diff --git a/proof_of_equivalence/.ipynb_checkpoints/Anemoi 2-to-1-checkpoint.ipynb b/proof_of_equivalence/.ipynb_checkpoints/Anemoi 2-to-1-checkpoint.ipynb new file mode 100644 index 0000000..fa1b204 --- /dev/null +++ b/proof_of_equivalence/.ipynb_checkpoints/Anemoi 2-to-1-checkpoint.ipynb @@ -0,0 +1,949 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 3, + "id": "50885b34", + "metadata": {}, + "outputs": [], + "source": [ + "# BLS12-381 Base field\n", + "BLS12_381_BASEFIELD = 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab\n", + "# BLS12-381 Scalar field\n", + "BLS12_381_SCALARFIELD = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001\n", + "\n", + "# BLS12-377 Base field = BW6_761 Scalar field\n", + "BLS12_377_BASEFIELD = 0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d44300000008508c00000000001\n", + "# BLS12-377 Scalar field = Ed_on_bls_12_377 Base field\n", + "BLS12_377_SCALARFIELD = 0x12ab655e9a2ca55660b44d1e5c37b00159aa76fed00000010a11800000000001\n", + "\n", + "# BN-254 Base field\n", + "BN_254_BASEFIELD = 0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47\n", + "# BN-254 Scalar field\n", + "BN_254_SCALARFIELD = 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001\n", + "\n", + "# Pallas Base field = Vesta Scalar field\n", + "PALLAS_BASEFIELD = 0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001\n", + "\n", + "# Vesta Base field = Pallas Scalar field\n", + "VESTA_BASEFIELD = 0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001\n", + "\n", + "# Small Goldilocks field\n", + "GOLDILOCKS_64_FIELD = 0xffffffff00000001" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "23180928", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "c309f191", + "metadata": {}, + "outputs": [], + "source": [ + "from sage.all import *\n", + "import hashlib\n", + "import itertools\n", + "\n", + "\n", + "COST_ALPHA = {\n", + " 3 : 2, 5 : 3, 7 : 4, 9 : 4,\n", + " 11 : 5, 13 : 5, 15 : 5, 17 : 5,\n", + " 19 : 6, 21 : 6, 23 : 6, 25 : 6,\n", + " 27 : 6, 29 : 7, 31 : 7, 33 : 6,\n", + " 35 : 7, 37 : 7, 39 : 7, 41 : 7,\n", + " 43 : 7, 45 : 7, 47 : 8, 49 : 7,\n", + " 51 : 7, 53 : 8, 55 : 8, 57 : 8,\n", + " 59 : 8, 61 : 8, 63 : 8, 65 : 7,\n", + " 67 : 8, 69 : 8, 71 : 9, 73 : 8,\n", + " 75 : 8, 77 : 8, 79 : 9, 81 : 8,\n", + " 83 : 8, 85 : 8, 87 : 9, 89 : 9,\n", + " 91 : 9, 93 : 9, 95 : 9, 97 : 8,\n", + " 99 : 8, 101 : 9, 103 : 9, 105 : 9,\n", + " 107 : 9, 109 : 9, 111 : 9, 113 : 9,\n", + " 115 : 9, 117 : 9, 119 : 9, 121 : 9,\n", + " 123 : 9, 125 : 9, 127 : 10,\n", + "}\n", + "\n", + "ALPHA_BY_COST = {\n", + " c : [x for x in range(3, 128, 2) if COST_ALPHA[x] == c]\n", + " for c in range(2, 11)\n", + "}\n", + "\n", + "PI_0 = 1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679\n", + "PI_1 = 8214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196\n", + "\n", + "def get_prime(N):\n", + " result = (1 << N) - 1\n", + " while not is_prime(result):\n", + " result -= 2\n", + " return result\n", + "\n", + "\n", + "def get_n_rounds(s, l, alpha):\n", + " r = 0\n", + " complexity = 0\n", + " kappa = {3:1, 5:2, 7:4, 9:7, 11:9}\n", + " assert alpha in kappa\n", + " while complexity < 2**s:\n", + " r += 1\n", + " complexity = binomial(\n", + " 4*l*r + kappa[alpha],\n", + " 2*l*r\n", + " )**2\n", + " r += 2 # considering the second model\n", + " r += min(5,l+1) # security margin\n", + " \n", + " return max(8, r)\n", + "\n", + "\n", + "# Linear layer generation\n", + "\n", + "def is_mds(m):\n", + " # Uses the Laplace expansion of the determinant to calculate the (m+1)x(m+1) minors in terms of the mxm minors.\n", + " # Taken from https://github.com/mir-protocol/hash-constants/blob/master/mds_search.sage.\n", + "\n", + " # 1-minors are just the elements themselves\n", + " if any(any(r == 0 for r in row) for row in m):\n", + " return False\n", + "\n", + " N = m.nrows()\n", + " assert m.is_square() and N >= 2\n", + "\n", + " det_cache = m\n", + "\n", + " # Calculate all the nxn minors of m:\n", + " for n in range(2, N+1):\n", + " new_det_cache = dict()\n", + " for rows in itertools.combinations(range(N), n):\n", + " for cols in itertools.combinations(range(N), n):\n", + " i, *rs = rows\n", + "\n", + " # Laplace expansion along row i\n", + " det = 0\n", + " for j in range(n):\n", + " # pick out c = column j; the remaining columns are in cs\n", + " c = cols[j]\n", + " cs = cols[:j] + cols[j+1:]\n", + "\n", + " # Look up the determinant from the previous iteration\n", + " # and multiply by -1 if j is odd\n", + " cofactor = det_cache[(*rs, *cs)]\n", + " if j % 2 == 1:\n", + " cofactor = -cofactor\n", + "\n", + " # update the determinant with the j-th term\n", + " det += m[i, c] * cofactor\n", + "\n", + " if det == 0:\n", + " return False\n", + " new_det_cache[(*rows, *cols)] = det\n", + " det_cache = new_det_cache\n", + " return True\n", + "\n", + "def M_2(x_input, b):\n", + " x = x_input[:]\n", + " x[0] += b*x[1]\n", + " x[1] += b*x[0]\n", + " return x\n", + "\n", + "def