diff --git a/frontends/concrete-python/examples/sha256/sha256.ipynb b/frontends/concrete-python/examples/sha256/sha256.ipynb deleted file mode 100644 index d373b04b28..0000000000 --- a/frontends/concrete-python/examples/sha256/sha256.ipynb +++ /dev/null @@ -1,840 +0,0 @@ -{ - "cells": [ - { - "attachments": {}, - "cell_type": "markdown", - "metadata": { - "id": "_FTzVxUkjQno" - }, - "source": [ - "# SHA-256 Implementation Using Concrete\n", - "\n", - "In this tutorial, we will explore the implementation of SHA-256, a widely used hashing algorithm, using concrete-python. Details about the algorithm can be found [here](https://en.wikipedia.org/wiki/SHA-2).\n" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "zXozpJvmcBH1", - "outputId": "79dfc00b-10cc-4ffd-d4b9-a10f18d8d01e" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n", - "Requirement already satisfied: concrete-python in /usr/local/lib/python3.10/dist-packages (1.0.0)\n", - "Requirement already satisfied: numpy>=1.23 in /usr/local/lib/python3.10/dist-packages (from concrete-python) (1.24.3)\n", - "Requirement already satisfied: scipy>=1.10 in /usr/local/lib/python3.10/dist-packages (from concrete-python) (1.10.1)\n", - "Requirement already satisfied: torch>=1.13 in /usr/local/lib/python3.10/dist-packages (from concrete-python) (2.0.0+cu118)\n", - "Requirement already satisfied: networkx>=2.6 in /usr/local/lib/python3.10/dist-packages (from concrete-python) (3.1)\n", - "Requirement already satisfied: typing-extensions in /usr/local/lib/python3.10/dist-packages (from torch>=1.13->concrete-python) (4.5.0)\n", - "Requirement already satisfied: triton==2.0.0 in /usr/local/lib/python3.10/dist-packages (from torch>=1.13->concrete-python) (2.0.0)\n", - "Requirement already satisfied: sympy in /usr/local/lib/python3.10/dist-packages (from torch>=1.13->concrete-python) (1.11.1)\n", - "Requirement already satisfied: jinja2 in /usr/local/lib/python3.10/dist-packages (from torch>=1.13->concrete-python) (3.1.2)\n", - "Requirement already satisfied: filelock in /usr/local/lib/python3.10/dist-packages (from torch>=1.13->concrete-python) (3.12.0)\n", - "Requirement already satisfied: cmake in /usr/local/lib/python3.10/dist-packages (from triton==2.0.0->torch>=1.13->concrete-python) (3.25.2)\n", - "Requirement already satisfied: lit in /usr/local/lib/python3.10/dist-packages (from triton==2.0.0->torch>=1.13->concrete-python) (16.0.2)\n", - "Requirement already satisfied: MarkupSafe>=2.0 in /usr/local/lib/python3.10/dist-packages (from jinja2->torch>=1.13->concrete-python) (2.1.2)\n", - "Requirement already satisfied: mpmath>=0.19 in /usr/local/lib/python3.10/dist-packages (from sympy->torch>=1.13->concrete-python) (1.3.0)\n" - ] - } - ], - "source": [ - "# Uncomment this line to install dependency\n", - "# ! pip install concrete-python\n", - "\n", - "# Required libraries\n", - "from concrete import fhe\n", - "import platform\n", - "import numpy as np" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": { - "id": "oCfjYazikbm_" - }, - "source": [ - "## Data Representation\n", - "As mentioned in the wiki page, all variables are $32$-bit unsigned integers. Additions should be calculated modulo $2^{32}$.\n", - "\n", - "While addition of 32-bit numbers are possible in the library, any other operations such modulizing, rotations, and bitwise operations are currently not possible. These operations require a lookup table with 32-bit inputs, but as of writing this tutorial, concrete-python supports up to 16-bit lookup tables. Higher precision lookup tables is still a research challenge in the homomorphic world and such a table would be dificult to compile and store at this moment.