + x34*x40 - x35*x40 - x37*x40 + x38*x40 - x40^2 + x0*x41 - x1*x41 - x4*x41 + x5*x41 - x6*x41 + x7*x41 + x8*x41 + x9*x41 + x10*x41 - x11*x41 - x12*x41 - x16*x41 + x17*x41 + x20*x41 - x21*x41 + x22*x41 - x23*x41 + x24*x41 + x26*x41 - x27*x41 + x29*x41 - x30*x41 - x31*x41 - x32*x41 - x33*x41 + x34*x41 - x35*x41 - x36*x41 - x37*x41 - x38*x41 + x39*x41 + x40*x41 + x1*x42 + x2*x42 + x4*x42 - x5*x42 - x6*x42 + x8*x42 + x11*x42 - x12*x42 - x14*x42 - x16*x42 - x17*x42 + x18*x42 + x20*x42 + x21*x42 + x22*x42 - x23*x42 - x24*x42 + x27*x42 + x29*x42 - x30*x42 + x33*x42 + x34*x42 + x36*x42 + x37*x42 + x38*x42 - x39*x42 - x40*x42 + x41*x42 - x0*x43 + x2*x43 + x3*x43 - x5*x43 + x6*x43 - x7*x43 + x9*x43 + x10*x43 + x11*x43 + x12*x43 + x13*x43 - x16*x43 - x17*x43 - x18*x43 + x21*x43 - x23*x43 + x24*x43 + x25*x43 + x26*x43 + x28*x43 + x31*x43 - x32*x43 + x33*x43 + x34*x43 + x35*x43 + x36*x43 - x37*x43 - x39*x43 + x40*x43 + x41*x43 - x43^2 + x0*x44 - x1*x44 - 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x9*x50 - x11*x50 - x12*x50 - x13*x50 - x14*x50 + x17*x50 + x18*x50 - x19*x50 + x20*x50 + x21*x50 - x25*x50 - x28*x50 - x29*x50 - x30*x50 - x31*x50 - x32*x50 - x34*x50 - x35*x50 - x36*x50 - x39*x50 + x40*x50 - x41*x50 - x43*x50 - x46*x50 + x47*x50 + x49*x50 - x50^2 + x2*x51 + x3*x51 + x4*x51 + x5*x51 - x8*x51 - x12*x51 - x13*x51 - x14*x51 - x15*x51 + x17*x51 + x18*x51 + x19*x51 - x20*x51 - x23*x51 - x28*x51 - x29*x51 + x30*x51 + x31*x51 + x32*x51 - x33*x51 - x34*x51 - x35*x51 - x37*x51 - x38*x51 + x41*x51 - x42*x51 - x45*x51 - x46*x51 + x47*x51 + x48*x51 - x49*x51 - x51^2 + x0*x52 - x2*x52 - x3*x52 + x4*x52 - x5*x52 + x6*x52 + x7*x52 - x8*x52 + x10*x52 - x11*x52 + x12*x52 - x13*x52 + x14*x52 + x15*x52 - x16*x52 + x18*x52 + x19*x52 - x20*x52 - x21*x52 + x22*x52 - x26*x52 - x27*x52 - x28*x52 + x29*x52 + x30*x52 - x32*x52 + x33*x52 + x34*x52 + x35*x52 - x36*x52 - x38*x52 + x40*x52 + x41*x52 + x42*x52 - x43*x52 + x44*x52 - x45*x52 + x46*x52 - x47*x52 - x48*x52 + x49*x52 + x50*x52 + x51*x52 + x52^2 - x1*x53 + x3*x53 + x4*x53 - x6*x53 + x7*x53 - x9*x53 - x10*x53 + x11*x53 - x12*x53 - x13*x53 - x14*x53 + x15*x53 + x16*x53 + x17*x53 - x18*x53 + x22*x53 - x23*x53 + x25*x53 + x26*x53 - x27*x53 + x28*x53 - x29*x53 - x32*x53 + x33*x53 + x34*x53 + x35*x53 - x37*x53 + x38*x53 - x40*x53 - x43*x53 - x45*x53 + x46*x53 + x47*x53 - x48*x53 + x49*x53 - x50*x53 + x51*x53 - x52*x53 + x53^2 - x1*x54 + x3*x54 - x4*x54 - x9*x54 + x13*x54 - x15*x54 - x17*x54 + x19*x54 - x20*x54 + x21*x54 - x22*x54 + x27*x54 + x28*x54 + x29*x54 + x31*x54 - x33*x54 + x35*x54 + x36*x54 - x37*x54 - x38*x54 + x39*x54 + x40*x54 - x41*x54 + x43*x54 - x44*x54 - x45*x54 + x49*x54 - x50*x54 - x51*x54 + x0*x55 + x2*x55 - x3*x55 + x4*x55 + x6*x55 + x7*x55 + x8*x55 - x9*x55 - x11*x55 - x12*x55 - x16*x55 + x17*x55 - x18*x55 - x19*x55 + x21*x55 - x22*x55 + x24*x55 + x26*x55 - x27*x55 - x28*x55 - x29*x55 - x30*x55 + x31*x55 + x32*x55 + x34*x55 - x37*x55 - x38*x55 - x40*x55 + x41*x55 - x43*x55 - x46*x55 + x47*x55 - x50*x55 - x51*x55 + x53*x55 + x54*x55 - x0*x56 - x2*x56 - x3*x56 + x4*x56 + x6*x56 + x9*x56 + x10*x56 + x11*x56 + x13*x56 + x14*x56 - x15*x56 + x16*x56 + x17*x56 - x18*x56 - x19*x56 + x20*x56 - x22*x56 - x24*x56 + x25*x56 - x26*x56 - x27*x56 + x28*x56 - x29*x56 + x31*x56 - x32*x56 - x35*x56 + x36*x56 - x38*x56 - x39*x56 + x42*x56 - x43*x56 + x44*x56 - x45*x56 + x46*x56 - x47*x56 - x49*x56 + x52*x56 - x53*x56 + x54*x56 - x55*x56 + x0*x57 + x1*x57 - x3*x57 + x4*x57 + x5*x57 + x6*x57 + x7*x57 - x9*x57 - x10*x57 + x11*x57 - x12*x57 - x14*x57 - x15*x57 - x16*x57 + x17*x57 + x19*x57 + x20*x57 - x22*x57 + x23*x57 - x24*x57 + x26*x57 - x32*x57 + x33*x57 + x36*x57 - x42*x57 + x44*x57 - x45*x57 - x46*x57 - x47*x57 - x50*x57 - x51*x57 + x52*x57 - x53*x57 + x56*x57 + x1*x58 + x2*x58 + x3*x58 + x4*x58 - x5*x58 + x7*x58 + x8*x58 - x9*x58 - x12*x58 + x13*x58 - x14*x58 - x15*x58 - x19*x58 - x20*x58 - x21*x58 - x24*x58 - x27*x58 + x28*x58 - x30*x58 + x31*x58 + x32*x58 - x33*x58 - x34*x58 - x35*x58 + x37*x58 + x41*x58 + x42*x58 + x45*x58 + x47*x58 + x48*x58 + x49*x58 - x51*x58 + x55*x58 + x56*x58 - x58^2 - x0 + x1 + x2 - x5 + x6 + x8 - x9 - x10 - x11 + x12 + x13 - x14 - x15 + x17 - x18 - x19 + x20 + x21 + x22 - x25 + x28 + x29 + x30 + x32 - x33 - x34 + x35 - x36 + x37 - x38 + x42 - x44 + x45 - x46 - x50 + x51 + x54 + x56 - x57 + x58 + 1) | |
| [(2, 1, 1, 1, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 1, 2, 2, 1, 0, 0, 1, 2, 0, 2, 0, 2, 1, 0, 2, 0, 1, 2, 2, 1, 0, 1, 2, 0, 2, 1, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 1, 2, 0, 0, 2, 2, 1, 1, 0, 1, 0, 2, 1, 2, 2, 1, 0, 1, 1, 2, 0, 1, 0, 2), (0, 1, 1, 1, 1, 2, 2, 0, 2, 0, 1, 2, 1, 1, 0, 2, 2, 1, 0, 0, 0, 2, 0, 2, 2, 0, 1, 2, 1, 1, 2, 1, 1, 0, 2, 1, 2, 1, 2, 2, 1, 2, 0, 1, 1, 0, 0, 2, 1, 0, 1, 2, 0, 2, 0, 0, 0, 0, 2, 1, 2, 0, 1, 1, 1, 1, 2, 0, 0, 0, 2, 1, 0, 2, 1), (2, 2, 0, 0, 1, 1, 0, 2, 2, 2, 1, 2, 2, 2, 0, 0, 0, 1, 2, 1, 1, 2, 0, 2, 1, 2, 0, 1, 0, 2, 1, 0, 2, 0, 1, 2, 1, 0, 0, 0, 0, 1, 0, 2, 2, 1, 0, 2, 0, 2, 2, 0, 2, 2, 1, 1, 0, 2, 0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 0, 1, 1, 1, 0, 1, 2), (2, 0, 0, 2, 2, 2, 2, 0, 1, 2, 2, 2, 0, 0, 1, 0, 2, 2, 0, 2, 2, 1, 0, 0, 1, 1, 2, 0, 2, 0, 2, 0, 1, 0, 1, 0, 2, 1, 2, 2, 2, 0, 1, 1, 0, 2, 0, 0, 1, 0, 2, 1, 2, 2, 1, 1, 1, 0, 1, 2, 2, 1, 2, 1, 2, 0, 0, 1, 2, 0, 1, 1, 0, 2, 1), (0, 0, 2, 1, 0, 2, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 2, 0, 1, 1, 0, 2, 1, 0, 1, 2, 2, 1, 0, 1, 2, 2, 1, 2, 0, 1, 0, 1, 0, 0, 1, 0, 2, 2, 0, 1, 2, 2, 2, 0, 2, 2, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2, 1, 1), (0, 0, 2, 0, 0, 1, 1, 2, 1, 0, 2, 2, 2, 2, 0, 0, 0, 1, 2, 1, 0, 1, 1, 0, 2, 0, 2, 2, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0, 2, 1, 1, 2, 2, 1, 2, 1, 0, 2, 0, 0, 1, 2, 1, 1, 0)] |
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