M_3(x_input, b):\n", + " x = x_input[:]\n", + " t = x[0] + b*x[2]\n", + " x[2] += x[1]\n", + " x[2] += b*x[0]\n", + " x[0] = t + x[2]\n", + " x[1] += t\n", + " return x\n", + "\n", + "\n", + "def M_4(x_input, b):\n", + " x = x_input[:]\n", + " x[0] += x[1]\n", + " x[2] += x[3]\n", + " x[3] += b*x[0]\n", + " x[1] = b*(x[1] + x[2])\n", + " x[0] += x[1]\n", + " x[2] += b*x[3]\n", + " x[1] += x[2]\n", + " x[3] += x[0]\n", + " return x\n", + "\n", + "def lfsr(x_input, b):\n", + " x = x_input[:]\n", + " l = len(x)\n", + " for r in range(0, l):\n", + " t = sum(b**(2**i) * x[i] for i in range(0, l))\n", + " x = x[1:] + [t]\n", + " return x\n", + "\n", + "def circulant_mds_matrix(field, l, coeff_upper_limit=None):\n", + " if coeff_upper_limit == None:\n", + " coeff_upper_limit = l+1\n", + " assert(coeff_upper_limit > l)\n", + " for v in itertools.combinations_with_replacement(range(1,coeff_upper_limit), l):\n", + " mat = matrix.circulant(list(v)).change_ring(field)\n", + " if is_mds(mat):\n", + " return(mat)\n", + " # In some cases, the method won't return any valid matrix,\n", + " # hence the need to increase the limit further.\n", + " return circulant_mds_matrix(field, l, coeff_upper_limit+1)\n", + "\n", + "def get_mds(field, l):\n", + " if l == 1:\n", + " return identity_matrix(field, 1)\n", + " if l <= 4: # low addition case\n", + " a = field.multiplicative_generator()\n", + " b = field.one()\n", + " t = 0\n", + " while True:\n", + " # we construct the matrix\n", + " mat = []\n", + " b = b*a\n", + " t += 1\n", + " for i in range(0, l):\n", + " x_i = [field.one() * (j == i) for j in range(0, l)]\n", + " if l == 2:\n", + " mat.append(M_2(x_i, b))\n", + " elif l == 3:\n", + " mat.append(M_3(x_i, b))\n", + " elif l == 4:\n", + " mat.append(M_4(x_i, b))\n", + " mat = Matrix(field, l, l, mat).transpose()\n", + " if is_mds(mat):\n", + " return mat\n", + " else: # circulant matrix case\n", + " return circulant_mds_matrix(field, l)\n", + "\n", + "# AnemoiPermutation class\n", + "\n", + "class AnemoiPermutation:\n", + " def __init__(self,\n", + " q=None,\n", + " alpha=None,\n", + " mat=None,\n", + " n_rounds=None,\n", + " n_cols=1,\n", + " security_level=128):\n", + " if q == None:\n", + " raise Exception(\"The characteristic of the field must be specified!\")\n", + " self.q = q\n", + " self.prime_field = is_prime(q) # if true then we work over a\n", + " # prime field with\n", + " # characteristic just under\n", + " # 2**N, otherwise the\n", + " # characteristic is 2**self\n", + " self.n_cols = n_cols # the number of parallel S-boxes in each round\n", + " self.security_level = security_level\n", + "\n", + " # initializing the other variables in the state:\n", + " # - q is the characteristic of the field\n", + " # - g is a generator of the multiplicative subgroup\n", + " # - alpha is the main exponent (in the center of the Flystel)\n", + " # - beta is the coefficient in the quadratic subfunction\n", + " # - gamma is the constant in the second quadratic subfunction\n", + " # - QUAD is the secondary (quadratic) exponent\n", + " # - from_field is a function mapping field elements to integers\n", + " # - to_field is a function mapping integers to field elements\n", + " self.F = GF(self.q)\n", + " if self.prime_field:\n", + " if alpha != None:\n", + " if gcd(alpha, self.q-1) != 1:\n", + " raise Exception(\"alpha should be co-prime with the characteristic!\")\n", + " else:\n", + " self.alpha = alpha\n", + " else:\n", + " self.alpha = 3\n", + " while gcd(self.alpha, self.q-1) != 1:\n", + " self.alpha += 1\n", + " self.QUAD = 2\n", + " self.to_field = lambda x : self.F(x)\n", + " self.from_field = lambda x : Integer(x)\n", + " else:\n", + " self.alpha = 3\n", + " self.QUAD = 3\n", + " self.to_field = lambda x : self.F.fetch_int(x)\n", + " self.from_field = lambda x : x.integer_representation()\n", + " self.g = self.F.multiplicative_generator()\n", + " self.beta = self.g\n", + " self.delta = self.g**(-1)\n", + " self.alpha_inv = inverse_mod(self.alpha, self.q-1)\n", + "\n", + " # total number of rounds\n", + " if n_rounds != None:\n", + " self.n_rounds = n_rounds\n", + " else:\n", + " self.n_rounds = get_n_rounds(self.security_level,\n", + " self.n_cols,\n", + " self.alpha)\n", + "\n", + " # Choosing constants: self.C and self.D are built from the\n", + " # digits of pi using an open butterfly\n", + " self.C = []\n", + " self.D = []\n", + " pi_F_0 = self.to_field(PI_0 % self.q)\n", + " pi_F_1 = self.to_field(PI_1 % self.q)\n", + " for r in range(0, self.n_rounds):\n", + " pi_0_r = pi_F_0**r\n", + " self.C.append([])\n", + " self.D.append([])\n", + " for i in range(0, self.n_cols):\n", + " pi_1_i = pi_F_1**i\n", + " pow_alpha = (pi_0_r + pi_1_i)**self.alpha\n", + " self.C[r].append(self.g * (pi_0_r)**2 + pow_alpha)\n", + " self.D[r].append(self.g * (pi_1_i)**2 + pow_alpha + self.delta)\n", + " self.mat = get_mds(self.F, self.n_cols)\n", + "\n", + "\n", + " def __str__(self):\n", + " result = \"Anemoi instance