From de7b7536ce74b18bdde9b27fd35cf6a44dd4ad95 Mon Sep 17 00:00:00 2001
From: hal8174 <henning.lindemann@pm.me>
Date: Sat, 5 Jul 2025 20:28:12 +0200
Subject: [PATCH] Initial commit

---
 .gitignore                                 |    1 +
 Cargo.lock                                 |  145 +
 Cargo.toml                                 |    8 +
 alan/Task-3-example_traces/test_msgs.csv   | 6000 ++++++++++++++++++++
 alan/Task-3-example_traces/test_traces.csv | 6000 ++++++++++++++++++++
 alan/attack.py                             |  122 +
 alan/multi-processing.py                   |   83 +
 src/main.rs                                |  173 +
 8 files changed, 12532 insertions(+)
 create mode 100644 .gitignore
 create mode 100644 Cargo.lock
 create mode 100644 Cargo.toml
 create mode 100644 alan/Task-3-example_traces/test_msgs.csv
 create mode 100644 alan/Task-3-example_traces/test_traces.csv
 create mode 100755 alan/attack.py
 create mode 100644 alan/multi-processing.py
 create mode 100644 src/main.rs

diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..ea8c4bf
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1 @@
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diff --git a/Cargo.lock b/Cargo.lock
new file mode 100644
index 0000000..e567b02
--- /dev/null
+++ b/Cargo.lock
@@ -0,0 +1,145 @@
+# This file is automatically @generated by Cargo.
+# It is not intended for manual editing.
+version = 4
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+ "cfg-if",
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+ "cpufeatures",
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diff --git a/Cargo.toml b/Cargo.toml
new file mode 100644
index 0000000..c62c531
--- /dev/null
+++ b/Cargo.toml
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diff --git a/alan/Task-3-example_traces/test_msgs.csv b/alan/Task-3-example_traces/test_msgs.csv
new file mode 100644
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diff --git a/alan/Task-3-example_traces/test_traces.csv b/alan/Task-3-example_traces/test_traces.csv
new file mode 100644
index 0000000..c21cdbb
--- /dev/null
+++ b/alan/Task-3-example_traces/test_traces.csv
@@ -0,0 +1,6000 @@
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+37,37,34,39,37,37,37,35,37,37,35,39,37,37,36,35,37,37,33,39,37,37,36,35,37,37,32,39,37,37,36,35,37,37,34,39,37,37,36,35,36,37,33,39,37,37,36,35,37,37,33,39,37,37,36,35,37,37,34,38,37,37,36,35,36,37,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36
+36,37,33,38,37,37,36,35,36,36,31,39,37,37,35,35,36,36,31,39,36,36,36,35,36,36,31,39,36,36,35,34,36,36,31,38,36,36,35,35,36,36,31,38,37,36,35,35,36,36,33,37,36,36,35,35,36,36,31,38,37,37,35,33,36,36,36,36,35,35,36,36,36,35,35,35,35,35,35,35,36,36,35,35,35,35,35
+35,35,31,37,36,36,35,33,35,36,31,37,36,36,35,34,35,35,31,37,36,36,35,33,35,35,31,37,36,36,35,33,35,35,31,37,35,35,35,35,35,35,31,37,35,36,35,34,35,35,32,36,36,36,35,34,35,35,31,37,36,36,35,33,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35
+35,35,31,37,36,35,35,33,35,35,31,37,35,35,35,33,35,35,31,37,35,35,35,33,35,35,31,37,35,35,35,33,35,35,31,36,35,35,35,33,35,35,31,37,35,35,35,33,35,35,31,36,35,35,35,33,35,35,31,36,35,35,35,33,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35