\n", - "\n", - "Thus, we need to break all the variables to **chunks** and work at the chunk level. Throughtout the code, *WIDTH* refers to the bitwidth of a chunk, and *NUM_CHUNKS* shows the number of chunks we need to represent a 32-bit data. These parameters are set at the begining of the code. We vary these parameters to see the impact of the *WIDTH* on the performance of the compiler and the circuit.\n", - "\n", - 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- "\n", - "Figure 1: Shows a break down of 32 bit of data into 4 chunks of 8 bit. This is not the only way to chunk the input." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "id": "yaz8cNzjQ1UW" - }, - "outputs": [], - "source": [ - "# Bitwidth of each chunk and number of chunks in each 32-bit number.\n", - "WIDTH, NUM_CHUNKS = 4, 8\n", - "\n", - "## Some other valid parameter sets\n", - "# WIDTH, NUM_CHUNKS= 8, 4\n", - "# WIDTH, NUM_CHUNKS= 2, 16\n", - "\n", - "assert WIDTH * NUM_CHUNKS == 32\n", - "\n", - "\n", - "def break_down_data(data, data_size):\n", - " all_chunks = [\n", - " [(x >> i * WIDTH) % (2**WIDTH) for i in range(data_size // WIDTH)[::-1]] for x in data\n", - " ]\n", - " return all_chunks\n", - "\n", - "\n", - "def reshape_data(data):\n", - " return np.array(data).reshape(-1, NUM_CHUNKS)\n", - "\n", - "\n", - "def chunks_to_uint32(chunks):\n", - " return int(sum([2 ** ((NUM_CHUNKS - 1 - i) * WIDTH) * x for i, x in enumerate(chunks)]))\n", - "\n", - "\n", - "def chunks_to_hexarray(chunks):\n", - " hexes = [hex(chunks_to_uint32(word))[2:] for word in chunks]\n", - " hexes = [\n", - " \"0\" * (8 - len(y)) + y for y in hexes\n", - " ] # Appending leadning zero to the ones that are less than 8 characters TODO: write better\n", - " result = \"\".join(hexes)\n", - " return result" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": { - "id": "u7pA-B3As9u4" - }, - "source": [ - "### Creating Chunks\n", - "There are two list of constants in the algorithm, K and H. Before executing the algorithm, we need to break them to chunks using `split_to_chunks` function.\n", - "\n", - "\n", - "The input of the algorithm is arbitrary bytes. We might need to break each byte to smaller chunks based on the value of *WIDTH* after padding the data as per instructed by the algorithm. `break_down_data` function returns a numpy array of shape (48,NUM_CHUNKS)" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": { - "id": "b8rlvVf42CIa" - }, - "source": [ - "## Operations\n", - "Now that the data is stores as chunks, we must modify all operations we need to work at the level of chunks. In this section we explain how we implemented the required operations. The main three category of operations that we need to implement SHA-256 are:\n", - "\n", - "* Bitwise operations (AND, OR, XOR, NEGATE)\n", - "* Shifts and Rotations\n", - "* Modular Addition " - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": { - "id": "zlM1RN-NnjDn" - }, - "source": [ - "### Bitwise Operations\n", - "Bitwise operations are easily implemented in concrete-numpy. A bitwise operation over a 32-bit number is equivalent to the same operation over the chunks." - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": { - "id": "CxCwJOao2KCt" - }, - "source": [ - "### Rotation and Shifts\n", - "To understand how rotations work, consider a small example with 4 chunks of width 4, representing a 16-bit number, as shown in Figure 1. Most significant bits are located at index 0. So a 16-bit number will be `[[chunk_0], [chunk_1], [chunk_2], [chunk_3]]` with WIDTH=4. There are two possible scenario for rotations:\n", - "\n", - "1. Any rotation by a multiple of WIDTH (in this case, 4) will result in rotating the array of chunks. For example, right rotate(4) will be `[[chunk_3], [chunk_0], [chunk_1], [chunk_2]]`.