over F_{:d} ({}), n_rounds={:d}, n_cols={:d}, s={:d}\".format(\n", + " self.q,\n", + " \"odd prime field\" if self.prime_field else \"characteristic 2\",\n", + " self.n_rounds,\n", + " self.n_cols,\n", + " self.security_level\n", + " )\n", + " result += \"\\nalpha={}, beta={}, \\ndelta={}\\nM_x=\\n{}\\ninv_alpha={}\\n\".format(\n", + " self.alpha,\n", + " self.beta,\n", + " self.delta,\n", + " self.mat,\n", + " self.alpha_inv\n", + " )\n", + " result += \"C={}\\nD={}\".format(\n", + " [[self.from_field(x) for x in self.C[r]] for r in range(0, self.n_rounds)],\n", + " [[self.from_field(x) for x in self.D[r]] for r in range(0, self.n_rounds)],\n", + " )\n", + " return result\n", + "\n", + "\n", + " # !SECTION! Sub-components\n", + "\n", + " def evaluate_sbox(self, _x, _y):\n", + " x, y = _x, _y\n", + " x -= self.beta*y**self.QUAD\n", + " y -= x**self.alpha_inv\n", + " x += self.beta*y**self.QUAD + self.delta\n", + " return x, y\n", + "\n", + " def linear_layer(self, _x, _y):\n", + " x, y = _x[:], _y[:]\n", + " x = self.mat*vector(x)\n", + " y = self.mat*vector(y[1:] + [y[0]])\n", + "\n", + " # Pseudo-Hadamard transform on each (x,y) pair\n", + " y += x\n", + " x += y\n", + " return list(x), list(y)\n", + "\n", + "\n", + " # !SECTION! Evaluation\n", + "\n", + " def eval_with_intermediate_values(self, _x, _y):\n", + " x, y = _x[:], _y[:]\n", + " result = [[x[:], y[:]]]\n", + " for r in range(0, self.n_rounds):\n", + " for i in range(0, self.n_cols):\n", + " x[i] += self.C[r][i]\n", + " y[i] += self.D[r][i]\n", + " x, y = self.linear_layer(x, y)\n", + " for i in range(0, self.n_cols):\n", + " x[i], y[i] = self.evaluate_sbox(x[i], y[i])\n", + " result.append([x[:], y[:]])\n", + " # final call to the linear layer\n", + " x, y = self.linear_layer(x, y)\n", + " result.append([x[:], y[:]])\n", + " return result\n", + "\n", + "\n", + " def input_size(self):\n", + " return 2*self.n_cols\n", + "\n", + "\n", + " def __call__(self, _x):\n", + " if len(_x) != self.input_size():\n", + " raise Exception(\"wrong input size!\")\n", + " else:\n", + " x, y = _x[:self.n_cols], _x[self.n_cols:]\n", + " u, v = self.eval_with_intermediate_values(x, y)[-1]\n", + " return u + v # concatenation, not a sum\n", + "\n", + "\n", + " # !SECTION! Writing full system of equations\n", + "\n", + " def get_polynomial_variables(self):\n", + " x_vars = []\n", + " y_vars = []\n", + " all_vars = []\n", + " for r in range(0, self.n_rounds+1):\n", + " x_vars.append([\"X{:02d}{:02d}\".format(r, i) for i in range(0, self.n_cols)])\n", + " y_vars.append([\"Y{:02d}{:02d}\".format(r, i) for i in range(0, self.n_cols)])\n", + " all_vars += x_vars[-1]\n", + " all_vars += y_vars[-1]\n", + " pol_ring = PolynomialRing(self.F, (self.n_rounds+1)*2*self.n_cols, all_vars)\n", + " pol_gens = pol_ring.gens()\n", + " result = {\"X\" : [], \"Y\" : []}\n", + " for r in range(0, self.n_rounds+1):\n", + " result[\"X\"].append([])\n", + " result[\"Y\"].append([])\n", + " for i in range(0, self.n_cols):\n", + " result[\"X\"][r].append(pol_gens[self.n_cols*2*r + i])\n", + " result[\"Y\"][r].append(pol_gens[self.n_cols*2*r + i + self.n_cols])\n", + " return result\n", + "\n", + "\n", + " def verification_polynomials(self, pol_vars):\n", + " equations = []\n", + " for r in range(0, self.n_rounds):\n", + " # the outputs of the open flystel are the state variables x, y at round r+1\n", + " u = pol_vars[\"X\"][r+1]\n", + " v = pol_vars[\"Y\"][r+1]\n", + " # the inputs of the open flystel are the state variables\n", + " # x, y at round r after undergoing the constant addition\n", + " # and the linear layer\n", + " x, y = pol_vars[\"X\"][r], pol_vars[\"Y\"][r]\n", + " x = [x[i] + self.C[r][i] for i in range(0, self.n_cols)]\n", + " y = [y[i] + self.D[r][i] for i in range(0, self.n_cols)]\n", + " x, y = self.linear_layer(x, y)\n", + " for i in range(0, self.n_cols):\n", + " equations.append(\n", + " (y[i]-v[i])**self.alpha + self.beta*y[i]**self.QUAD - x[i]\n", + " )\n", + " equations.append(\n", + " (y[i]-v[i])**self.alpha + self.beta*v[i]**self.QUAD + self.delta - u[i]\n", + " )\n", + " return equations\n", + "\n", + "\n", + " def print_verification_polynomials(self):\n", + " p_vars = self.get_polynomial_variables()\n", + " eqs = self.verification_polynomials(p_vars)\n", + " variables_string = \"\"\n", + " for r in range(0, self.n_rounds+1):\n", + " variables_string += str(p_vars[\"X\"][r])[1:-1] + \",\" + str(p_vars[\"Y\"][r])[1:-1] + \",\"\n", + " print(variables_string[:-1].replace(\" \", \"\"))\n", + " print(self.q)\n", + " for f in eqs:\n", + " print(f)\n", + "\n", + "\n", + "\n", + "# !SECTION! Modes of operation\n", + "\n", + "\n", + "def jive(P, b, _x):\n", + " if b < 2:\n", + " raise Exception(\"b must be at least equal to 2\")\n", + " if P.input_size() % b != 0:\n", + " raise Exception(\"b must divide the input size!