+35,35,31,37,35,35,35,34,35,35,31,37,36,36,35,33,35,35,31,37,36,36,35,33,35,35,31,37,35,35,35,33,35,35,31,37,35,35,35,33,35,35,31,37,35,35,35,33,35,35,31,37,35,35,35,33,35,35,31,37,35,35,35,33,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35
+38,38,33,39,39,39,37,35,37,38,35,39,39,39,37,35,37,37,34,39,39,39,37,35,37,37,33,39,39,39,37,35,37,37,35,39,38,38,37,36,37,37,33,39,39,39,37,35,37,37,34,39,38,38,37,35,37,37,33,39,38,38,37,35,37,38,37,37,37,37,37,37,37,37,37,37,37,37,37,37,37,37,37,37,37,37,37
+38,38,35,39,39,39,37,36,37,39,35,39,39,39,37,36,38,38,35,39,39,39,37,36,38,38,35,39,39,39,37,35,38,38,35,39,39,39,37,36,38,38,35,39,39,39,37,35,37,38,35,39,39,39,37,36,37,38,33,39,39,39,37,35,37,38,37,37,37,37,38,37,37,37,37,37,37,37,37,37,37,37,37,37,37,37,37
+35,35,31,36,35,35,35,33,35,35,30,37,35,35,35,33,35,35,31,36,35,35,35,33,35,35,31,36,35,35,35,33,35,35,31,36,35,35,35,33,35,35,31,37,35,36,35,35,35,36,32,37,36,36,36,35,36,36,32,38,37,37,36,35,36,37,37,37,36,37,37,37,37,37,37,37,37,37,37,37,37,37,37,37,37,37,37
+39,39,35,41,39,39,39,37,39,39,35,42,39,39,39,37,39,39,35,40,39,39,38,37,39,39,35,42,39,39,39,36,39,39,35,40,39,39,39,37,39,39,35,40,39,39,38,37,39,39,35,40,39,39,38,37,39,39,35,40,39,39,39,37,39,39,39,39,38,38,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39
+35,35,31,37,35,36,35,34,35,35,31,37,36,36,35,33,35,35,31,37,36,36,35,33,35,35,31,37,35,35,35,33,35,35,31,37,36,36,35,33,35,35,31,37,35,35,35,34,35,35,31,37,36,36,35,34,35,35,31,36,35,35,35,33,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35
+37,37,33,39,38,38,37,35,37,37,33,39,39,39,37,35,37,37,34,39,39,39,37,35,38,39,35,40,39,39,38,36,39,39,35,40,39,39,39,37,39,39,35,42,39,39,39,37,39,39,35,42,39,39,39,37,39,39,36,42,39,39,39,37,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39
+39,39,36,43,40,40,39,37,39,39,36,42,39,39,39,38,39,39,36,42,39,39,39,37,39,39,36,43,39,40,39,37,39,39,37,42,39,39,39,38,39,39,36,42,39,39,39,38,39,39,36,42,39,39,39,37,39,39,36,42,39,39,39,38,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39
+35,35,33,37,36,36,35,35,35,36,31,37,36,36,35,34,35,35,31,37,36,36,35,35,35,36,31,37,36,36,35,35,35,36,31,37,36,36,35,35,35,35,31,37,36,36,35,33,35,35,31,37,36,36,35,34,35,35,31,37,36,36,35,33,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35
+36,36,33,39,37,37,36,35,37,37,33,39,38,38,37,35,37,37,35,39,38,38,37,35,37,37,33,39,38,38,37,35,37,37,35,39,37,37,37,35,37,37,35,39,38,38,37,36,37,37,35,39,39,39,38,36,38,38,35,40,39,39,38,36,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39
+39,39,36,43,39,39,39,38,39,39,36,43,39,40,39,37,39,39,36,43,39,39,39,37,39,39,36,43,40,40,39,37,39,39,36,43,39,39,39,39,39,39,35,43,40,40,39,37,39,39,36,43,39,39,39,38,39,39,36,42,39,39,39,37,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39
diff --git a/alan/attack.py b/alan/attack.py
new file mode 100755
index 0000000..d475586
--- /dev/null
+++ b/alan/attack.py
@@ -0,0 +1,122 @@
+#!/usr/bin/env python3
+import numpy as np
+import matplotlib.pyplot as plt
+import aes
+
+D = 6000  # Number of power traces (Number of Samples)
+T = 87  # Number of data points per power trace (Points in time)
+KEY_GUESSES = np.arange(256, dtype=np.uint8)
+
+
+def calculate_models(
+    ciphertexts: np.ndarray[np.ndarray[np.uint8]],
+) -> np.ndarray[np.ndarray[np.ndarray[np.uint8]]]:
+    """
+    Calculates for each sample ciphertext c the state just before the last
+    SubBytes operation of the AddKey step in the last round of AES.