\n", - "\n", - "2. For rotations less than WIDTH, for example `y`, we break every chunk into two parts of bitlength, `WIDTH-y` and `y`. We need to add the low `y`-bits of each chunk with the high `WIDTH-y` bits of the next chunk. Figure 2 illustrated this process. We leverage two lookup tables to extract the two segments of each chunk.\n", - "\n", - "\n", - "3. Rotations by other amounts are broken into the two steps described above.\n", - "\n", - 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- ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": { - "id": "575ogsJhFDIo" - }, - "source": [ - "### Shift\n", - "The shift operation is the same as rotation, but we prepend the encrypted scalar zero when we move the bits to the right." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "id": "TRAFRZime-Jv" - }, - "outputs": [], - "source": [ - "def right_rotate_list_of_chunks(list_to_rotate, amount):\n", - " return np.concatenate((list_to_rotate[-amount:], list_to_rotate[:-amount]))\n", - "\n", - "\n", - "def right_shift_list_of_chunks(list_to_rotate, amount):\n", - " return np.concatenate(([0] * list_to_rotate[-amount:].shape[0], list_to_rotate[:-amount]))\n", - "\n", - "\n", - "def left_shift_list_of_chunks(list_to_rotate, amount):\n", - " return np.concatenate((list_to_rotate[amount:], [0] * list_to_rotate[:amount].shape[0]))\n", - "\n", - "\n", - "def rotate_less_than_width(chunks, shift):\n", - " raised_low_bits = fhe.univariate(lambda x: (x % 2**shift) << (WIDTH - shift))(chunks)\n", - " shifted_raised_low_bits = right_rotate_list_of_chunks(raised_low_bits, 1)\n", - "\n", - " high_bits = chunks >> shift\n", - " return shifted_raised_low_bits + high_bits\n", - "\n", - "\n", - "def right_rotate(chunks, rotate_amount):\n", - " x = rotate_amount // WIDTH\n", - " y = rotate_amount % WIDTH\n", - " rotated_chunks = right_rotate_list_of_chunks(chunks, x) if x != 0 else chunks\n", - " rotated = rotate_less_than_width(rotated_chunks, y) if y != 0 else rotated_chunks\n", - "\n", - " return rotated\n", - "\n", - "\n", - "def right_shift(chunks, shift_amount):\n", - " x = shift_amount // WIDTH\n", - " y = shift_amount % WIDTH\n", - " shifted_chunks = right_shift_list_of_chunks(chunks, x) if x != 0 else chunks\n", - "\n", - " if y != 0:\n", - " # shift within chunks\n", - " raised_low_bits = fhe.univariate(lambda x: (x % 2**y) << (WIDTH - y))(shifted_chunks)\n", - " shifted_raised_low_bits = right_shift_list_of_chunks(raised_low_bits, 1)\n", - " high_bits = shifted_chunks >> y\n", - " result = shifted_raised_low_bits + high_bits\n", - " else:\n", - " result = shifted_chunks\n", - " return result" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": { - "id": "SKg8mKFOPXSV" - }, - "source": [ - "### Modular 32-bit Addition\n", - "Modular 32-bit addition is frequently used in SHA256. While Concrete supports additions of 32-bit numbers, modulizing the result requires a lookup table which is too large for Concrete. Hence, the addition must be done over chunks.\n", - "\n", - "Below is the function to add two 32-bit numbers mod $2^{32}$." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": { - "id": "EJEPvp2wQms9" - }, - "outputs": [], - "source": [ - "def add_two_32_bits(a, b):\n", - " added = np.sum([a, b], axis=0)\n", - "\n", - " for i in range(NUM_CHUNKS):\n", - " results = added % (2**WIDTH)\n", - " if i < NUM_CHUNKS - 1:\n", - " carries = added >> WIDTH\n", - " added = left_shift_list_of_chunks(carries, 1) + results\n", - "\n", - " return results" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": { - "id": "Uo6o_QMQn_fw" - }, - "outputs": [], - "source": [ - "# Testing the addition function, adding four 32-bit numbers\n", - "test_inputs = np.random.randint(0, 2**32, size=(2,))\n", - "input_chunks = break_down_data(test_inputs, 32)\n", - "\n", - "assert chunks_to_uint32(add_two_32_bits(input_chunks[0], input_chunks[1])) == np.sum(\n", - " test_inputs\n", - ") % (2**32)" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": { - "id": "IOr8DTRJRYTl" - }, - "source": [ - "Adding two 4-bit numbers results in a 5-bit number. We then use two lookup tables:\n", - "\n", - "* `extract_carry` which extracts the carry of adding two chunks\n", - "* `extract_result` which extracts the 4-bit chunk which results from adding two chunks (without the carry)\n", - "\n", - "Each carry must now be added to the chunk next chunk and this process is repeated for as many chunks as there are. The figure below illustrates this process.\n", - "\n", - "![add-chunks.png](data:image/png;base64,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)\n", - "\n" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": { - "id": "4-dQk0wbtPOe" - }, - "source": [ - "The benefit of this addition algorithm is that it can be extended to the case where more two 32-bit numbers are added. The only difference is that the carry from the first iteration of the loop can be larger than 1. Specifically, by adding $k$ 4-bit numbers, the carry can be as big as $\\log_2 k$. For correctness, $\\log_2 k$ must be less than 4 or $k<16$.\n", - "\n", - "In our implementation of SHA-256, we only have two input and four input additions, so we only implement those.\n", - "\n", - "For four input addition, he first iteration of the loop, we use a different lookup table that extract a 2-bit carry and rest of the chunk. The rest of the algorithm does not change." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "id": "obO8wHRbXHfj" - }, - "outputs": [], - "source": [ - "def add_four_32_bits(a, b, c, d):\n", - " added = np.sum([a, b, c, d], axis=0)\n", - "\n", - " # First iteration of the loop is seperated\n", - " carries = added >> WIDTH\n", - " results = added % (2**WIDTH)\n", - " shifted_carries = left_shift_list_of_chunks(carries, 1)\n", - " added = shifted_carries + results\n", - "\n", - " for i in range(1, NUM_CHUNKS):\n", - " results = added % (2**WIDTH)\n", - "\n", - " # In the last iteration, carries need not be calculated\n", - " if i != NUM_CHUNKS - 1:\n", - " carries = added >> WIDTH\n", - " shifted_carries = left_shift_list_of_chunks(carries, 1)\n", - " added = shifted_carries + results\n", - "\n", - " return results" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": { - "id": "zcwnDdPFdqE1" - }, - "outputs": [], - "source": [ - "# Testing the addition function, adding four 32-bit numbers\n", - "\n", - "for _ in range(1000):\n", - " test_inputs = np.random.randint(0, 2**32, size=(4,))\n", - " input_chunks = break_down_data(test_inputs, 32)\n", - "\n", - " assert chunks_to_uint32(\n", - " add_four_32_bits(input_chunks[0], input_chunks[1], input_chunks[2], input_chunks[3])\n", - " ) == np.sum(test_inputs) % (2**32)" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": { - "id": "1g6eEdhGoJl9" - }, - "source": [ - "## Operations for SHA-256\n", - "\n", - "Using the basic operations from the previous section, we can now implement all the necessary functions for SHA256" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": { - "id": "uo7HfO1DpVFK" - }, - "outputs": [], - "source": [ - "# Used in the expansion\n", - "\n", - "\n", - "def s0(w):\n", - " return right_rotate(w, 7) ^ right_rotate(w, 18) ^ right_shift(w, 3)\n", - "\n", - "\n", - "def s1(w):\n", - " return right_rotate(w, 17) ^ right_rotate(w, 19) ^ right_shift(w, 10)\n", - "\n", - "\n", - "# Used in main loop\n", - "\n", - "\n", - "def S0(a_word): # noqa: N802\n", - " return right_rotate(a_word, 2) ^ right_rotate(a_word, 13) ^ right_rotate(a_word, 22)\n", - "\n", - "\n", - "def