\")\n", + " c = P.input_size()/b # length of the compressed output\n", + " # Output size check: we allow the output size to be 3 bits shorter than\n", + " # the theoretical target, as commonly used finite fields usually have a\n", + " # characteristic size slightly under 2**256.\n", + " if c * P.F.cardinality().nbits() < 2 * P.security_level - 3:\n", + " raise Exception(f\"digest size is too small for the targeted security level!\")\n", + " x = _x[:]\n", + " u = P(x)\n", + " compressed = []\n", + " for i in range(0, c):\n", + " compressed.append(sum(x[i+c*j] + u[i+c*j]\n", + " for j in range(0, b)))\n", + " return compressed\n", + "\n", + "\n", + "def sponge_hash(P, r, h, _x):\n", + " x = _x[:]\n", + " if P.input_size() <= r:\n", + " raise Exception(\"rate must be strictly smaller than state size!\")\n", + " # Digest size and capacity check: we allow the digest size to be 3 bits\n", + " # shorter than the theoretical target, as commonly used finite fields\n", + " # usually have a characteristic size slightly under 2**256.\n", + " if h * P.F.cardinality().nbits() < 2 * P.security_level - 3:\n", + " raise Exception(f\"digest size is too small for the targeted security level!\")\n", + " capacity = P.input_size() - r\n", + " if capacity * P.F.cardinality().nbits() < 2 * P.security_level - 3:\n", + " raise Exception(f\"capacity is too small for the targeted security level!\")\n", + "\n", + " # message padding (and domain separator computation)\n", + " if len(x) % r == 0 and len(x) != 0:\n", + " sigma = 1\n", + " else:\n", + " sigma = 0\n", + " x += [1]\n", + " # if x is still not long enough, append 0s\n", + " if len(x) % r != 0:\n", + " x += (r - (len(x) % r))*[0]\n", + " padded_x = [[x[pos+i] for i in range(0, r)]\n", + " for pos in range(0, len(x), r)]\n", + " # absorption phase\n", + " internal_state = [0] * P.input_size()\n", + " for pos in range(0, len(padded_x)):\n", + " for i in range(0, r):\n", + " internal_state[i] += padded_x[pos][i]\n", + " internal_state = P(internal_state)\n", + " if pos == len(padded_x)-1:\n", + " # adding sigma if it is the last block\n", + " internal_state[-1] += sigma\n", + " # squeezing\n", + " digest = []\n", + " pos = 0\n", + " while len(digest) < h:\n", + " digest.append(internal_state[pos])\n", + " pos += 1\n", + " if pos == r:\n", + " pos = 0\n", + " internal_state = P(internal_state)\n", + " return digest\n", + "\n", + "\n", + "# !SECTION! Tests\n", + "\n", + "def check_polynomial_verification(n_tests=10, q=2**63, alpha=3, n_rounds=3, n_cols=1):\n", + " A = AnemoiPermutation(q=q, alpha=alpha, n_rounds=n_rounds, n_cols=n_cols)\n", + " # formal polynomial variables and equations\n", + " p_vars = A.get_polynomial_variables()\n", + " eqs = A.verification_polynomials(p_vars)\n", + " A.print_verification_polynomials()\n", + " # for n_tests random inputs, we check that the equations are\n", + " # coherent with the actual intermediate values\n", + " print(\"\\n ======== Verification:\")\n", + " print(A)\n", + " print(\"{} equations in {} variables.\".format(\n", + " len(eqs),\n", + " (A.n_rounds+1) * 2 * A.n_cols,\n", + " ))\n", + " for t in range(0, n_tests):\n", + " # generate random input\n", + " x = [A.to_field(randint(0, A.q - 1))\n", + " for i in range(0, A.n_cols)]\n", + " y = [A.to_field(randint(0, A.q - 1))\n", + " for i in range(0, A.n_cols)]\n", + " # generate intermediate values, formal polynomial variables,\n", + " # and equations\n", + " iv = A.eval_with_intermediate_values(x, y)\n", + " p_vars = A.get_polynomial_variables()\n", + " eqs = A.verification_polynomials(p_vars)\n", + " # obtain variable assignment from the actual evaluation\n", + " assignment = {}\n", + " for r in range(0, A.n_rounds+1):\n", + " for i in range(0, A.n_cols):\n", + " assignment[p_vars[\"X\"][r][i]] = iv[r][0][i]\n", + " assignment[p_vars[\"Y\"][r][i]] = iv[r][1][i]\n", + " # printing the value of the equations for the actual\n", + " # intermediate states\n", + " print(\"\\n--- \", t, \"(all values except the input should be 0)\")\n", + " print(\"input: \", x, y)\n", + " for r in range(0, A.n_rounds):\n", + " polynomial_values = [eqs[r*2*A.n_cols + i].subs(assignment)\n", + " for i in range(0, 2*A.n_cols)]\n", + " print(\"round {:3d}: {}\\n {}\".format(\n", + " r,\n", + " polynomial_values[0::2],\n", + " polynomial_values[1::2]\n", + " ))\n", + "\n", + "\n", + "def test_jive(n_tests=10,\n", + " q=2**63, alpha=3,\n", + " n_rounds=None,\n", + " n_cols=1,\n", + " b=2,\n", + " security_level=32):\n", + " A = AnemoiPermutation(q=q, alpha=alpha, n_rounds=n_rounds, n_cols=n_cols, security_level=security_level)\n", + " print(A)\n", + " for t in range(0, n_tests):\n", + " # generate random input\n", + " x = [A.to_field(randint(0, A.q - 1))\n", + " for i in range(0, A.n_cols)]\n", + " y = [A.to_field(randint(0, A.q - 1))\n", + " for i in range(0, A.n_cols)]\n", + " print(\"x = {}\\ny = {}\\nAnemoiJive_{}(x,y) = {}\".format(\n", + " x,\n", + " y,\n", + " b,\n", + " jive(A, b, x + y)\n", + " ))\n", + "\n", + "\n", + "def test_sponge(n_tests=10,\n", + " q=2**63,\n", + " alpha=3,\n", + " n_rounds=None,\n", + " n_cols=1,\n", + " b=2,\n", + " security_level=32):\n", + " A = AnemoiPermutation(q=q, alpha=alpha, n_rounds=n_rounds, n_cols=n_cols, security_level=security_level)\n", + " print(A)\n", + " for t in range(0, n_tests):\n", + " # generate random input of length t\n", + " x = [A.to_field(randint(0, A.q - 1))\n", + " for i in range(0, t)]\n", + " print(\"x = {}\\nAnemoiSponge(x) = {}\".format(\n", + " x,\n", + " sponge_hash(A, 2, 2, x)\n", + " ))\n", + "\n", + "def generate_test_vectors_jive(P, b, n):\n", + " assert n >= 4, \"The number of test vectors should be greater than 4.