+
+    In order to do this we calculate: sbox^-1 (c ⊕ k_hyp)
+    and return an numpy array with this form
+    [
+        [ # first ciphertext sample c1
+            [c_1_0  ⊕ 0, c_1_0  ⊕ 1, ..., c_1_0  ⊕ 255], # first byte of c1
+            [c_1_1  ⊕ 0, c_1_1  ⊕ 1, ..., c_1_1  ⊕ 255], # second byte of c1
+            ...,
+            [c_1_15 ⊕ 0, c_1_15 ⊕ 1, ..., c_1_15 ⊕ 255], # 16'th byte of c1
+        ],
+        [ # second ciphertext sample c2
+            [c_2_0  ⊕ 0, c_2_0  ⊕ 1, ..., c_2_0  ⊕ 255],
+            [c_2_1  ⊕ 0, c_2_1  ⊕ 1, ..., c_2_1  ⊕ 255],
+            ...,
+            [c_2_15 ⊕ 0, c_2_15 ⊕ 1, ..., c_2_15 ⊕ 255],
+        ],
+        ...,
+        [ # last ciphertext sample cD
+            [c_D_0  ⊕ 0, c_D_0  ⊕ 1, ..., c_D_0  ⊕ 255],
+            [c_D_1  ⊕ 0, c_D_1  ⊕ 1, ..., c_D_1  ⊕ 255],
+            ...,
+            [c_D_15 ⊕ 0, c_D_15 ⊕ 1, ..., c_D_15 ⊕ 255],
+        ],
+    ]
+
+    Args:
+        ciphertexts:
+            An array of all samples (ciphertexts) as an np.ndarray of np.ndarrays
+            for each byte as np.uint8.
+
+    Returns:
+        models:
+            An np.ndarray with each model of the state before the SubBytes
+            operation of the AddKey step in the last round of AES.
+                - axis 0: Samples/Ciphertexts
+                - axis 1: Bytes per sample
+                - axis 2: Byte xor k_hyp
+    """
+
+    # duplicate each ciphertext 256 times to xor with all possible keys.
+    models = np.repeat(ciphertexts, 256, axis=0).reshape((D, 256, 16))
+
+    # create a view of models with the inner axis swaped, so when we xor with
+    # KEY_GUESSES numpy can use broadcast.
+    models_view = np.swapaxes(models, 1, 2)
+
+    # c ⊕ k_hyp
+    np.bitwise_xor(models_view, KEY_GUESSES, out=models_view)
+
+    # apply reverse rbox to all bytes. (rsbox(c ⊕ k_hyp))
+    models = np.vectorize(lambda x: aes.core.rsbox(x))(models)
+    return models
+
+
+def read_msgs(file_name: str) -> np.ndarray[np.ndarray[np.ndarray[np.uint8]]]:
+    msgs = np.empty((D, 3, 16), dtype=np.uint8)
+
+    with open(file_name, 'r') as fd:
+        for idx, (key, plain_text) in enumerate(
+            (line.strip().split(',') for line in fd)
+        ):
+            msgs[idx][0] = np.frombuffer(bytes.fromhex(key), dtype=np.uint8)         # key
+            msgs[idx][1] = np.frombuffer(bytes.fromhex(plain_text), dtype=np.uint8)  # plain text
+            msgs[idx][2] = np.array(                                                 # ciphertext
+                aes.aes(int(key, 16), 128).enc_once(int(plain_text, 16)), dtype=np.uint8
+            )
+
+    return msgs
+
+def read_traces(file_name: str) -> np.ndarray[np.ndarray[np.uint8]]:
+    return np.loadtxt(file_name, delimiter=",", dtype=np.uint8)
+
+
+if __name__ == "__main__":
+    msgs = read_msgs("Task-3-example_traces/test_msgs.csv")
+    traces = read_traces("Task-3-example_traces/test_traces.csv")
+    models = calculate_models(msgs[:, 2])
+
+    np.set_printoptions(formatter={"int": hex})