S1(e_word): # noqa: N802\n", - " return right_rotate(e_word, 6) ^ right_rotate(e_word, 11) ^ right_rotate(e_word, 25)\n", - "\n", - "\n", - "def Ch(e_word, f_word, g_word): # noqa: N802\n", - " return (e_word & f_word) ^ ((2**WIDTH - 1 - e_word) & g_word)\n", - "\n", - "\n", - "def Maj(a_word, b_word, c_word): # noqa: N802\n", - " return (a_word & b_word) ^ (a_word & c_word) ^ (b_word & c_word)\n", - "\n", - "\n", - "def main_loop(args, w_i_plus_k_i):\n", - " a, b, c, d, e, f, g, h = args\n", - " temp1 = add_four_32_bits(h, S1(e), Ch(e, f, g), w_i_plus_k_i)\n", - " temp2 = add_two_32_bits(S0(a), Maj(a, b, c))\n", - " new_a = add_two_32_bits(temp1, temp2)\n", - " new_e = add_two_32_bits(d, temp1)\n", - " return np.array([new_a, a, b, c, new_e, e, f, g])" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": { - "id": "biM997KmvwUL" - }, - "source": [ - "We also need a function to pad the input as the first step of SHA256." - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": { - "id": "fZ-3sEH5vopA" - }, - "source": [ - "Moreover, we need a function to parse the input given to the program. The input is given as bytes, but the chunks might be smaller. We extract smaller chunks from bytes using lookup tables." - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": { - "id": "L4leg-z_skkU" - }, - "source": [ - "## Bringing it all together\n", - "Using all the components from the above, we can implement SHA256 as shown below." - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": { - "id": "tmSfvdpyrwUx" - }, - "outputs": [], - "source": [ - "K = [\n", - " 0x428A2F98,\n", - " 0x71374491,\n", - " 0xB5C0FBCF,\n", - " 0xE9B5DBA5,\n", - " 0x3956C25B,\n", - " 0x59F111F1,\n", - " 0x923F82A4,\n", - " 0xAB1C5ED5,\n", - " 0xD807AA98,\n", - " 0x12835B01,\n", - " 0x243185BE,\n", - " 0x550C7DC3,\n", - " 0x72BE5D74,\n", - " 0x80DEB1FE,\n", - " 0x9BDC06A7,\n", - " 0xC19BF174,\n", - " 0xE49B69C1,\n", - " 0xEFBE4786,\n", - " 0x0FC19DC6,\n", - " 0x240CA1CC,\n", - " 0x2DE92C6F,\n", - " 0x4A7484AA,\n", - " 0x5CB0A9DC,\n", - " 0x76F988DA,\n", - " 0x983E5152,\n", - " 0xA831C66D,\n", - " 0xB00327C8,\n", - " 0xBF597FC7,\n", - " 0xC6E00BF3,\n", - " 0xD5A79147,\n", - " 0x06CA6351,\n", - " 0x14292967,\n", - " 0x27B70A85,\n", - " 0x2E1B2138,\n", - " 0x4D2C6DFC,\n", - " 0x53380D13,\n", - " 0x650A7354,\n", - " 0x766A0ABB,\n", - " 0x81C2C92E,\n", - " 0x92722C85,\n", - " 0xA2BFE8A1,\n", - " 0xA81A664B,\n", - " 0xC24B8B70,\n", - " 0xC76C51A3,\n", - " 0xD192E819,\n", - " 0xD6990624,\n", - " 0xF40E3585,\n", - " 0x106AA070,\n", - " 0x19A4C116,\n", - " 0x1E376C08,\n", - " 0x2748774C,\n", - " 0x34B0BCB5,\n", - " 0x391C0CB3,\n", - " 0x4ED8AA4A,\n", - " 0x5B9CCA4F,\n", - " 0x682E6FF3,\n", - " 0x748F82EE,\n", - " 0x78A5636F,\n", - " 0x84C87814,\n", - " 0x8CC70208,\n", - " 0x90BEFFFA,\n", - " 0xA4506CEB,\n", - " 0xBEF9A3F7,\n", - " 0xC67178F2,\n", - "]\n", - "H = [0x6A09E667, 0xBB67AE85, 0x3C6EF372, 0xA54FF53A, 0x510E527F, 0x9B05688C, 0x1F83D9AB, 0x5BE0CD19]" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": { - "id": "NHGCiC-Gk_tw" - }, - "outputs": [], - "source": [ - "k_in = reshape_data(break_down_data(K, 32))\n", - "h_in = reshape_data(break_down_data(H, 32))" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": { - "id": "yTiMkmBsHmKy" - }, - "outputs": [], - "source": [ - "def uint64_to_bin(uint64: int):\n", - " return \"\".join([str(uint64 >> i & 1) for i in range(63, -1, -1)])\n", - "\n", - "\n", - "def sha256_preprocess(text):\n", - " \"\"\"\n", - " Takes a message of arbitrary length and returns a message\n", - " of length that is a multiple of 512 bits, with the original message padded\n", - " with a 1 bit, followed by 0 bits, followed by the original message length\n", - " in bits\n", - " \"\"\"\n", - " data = text\n", - " # convert to uint4 and group into 32 bit words (8 uint4s)\n", - " # #log (\"data is:\", data, data.shape)\n", - " message_len = data.shape[0] * 8 # denoted as 'l' in spec\n", - " # find padding length 'k'\n", - " k = (((448 - 1 - message_len) % 512) + 512) % 512\n", - " # #log (\"k is:\", k)\n", - " zero_pad_width_in_bits = k\n", - " padstring = \"1\" + \"0\" * zero_pad_width_in_bits + str(uint64_to_bin(message_len))\n", - " # log (\"padstring size:\", len(padstring))\n", - " # log (\"padstring is:\", padstring)\n", - "\n", - " total_size = len(padstring) + message_len\n", - " # log (\"total size:\", total_size)\n", - " assert total_size % 512 == 0\n", - "\n", - " pad = np.array(\n", - " [int(padstring[i : i + 8], 2) for i in range(0, len(padstring), 8)], dtype=np.uint8\n", - " )\n", - " padded = np.concatenate((data, pad))\n", - " words = break_down_data(padded, 8)\n", - " chunks = reshape_data(words)\n", - " return chunks" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": { - "id": "3ox6Zs-ysoLr" - }, - "outputs": [], - "source": [ - "# Number of rounds must be 64 to have correct SHA256\n", - "# If looking to get a faster run, reduce the number of rounds (but it will not be correct)\n", - "\n", - "\n", - "def sha256(data, number_of_rounds=64):\n", - " h_chunks = fhe.zeros((len(h_in), NUM_CHUNKS))\n", - " k_chunks = fhe.zeros((len(k_in), NUM_CHUNKS))\n", - " h_chunks += h_in\n", - " k_chunks += k_in\n", - "\n", - " num_of_iters = data.shape[0] * 32 // 512\n", - " for chunk_iter in range(0, num_of_iters):\n", - "\n", - " # Initializing the variables\n", - " chunk = data[chunk_iter * 16 : (chunk_iter + 1) * 16]\n", - " w = [None for _ in range(number_of_rounds)]\n", - " # Starting the main loop and expansion\n", - " working_vars = h_chunks\n", - " for j in range(0, number_of_rounds):\n", - " if j < 16:\n", - " w[j] = chunk[j]\n", - " else:\n", - " w[j] = add_four_32_bits(w[j - 16], s0(w[j - 15]), w[j - 7], s1(w[j - 2]))\n", - " w_i_k_i = add_two_32_bits(w[j], k_chunks[j])\n", - " working_vars = main_loop(working_vars, w_i_k_i)\n", - "\n", - " # Accumulating the results\n", - " for j in range(8):\n", - " h_chunks[j] = fhe.array(add_two_32_bits(h_chunks[j], working_vars[j]))\n", - " return h_chunks" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": { - "id": "w89rhSOh4In2" - }, - "source": [ - "We can test the correctness of this function as below (this is not in encrypted form yet)" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "006LZp7c0yBA", - "outputId": "31588127-23e9-4b49-e481-d14842e336e7" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - " SHA256: a412c46b0be134c593b0ad520d4a4c4e1d8aecca799be0be2c4d233ccf455cb7\n", - "Our SHA256: a412c46b0be134c593b0ad520d4a4c4e1d8aecca799be0be2c4d233ccf455cb7\n", - "Match: True\n" - ] - } - ], - "source": [ - "import hashlib\n", - "\n", - "text = (\n", - " b\"Lorem ipsum dolor sit amet, consectetur adipiscing elit. \"\n", - " b\"Curabitur bibendum, urna eu bibendum egestas, neque augue eleifend odio, \"\n", - " b\"et sagittis viverra. and more than 150\"\n", - ")\n", - "\n", - "result = sha256(sha256_preprocess(np.frombuffer(text, dtype=np.uint8)))\n", - "\n", - "m = hashlib.sha256()\n", - "m.update(text)\n", - "\n", - "print(\" SHA256:\", m.hexdigest())\n", - "print(\"Our SHA256:\", chunks_to_hexarray(result))\n", - "print(\"Match:\", chunks_to_hexarray(result) == m.hexdigest())" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": { - "id": "1uHN9GXgla_z" - }, - "outputs": [], - "source": [ - "class HomomorphicSHA: # noqa: N802\n", - " circuit: fhe.Circuit\n", - "\n", - " def __init__(self, input_size_in_bytes=150, number_of_rounds=64) -> None:\n", - " self.input_size_in_bytes = input_size_in_bytes\n", - " assert 0 <= number_of_rounds <= 64, \"Number of rounds must be betweem zero and 64\"\n", - " self.number_of_rounds = number_of_rounds\n", - " inputset = [\n", - " sha256_preprocess(np.random.randint(0, 2**8, size=(input_size_in_bytes,)))\n", - " for _ in range(100)\n", - " ]\n", - " # Compilation of the circuit should take a few minutes\n", - " compiler = fhe.Compiler(\n", - " lambda data: sha256(data, self.number_of_rounds), {\"data\": \"encrypted\"}\n", - " )\n", - " self.circuit = compiler.compile(\n", - " inputset=inputset,\n", - " configuration=fhe.Configuration(\n", - " enable_unsafe_features=True,\n", - " use_insecure_key_cache=True,\n", - " insecure_key_cache_location=\".keys\",\n", - " dataflow_parallelize=platform.system() != \"Darwin\",\n", - " ),\n", - " verbose=False,\n", - " )\n", - "\n", - " def getSHA(self, data): # noqa: N802\n", - " assert (\n", - " len(data) == self.input_size_in_bytes\n", - " ), f\"Input size is not correct, should be {self.input_size_in_bytes} bytes/characters\"\n", - " return self.circuit.encrypt_run_decrypt(sha256_preprocess(data))\n", - "\n", - " def getPlainSHA(self, data): # noqa: N802\n", - " return sha256(sha256_preprocess(data), self.number_of_rounds)" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": { - "id": "SpxY6dScee-k" - }, - "source": [ - "Now we are ready to compile the circuit! Note that **the compilation will take a long time**, so if you are looking to get a test run, you can set the number of rounds to something smaller than 64." - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": { - "id": "P0cMOZUGee-k" - }, - "outputs": [], - "source": [ - "# Warning: This will compile the circuit and will take a few minutes\n", - "\n", - "input_size_in_bytes = 150\n", - "running_small_example = True\n", - "\n", - "if running_small_example:\n", - " number_of_rounds = 2\n", - " sha = HomomorphicSHA(input_size_in_bytes, number_of_rounds)\n", - "else:\n", - " sha = HomomorphicSHA(input_size_in_bytes)" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": { - "id": "zz1rd7VWee-k" - }, - "source": [ - "And after compilation, we are ready to run the circuit. Remember that the input size has to match what you gave in the previous cell. Our function will check this first to make sure the input is of the correct size. " - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "EkF0UxTcv_cQ", - "outputId": "c4e2c710-02bc-40e2-a921-4a29ac88380b" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "This cell is disabled. It can takes hours. If you want to run this cell, set accept_a_very_long_run=True\n" - ] - } - ], - "source": [ - "# WARNING: This takes a LONG time\n", - "accept_a_very_long_run = False\n", - "if not accept_a_very_long_run:\n", - " print(\n", - " \"This cell is disabled. It can takes hours. If you want to run this \"\n", - " \"cell, set accept_a_very_long_run=True\"\n", - " )\n", - "else:\n", - " text = (\n", - " b\"Lorem ipsum dolor sit amet, consectetur adipiscing elit. \"\n", - " b\"Curabitur bibendum, urna eu bibendum egestas, neque augue eleifend odio, \"\n", - " b\"et sagittis viverra.\"\n", - " )\n", - " input_bytes = np.frombuffer(text, dtype=np.uint8)\n", - " encrypted_evaluation = sha.getSHA(input_bytes)\n", - "\n", - " print(\"Encrypted Evaluation: \", chunks_to_hexarray(encrypted_evaluation))\n", - " print(\" Plain Evaluation: \", chunks_to_hexarray(sha.getPlainSHA(input_bytes)))" - ] - } - ], - "metadata": { - "colab": { - "provenance": [] - }, - "kernelspec": { - "display_name": "Python 3.10.7 64-bit", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.10.7" - }, - "vscode": { - "interpreter": { - "hash": "31f2aee4e71d21fbe5cf8b01ff0e069b9275f58929596ceb00d14d90e3e16cd6" - } - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}