\"\n", + " m = hashlib.sha512(str(P).encode())\n", + " m.update(\"Jive test vectors\".encode())\n", + " m.update(f\"B={b}\".encode())\n", + " seed = Integer(m.digest().hex(), 16)\n", + "\n", + " inputs = []\n", + " outputs = []\n", + " inputs.append([P.F(0) for _ in range(P.input_size())])\n", + " inputs.append([P.F(1) for _ in range(P.input_size())])\n", + " inputs.append([P.F(0) for _ in range(P.n_cols)] + [P.F(1) for _ in range(P.n_cols)])\n", + " inputs.append([P.F(1) for _ in range(P.n_cols)] + [P.F(0) for _ in range(P.n_cols)])\n", + " for i in range(n - 4):\n", + " input = []\n", + " for _ in range(P.input_size()):\n", + " input.append(P.to_field(seed))\n", + " m.update(str(seed).encode())\n", + " seed = Integer(m.digest().hex(), 16)\n", + " inputs.append(input)\n", + " for input in inputs:\n", + " outputs.append(jive(P, b, input))\n", + "\n", + " print(\n", + " \"Test vectors for Anemoi instance over F_{:d}, n_rounds={:d}, n_cols={:d}, s={:d}\".format(\n", + " P.q,\n", + " P.n_rounds,\n", + " P.n_cols,\n", + " P.security_level)\n", + " )\n", + " return (inputs, outputs)\n", + "\n", + "\n", + "def generate_test_vectors_sponge(P, r, h, n):\n", + " assert n >= 4, \"The number of test vectors should be greater than 4.\"\n", + " m = hashlib.sha512(str(P).encode())\n", + " m.update(\"Sponge test vectors\".encode())\n", + " m.update(f\"R={r}\".encode())\n", + " m.update(f\"H={h}\".encode())\n", + " seed = Integer(m.digest().hex(), 16)\n", + "\n", + " inputs = []\n", + " outputs = []\n", + " inputs.append([P.F(0) for _ in range(P.input_size())])\n", + " inputs.append([P.F(1) for _ in range(P.input_size())])\n", + " inputs.append([P.F(0) for _ in range(P.n_cols)] + [P.F(1) for _ in range(P.n_cols)])\n", + " inputs.append([P.F(1) for _ in range(P.n_cols)] + [P.F(0) for _ in range(P.n_cols)])\n", + " for i in range(n - 4):\n", + " input = []\n", + " for _ in range(i+1):\n", + " input.append(P.to_field(seed))\n", + " m.update(str(seed).encode())\n", + " seed = Integer(m.digest().hex(), 16)\n", + " inputs.append(input)\n", + " for input in inputs:\n", + " outputs.append(sponge_hash(P, r, h, input))\n", + "\n", + " print(\n", + " \"Test vectors for Anemoi instance over F_{:d}, n_rounds={:d}, n_cols={:d}, s={:d}\".format(\n", + " P.q,\n", + " P.n_rounds,\n", + " P.n_cols,\n", + " P.security_level)\n", + " )\n", + " return (inputs, outputs)\n", + "\n", + "\n", + "def generate_test_vectors_sbox(P, n):\n", + " assert n >= 4, \"The number of test vectors should be greater than 4.\"\n", + " m = hashlib.sha512(str(P).encode())\n", + " m.update(\"S-Box test vectors\".encode())\n", + " seed = Integer(m.digest().hex(), 16)\n", + "\n", + " inputs = []\n", + " outputs = []\n", + " inputs.append([P.F(0) for _ in range(P.input_size())])\n", + " inputs.append([P.F(1) for _ in range(P.input_size())])\n", + " inputs.append([P.F(0) for _ in range(P.n_cols)] + [P.F(1) for _ in range(P.n_cols)])\n", + " inputs.append([P.F(1) for _ in range(P.n_cols)] + [P.F(0) for _ in range(P.n_cols)])\n", + "\n", + " for _ in range(n - 4):\n", + " input = []\n", + " for _ in range(P.input_size()):\n", + " input.append(P.to_field(seed))\n", + " m.update(str(seed).encode())\n", + " seed = Integer(m.digest().hex(), 16)\n", + " inputs.append(input)\n", + " for input in inputs:\n", + " x = [0 for i in range(P.n_cols)]\n", + " y = [0 for i in range(P.n_cols)]\n", + " for i in range(P.n_cols):\n", + " x[i], y[i] = P.evaluate_sbox(input[i], input[P.n_cols + i])\n", + " x.extend(y)\n", + " outputs.append(x)\n", + "\n", + " return (inputs, outputs)\n", + "\n", + "\n", + "def generate_test_vectors_mds(P, n):\n", + " assert n >= 4, \"The number of test vectors should be greater than 4.\"\n", + " m = hashlib.sha512(str(P).encode())\n", + " m.update(\"MDS test vectors\".encode())\n", + " seed = Integer(m.digest().hex(), 16)\n", + "\n", + " inputs = []\n", + " outputs = []\n", + " inputs.append([P.F(0) for _ in range(P.input_size())])\n", + " inputs.append([P.F(1) for _ in range(P.input_size())])\n", + " inputs.append([P.F(0) for _ in range(P.n_cols)] + [P.F(1) for _ in range(P.n_cols)])\n", + " inputs.append([P.F(1) for _ in range(P.n_cols)] + [P.F(0) for _ in range(P.n_cols)])\n", + " for _ in range(n - 4):\n", + " input = []\n", + " for _ in range(P.input_size()):\n", + " input.append(P.to_field(seed))\n", + " m.update(str(seed).encode())\n", + " seed = Integer(m.digest().hex(), 16)\n", + " inputs.append(input)\n", + " for input in inputs:\n", + " x,y = P.linear_layer(input[0:P.n_cols], input[P.n_cols:])\n", + " x.extend(y)\n", + " outputs.append(x)\n", + "\n", + " return (inputs, outputs)\n", + "\n", + "\n", + "if __name__ == \"__main__\":\n", + "\n", + " # These are the first circulant matrices being found by the circulant_mds_matrix()\n", + " # method above. These are precomputed for faster initiatialization of large Anemoi\n", + " # instances.