+    last_round_key = aes.core.key_expansion(msgs[0][0].tolist())[-16:]
+    
+
+    for bit in range(128):
+        # i'th row, and j'th col is the correlation coefficient of key_hyp = i and time sample j
+        r = np.corrcoef(
+            np.bitwise_and(models[:, :, bit//8], np.array([2**(bit % 8)], dtype=np.uint8)),
+            traces,
+            rowvar=False
+        )[:256, -87:]
+
+        guess = np.argmax(np.max(np.abs(r), axis=1))
+        # print(guess)
+        
+    exit(0)
+        # tmp = np.sort(r.flatten())
+        # confidence = max(abs(tmp[0] - tmp[1]), abs(tmp[-2] - tmp[-1]))
+        # if confidence > 0.005:
+        #     fig, axs = plt.subplots(1, 1, layout='constrained')
+        #     axs.set_title(f"Bit {bit%8 + 1} of Byte {bit//8 + 1} (Confidence: {confidence:.6f})")
+        #     axs.plot(r.transpose(), alpha=0.3, color='grey')
+        #     axs.plot(r[last_round_key[bit//8]], color="blue")
+        #     axs.plot(r[guess], color="red")
+        #     axs.set_xlabel("Time Samples")
+        #     axs.set_ylabel("Correlation")
+        #     axs.grid(True)
+        #     plt.show()
diff --git a/alan/multi-processing.py b/alan/multi-processing.py
new file mode 100644
index 0000000..d4740d2
--- /dev/null
+++ b/alan/multi-processing.py
@@ -0,0 +1,83 @@
+#!/usr/bin/python3
+import numpy as np
+import matplotlib.pyplot as plt
+from multiprocessing import Pool
+import aes
+
+D = 6000  # Number of power traces (Number of Samples)
+T = 87  # Number of data points per power trace (Points in time)
+KEY_GUESSES = np.arange(256, dtype=np.uint8)
+
+
+def calculate_models(
+    ciphertext: np.ndarray[np.ndarray[np.uint8]],
+) -> np.ndarray[np.ndarray[np.ndarray[np.uint8]]]:
+
+    # duplicate each ciphertext 256 times to xor with all possible keys.
+    models = np.repeat(ciphertext, 256).reshape(16,256)
+
+    # create a view of models with the inner axis swaped, so when we xor with
+    # KEY_GUESSES numpy can use broadcast.
+    models_view = np.swapaxes(models, 0, 1)
+
+    # c ⊕ k_hyp
+    np.bitwise_xor(models, KEY_GUESSES, out=models)
+
+    # apply reverse rbox to all bytes. (rsbox(c ⊕ k_hyp))
+    models = np.vectorize(lambda x: aes.core.rsbox(x))(models_view)
+    return models
+
+
+def read_msgs(file_name: str) -> np.ndarray[np.ndarray[np.ndarray[np.uint8]]]:
+    msgs = np.empty((D, 3, 16), dtype=np.uint8)
+
+    with open(file_name, 'r') as fd:
+        for idx, (key, plain_text) in enumerate(
+            (line.strip().split(',') for line in fd)
+        ):
+            msgs[idx][0] = np.frombuffer(bytes.fromhex(key), dtype=np.uint8)         # key
+            msgs[idx][1] = np.frombuffer(bytes.fromhex(plain_text), dtype=np.uint8)  # plain text
+            msgs[idx][2] = np.array(                                                 # ciphertext
+                aes.aes(int(key, 16), 128).enc_once(int(plain_text, 16)), dtype=np.uint8
+            )
+
+    return msgs
+
+def read_traces(file_name: str) -> np.ndarray[np.ndarray[np.uint8]]:
+    return np.loadtxt(file_name, delimiter=",", dtype=np.uint8)
+
+
+if __name__ == "__main__":