\n", + " CIRCULANT_FP5_MDS_MATRIX = matrix.circulant([1, 1, 3, 4, 5])\n", + " CIRCULANT_FP6_MDS_MATRIX = matrix.circulant([1, 1, 3, 4, 5, 6])\n", + " CIRCULANT_FP7_MDS_MATRIX = matrix.circulant([1, 2, 3, 5, 5, 6, 7])\n", + " CIRCULANT_FP8_MDS_MATRIX = matrix.circulant([1, 2, 3, 5, 7, 8, 8, 9])\n", + " CIRCULANT_FP9_MDS_MATRIX = matrix.circulant([1, 3, 5, 6, 8, 9, 9, 10, 11])\n", + " CIRCULANT_FP10_MDS_MATRIX = matrix.circulant([1, 2, 5, 6, 8, 11, 11, 12, 13, 14])\n", + "\n", + " # 128-bit security level instantiations\n", + "\n", + " A_BLS_12_381_BASEFIELD_1_COL_128_BITS = AnemoiPermutation(\n", + " q=BLS12_381_BASEFIELD,\n", + " n_cols=1,\n", + " security_level=128\n", + " )\n", + " A_BLS_12_381_BASEFIELD_2_COL_128_BITS = AnemoiPermutation(\n", + " q=BLS12_381_BASEFIELD,\n", + " n_cols=2,\n", + " security_level=128\n", + " )\n", + " A_BLS_12_381_BASEFIELD_3_COL_128_BITS = AnemoiPermutation(\n", + " q=BLS12_381_BASEFIELD,\n", + " n_cols=3,\n", + " security_level=128\n", + " )\n", + "\n", + " A_JUBJUB_BASEFIELD_1_COL_128_BITS = AnemoiPermutation(\n", + " q=BLS12_381_SCALARFIELD,\n", + " n_cols=1,\n", + " security_level=128\n", + " )\n", + " A_JUBJUB_BASEFIELD_2_COL_128_BITS = AnemoiPermutation(\n", + " q=BLS12_381_SCALARFIELD,\n", + " n_cols=2,\n", + " security_level=128\n", + " )\n", + " A_JUBJUB_BASEFIELD_3_COL_128_BITS = AnemoiPermutation(\n", + " q=BLS12_381_SCALARFIELD,\n", + " n_cols=3,\n", + " security_level=128\n", + " )\n", + "\n", + " A_BLS_12_377_BASEFIELD_1_COL_128_BITS = AnemoiPermutation(\n", + " q=BLS12_377_BASEFIELD,\n", + " n_cols=1,\n", + " security_level=128\n", + " )\n", + " A_BLS_12_377_BASEFIELD_2_COL_128_BITS = AnemoiPermutation(\n", + " q=BLS12_377_BASEFIELD,\n", + " n_cols=2,\n", + " security_level=128\n", + " )\n", + " A_BLS_12_377_BASEFIELD_3_COL_128_BITS = AnemoiPermutation(\n", + " q=BLS12_377_BASEFIELD,\n", + " n_cols=3,\n", + " security_level=128\n", + " )\n", + "\n", + " A_ED_ON_BLS_12_377_BASEFIELD_1_COL_128_BITS = AnemoiPermutation(\n", + " q=BLS12_377_SCALARFIELD,\n", + " n_cols=1,\n", + " security_level=128\n", + " )\n", + " A_ED_ON_BLS_12_377_BASEFIELD_2_COL_128_BITS = AnemoiPermutation(\n", + " q=BLS12_377_SCALARFIELD,\n", + " n_cols=2,\n", + " security_level=128\n", + " )\n", + " A_ED_ON_BLS_12_377_BASEFIELD_3_COL_128_BITS = AnemoiPermutation(\n", + " q=BLS12_377_SCALARFIELD,\n", + " n_cols=3,\n", + " security_level=128\n", + " )\n", + "\n", + " A_BN_254_BASEFIELD_1_COL_128_BITS = AnemoiPermutation(\n", + " q=BN_254_BASEFIELD,\n", + " n_cols=1,\n", + " security_level=128\n", + " )\n", + " A_BN_254_BASEFIELD_2_COL_128_BITS = AnemoiPermutation(\n", + " q=BN_254_BASEFIELD,\n", + " n_cols=2,\n", + " security_level=128\n", + " )\n", + " A_BN_254_BASEFIELD_3_COL_128_BITS = AnemoiPermutation(\n", + " q=BN_254_BASEFIELD,\n", + " n_cols=3,\n", + " security_level=128\n", + " )\n", + "\n", + " A_BN_254_SCALARFIELD_1_COL_128_BITS = AnemoiPermutation(\n", + " q=BN_254_SCALARFIELD,\n", + " n_cols=1,\n", + " security_level=128\n", + " )\n", + " A_BN_254_SCALARFIELD_2_COL_128_BITS = AnemoiPermutation(\n", + " q=BN_254_SCALARFIELD,\n", + " n_cols=2,\n", + " security_level=128\n", + " )\n", + " A_BN_254_SCALARFIELD_3_COL_128_BITS = AnemoiPermutation(\n", + " q=BN_254_SCALARFIELD,\n", + " n_cols=3,\n", + " security_level=128\n", + " )\n", + "\n", + " A_PALLAS_BASEFIELD_1_COL_128_BITS = AnemoiPermutation(\n", + " q=PALLAS_BASEFIELD,\n", + " n_cols=1,\n", + " security_level=128\n", + " )\n", + " A_PALLAS_BASEFIELD_2_COL_128_BITS = AnemoiPermutation(\n", + " q=PALLAS_BASEFIELD,\n", + " n_cols=2,\n", + " security_level=128\n", + " )\n", + " A_PALLAS_BASEFIELD_3_COL_128_BITS = AnemoiPermutation(\n", + " q=PALLAS_BASEFIELD,\n", + " n_cols=3,\n", + " security_level=128\n", + " )\n", + "\n", + " A_VESTA_BASEFIELD_1_COL_128_BITS = AnemoiPermutation(\n", + " q=VESTA_BASEFIELD,\n", + " n_cols=1,\n", + " security_level=128\n", + " )\n", + " A_VESTA_BASEFIELD_2_COL_128_BITS = AnemoiPermutation(\n", + " q=VESTA_BASEFIELD,\n", + " n_cols=2,\n", + " security_level=128\n", + " )\n", + " A_VESTA_BASEFIELD_3_COL_128_BITS = AnemoiPermutation(\n", + " q=VESTA_BASEFIELD,\n", + " n_cols=3,\n", + " security_level=128\n", + " )\n", + "\n", + " A_GOLDILOCKS_64_FIELD_4_COL_128_BITS = AnemoiPermutation(\n", + " q=GOLDILOCKS_64_FIELD,\n", + " n_cols=4,\n", + " security_level=128\n", + " )\n", + " A_GOLDILOCKS_64_FIELD_5_COL_128_BITS = AnemoiPermutation(\n", + " q=GOLDILOCKS_64_FIELD,\n", + " mat=CIRCULANT_FP5_MDS_MATRIX,\n", + " n_cols=5,\n", + " security_level=128)\n", + " A_GOLDILOCKS_64_FIELD_6_COL_128_BITS = AnemoiPermutation(\n", + " q=GOLDILOCKS_64_FIELD,\n", + " mat=CIRCULANT_FP6_MDS_MATRIX,\n", + " n_cols=6,\n", + " security_level=128)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4de5d23c", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "55940b58", + "metadata": {}, + "outputs": [], + "source": [ + "A_2 = AnemoiPermutation(q=BLS12_381_SCALARFIELD, alpha=5, n_rounds=None, n_cols=1, security_level=128)\n", + "A_4 = AnemoiPermutation(q=BLS12_381_SCALARFIELD, alpha=5, n_rounds=None, n_cols=2, security_level=128)\n", + "A_16 = AnemoiPermutation(q=BLS12_381_SCALARFIELD, alpha=5, n_rounds=None, n_cols=8, security_level=128)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "1714dd8a", + "metadata": {}, + "outputs": [], + "source": [ + "def h4(a,b,c,d):\n", + " return jive(A_4,4,[a,b,c,d])[0]\n", + "def h2(x,y):\n", + " return jive(A_2,2,[x,y])[0]\n", + "def h16(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p):\n", + " return jive(A_4,16,[a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p])[0]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6fb511da", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d149c137", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "SageMath 9.5", + "language": "sage", + "name": "sagemath" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/proof_of_equivalence/.ipynb_checkpoints/MinPos-checkpoint.ipynb b/proof_of_equivalence/.ipynb_checkpoints/MinPos-checkpoint.ipynb new file mode 100644 index 0000000..c2aa8a7 --- /dev/null +++ b/proof_of_equivalence/.ipynb_checkpoints/MinPos-checkpoint.ipynb @@ -0,0 +1,348 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 126, + "id": "30834567", + "metadata": {}, + "outputs": [], + "source": [ + "p = 65000549695646603732796438742359905742570406053903786389881062969044166799969\n", + "import json\n", + "F= FiniteField(p)\n", + "\n", + "n = 15 #nombre de robot\n", + "m = 20 #nombre de tache\n", + "borne = 127 # positions entre 0 et borne" + ] + }, + { + "cell_type": "code", + "execution_count": 127, + "id": "69686a85", + "metadata": {}, + "outputs": [], + "source": [ + "robots = [[F(int(random()*borne)),F(int(random()*borne))] for i in range(n)]\n", + "\n", + "taches = [[F(int(random()*borne)),F(int(random()*borne))] for i in range(m)]\n" + ] + }, + { + "cell_type": "raw", + "id": "4cc0e6c8", + "metadata": {}, + "source": [] + }, + { + "cell_type": "raw", + "id": "1aed5f4e", + "metadata": {}, + "source": [] + }, + { + "cell_type": "code", + "execution_count": 128, + "id": "ce20e261", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[[96, 16],\n", + " [106, 13],\n", + " [63, 13],\n", + " [54, 57],\n", + " [80, 41],\n", + " [11, 78],\n", + " [96, 66],\n", + " [88, 69],\n", + " [99, 55],\n", + " [68, 118],\n", + " [2, 92],\n", + " [86, 28],\n", + " [61, 77],\n", + " [96, 74],\n", + " [114, 111]]" + ] + }, + "execution_count": 128, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "robots" + ] + }, + { + "cell_type": "code", + "execution_count": 129, + "id": "edc621d1", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[[14, 92],\n", + " [12, 55],\n", + " [68, 78],\n", + " [102, 2],\n", + " [37, 41],\n", + " [98, 64],\n", + " [101, 69],\n", + " [121, 53],\n", + " [71, 84],\n", + " [80, 115],\n", + " [127, 44],\n", + " [68, 105],\n", + " [14, 117],\n", + " [127, 61],\n", + " [65, 67],\n", + " [17, 27],\n", + " [39, 97],\n", + " [45, 60],\n", + " [30, 22],\n", + " [49, 3]]" + ] + }, + "execution_count": 129, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "taches" + ] + }, + { + "cell_type": "code", + "execution_count": 130, + "id": "f46a80f9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "La tache 1 est attribuée à : Robot 11 \n", + "La tache 2 est attribuée à : Robot 6 \n", + "La tache 3 est attribuée à : Robot 8 Robot 13 \n", + "La tache 4 est attribuée à : Robot 1 Robot 2 \n", + "La tache 5 est attribuée à : Robot 4 Robot 5 \n", + "La tache 6 est attribuée à : Robot 7 \n", + "La tache 7 est attribuée à : Robot 14 \n", + "La tache 8 est attribuée à : Robot 9 \n", + "La tache 9 est attribuée à : -\n", + "La tache 10 est attribuée à : Robot 10 Robot 15 \n", + "La tache 11 est attribuée à : -\n", + "La tache 12 est attribuée à : -\n", + "La tache 13 est attribuée à : -\n", + "La tache 14 est attribuée à : -\n", + "La tache 15 est attribuée à : -\n", + "La tache 16 est attribuée à : -\n", + "La tache 17 est attribuée à : -\n", + "La tache 18 est attribuée à : -\n", + "La tache 19 est attribuée à : Robot 3 \n", + "La tache 20 est attribuée à : Robot 12 \n" + ] + } + ], + "source": [ + "#Algo\n", + "distance = [[F((taches[i][0] - robots[j][0])**2 + (taches[i][1] - robots[j][1])**2) for i in range(m)] for j in range(n)]\n", + "\n", + "position = [[F(0) for j in range(m)] for i in range(n)] # calcul des P_ij\n", + "for i in range(n):\n", + " for k in range(n):\n", + " if(k != i):\n", + " for j in range(m):\n", + " if(distance[k][j] < distance[i][j]):\n", + " position[i][j] += 1\n", + " \n", + " \n", + " \n", + "attribution = [[F(0) for j in range(m)] for i in range(n)] # attribution correspond à la matrice A du papier\n", + "attribution_v2 = [F(0) for i in range(n)] # attribution_v2 la case i représente la tache assigné au robot i.\n", + "\n", + "for i in range(n):\n", + " mini = position[i][0]\n", + " idx = 0\n", + " for j in range(m):\n", + " if(position[i][j] < mini):\n", + " idx = j\n", + " mini = position[i][j]\n", + " attribution[i][idx] = 1\n", + " attribution_v2[i] = idx+1\n", + "\n", + "for j in range(m):\n", + " compteur = True\n", + " print(\"La tache \"+str(j+1)+\" est attribuée à :\", end='')\n", + " for i in range(n):\n", + " if(attribution[i][j]):\n", + " print(\" Robot \"+str(i+1)+\" \",end='')\n", + " compteur = False\n", + " if(compteur):\n", + " print(\" -\",end=\"\")\n", + " print()" + ] + }, + { + "cell_type": "code", + "execution_count": 131, + "id": "ebf05832", + "metadata": {}, + "outputs": [], + "source": [ + "sortie = [\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"1\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"1\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"1\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"1\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"1\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"1\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"1\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"1\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"1\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"1\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\",\"0\"]" + ] + }, + { + "cell_type": "code", + "execution_count": 132, + "id": "a965d7f6", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[[13, 12, 13, 1, 9, 8, 9, 7, 13, 12, 3, 13, 13, 8, 11, 7, 13, 12, 6, 2],\n", + " [14, 13, 14, 0, 12, 10, 10, 4, 14, 14, 1, 14, 14, 6, 14, 11, 14, 13, 10, 5],\n", + " [10, 4, 11, 3, 1, 12, 12, 11, 12, 13, 9, 12, 12, 11, 9, 1, 12, 5, 0, 0],\n", + " [3, 2, 2, 9, 0, 7, 8, 10, 4, 7, 11, 6, 4, 10, 1, 0, 4, 0, 1, 4],\n", + " [6, 5, 6, 4, 2, 4, 4, 4, 7, 8, 7, 9, 9, 4, 3, 3, 8, 3, 2, 3],\n", + " [1, 0, 10, 12, 4, 13, 13, 13, 10, 9, 13, 8, 1, 13, 10, 2, 1, 2, 4, 10],\n", + " [8, 9, 4, 6, 9, 0, 0, 1, 3, 5, 2, 5, 7, 1, 4, 10, 7, 6, 11, 9],\n", + " [5, 6, 1, 7, 6, 3, 2, 3, 1, 4, 6, 2, 5, 3, 2, 8, 5, 4, 7, 8],\n", + " [9, 11, 5, 5, 8, 1, 3, 0, 6, 6, 0, 7, 10, 0, 6, 9, 9, 10, 9, 6],\n", + " [4, 8, 7, 13, 13, 11, 11, 12, 5, 0, 12, 0, 2, 12, 8, 13, 2, 11, 13, 13],\n", + " [0, 1, 12, 14, 7, 14, 14, 14, 11, 10, 14, 10, 0, 14, 13, 5, 3, 9, 8, 12],\n", + " [11, 7, 8, 2, 5, 5, 6, 6, 9, 11, 5, 11, 11, 7, 7, 6, 11, 7, 3, 1],\n", + " [2, 3, 0, 10, 3, 6, 5, 9, 0, 2, 10, 1, 3, 9, 0, 4, 0, 1, 5, 7],\n", + " [7, 10, 3, 8, 11, 2, 1, 2, 2, 3, 4, 3, 6, 2, 5, 12, 6, 8, 12, 11],\n", + " [12, 14, 9, 11, 14, 9, 7, 8, 8, 1, 8, 4, 8, 5, 12, 14, 10, 14, 14, 14]]" + ] + }, + "execution_count": 132, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "position" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5942b82d", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 133, + "id": "1c13076f", + "metadata": {}, + "outputs": [], + "source": [ + "#Algo v3\n", + "distance = [[F((taches[i][0] - robots[j][0])**2 + (taches[i][1] - robots[j][1])**2) for i in range(m)] for j in range(n)]\n", + "distance2 = [[F((taches[i][0] - robots[j][0])**2 + (taches[i][1] - robots[j][1])**2) for i in range(m)] for j in range(n)]\n", + "position = [[F(i) for j in range(m)] for i in range(n)]\n", + "\n", + "for j in range(m): #PAS PROUVé\n", + " for i in range(n):\n", + " for k in range(i+1,n):\n", + " if(distance2[k][j]= 0; i--){ + intermediate_values[i] <== coefficients[i + 1] + intermediate_values[i+1] * evaluation_point; + } + + result <== coefficients[0] + intermediate_values[0] * evaluation_point; +} + +template proof_of_equivalence(){ + signal input coefficients[2048]; + signal input da_commitment[2]; + + signal output x_0; + signal output y_0; + signal output coefficients_hash; + + //Hash of the coefficients + component coefficient_hasher = coefficient_hash(); + for(var i = 0; i<2048; i++){ + coefficient_hasher.coefficients[i] <== coefficients[i]; + } + coefficients_hash <== coefficient_hasher.hash; + + //Hash the coefficient hash with the da_commitment + component point_drawer = drawn_random_point(); + point_drawer.da_commitment[0] <== da_commitment[0]; + point_drawer.da_commitment[1] <== da_commitment[1]; + point_drawer.hash_of_data <== coefficients_hash; + x_0 <== point_drawer.x_0; + + //Evaluate the polynomial at x_0 + component evaluator = evaluate_polynomial(); + evaluator.evaluation_point <== x_0; + for(var i =0; i<2048; i++){ + evaluator.coefficients[i] <== coefficients[i]; + } + + y_0 <== evaluator.result; +} + + +component main {public [da_commitment]} = proof_of_equivalence(); \ No newline at end of file