+    msgs = read_msgs("Task-3-example_traces/test_msgs.csv")
+    traces = read_traces("Task-3-example_traces/test_traces.csv")
+    with Pool() as pool:
+        models = pool.map(calculate_models, msgs[:, 2])
+
+    models = np.stack(models)
+    
+    # np.set_printoptions(formatter={"int": hex})
+    last_round_key = aes.core.key_expansion(msgs[0][0].tolist())[-16:]
+
+    for bit in range(128):
+        # i'th row, and j'th col is the correlation coefficient of key_hyp i and time sample j
+        model = np.bitwise_and(models[:, :, bit//8], np.array([2**(bit % 8)], dtype=np.uint8))
+        r = np.corrcoef(
+            model,
+            traces,
+            rowvar=False
+        )[:256, -87:]
+
+        guess = np.argmax(np.max(np.abs(r), axis=1))
+        
+        # tmp = np.sort(r.flatten())
+        # confidence = max(abs(tmp[0] - tmp[1]), abs(tmp[-2] - tmp[-1]))
+        # if confidence > 0.005:
+        #     fig, axs = plt.subplots(1, 1, layout='constrained')
+        #     axs.set_title(f"Bit {bit%8 + 1} of Byte {bit//8 + 1} (Confidence: {confidence:.6f})")
+        #     axs.plot(r.transpose(), alpha=0.3, color='grey')
+        #     axs.plot(r[last_round_key[bit//8]], color="blue")
+        #     axs.plot(r[guess], color="red")
+        #     axs.set_xlabel("Time Samples")
+        #     axs.set_ylabel("Correlation")
+        #     axs.grid(True)
+        #     plt.show()
diff --git a/src/main.rs b/src/main.rs
new file mode 100644
index 0000000..3751241
--- /dev/null
+++ b/src/main.rs
@@ -0,0 +1,173 @@
+#![feature(int_from_ascii)]
+
+use std::{
+    io::{BufRead, Read},
+    path::Path,
+};
+
+use aes::{
+    Aes128,
+    cipher::{BlockEncrypt, KeyInit, generic_array::GenericArray},
+};
+use rayon::iter::{IntoParallelIterator, ParallelIterator};
+
+static RSBOX: [u8; 256] = [
+    0x52, 0x09, 0x6a, 0xd5, 0x30, 0x36, 0xa5, 0x38, 0xbf, 0x40, 0xa3, 0x9e, 0x81, 0xf3, 0xd7, 0xfb,
+    0x7c, 0xe3, 0x39, 0x82, 0x9b, 0x2f, 0xff, 0x87, 0x34, 0x8e, 0x43, 0x44, 0xc4, 0xde, 0xe9, 0xcb,
+    0x54, 0x7b, 0x94, 0x32, 0xa6, 0xc2, 0x23, 0x3d, 0xee, 0x4c, 0x95, 0x0b, 0x42, 0xfa, 0xc3, 0x4e,
+    0x08, 0x2e, 0xa1, 0x66, 0x28, 0xd9, 0x24, 0xb2, 0x76, 0x5b, 0xa2, 0x49, 0x6d, 0x8b, 0xd1, 0x25,
+    0x72, 0xf8, 0xf6, 0x64, 0x86, 0x68, 0x98, 0x16, 0xd4, 0xa4, 0x5c, 0xcc, 0x5d, 0x65, 0xb6, 0x92,
+    0x6c, 0x70, 0x48, 0x50, 0xfd, 0xed, 0xb9, 0xda, 0x5e, 0x15, 0x46, 0x57, 0xa7, 0x8d, 0x9d, 0x84,
+    0x90, 0xd8, 0xab, 0x00, 0x8c, 0xbc, 0xd3, 0x0a, 0xf7, 0xe4, 0x58, 0x05, 0xb8, 0xb3, 0x45, 0x06,
+    0xd0, 0x2c, 0x1e, 0x8f, 0xca, 0x3f, 0x0f, 0x02, 0xc1, 0xaf, 0xbd, 0x03, 0x01, 0x13, 0x8a, 0x6b,
+    0x3a, 0x91, 0x11, 0x41, 0x4f, 0x67, 0xdc, 0xea, 0x97, 0xf2, 0xcf, 0xce, 0xf0, 0xb4, 0xe6, 0x73,
+    0x96, 0xac, 0x74, 0x22, 0xe7, 0xad, 0x35, 0x85, 0xe2, 0xf9, 0x37, 0xe8, 0x1c, 0x75, 0xdf, 0x6e,
+    0x47, 0xf1, 0x1a, 0x71, 0x1d, 0x29, 0xc5, 0x89, 0x6f, 0xb7, 0x62, 0x0e, 0xaa, 0x18, 0xbe, 0x1b,
+    0xfc, 0x56, 0x3e, 0x4b, 0xc6, 0xd2, 0x79, 0x20, 0x9a, 0xdb, 0xc0, 0xfe, 0x78, 0xcd, 0x5a, 0xf4,
+    0x1f, 0xdd, 0xa8, 0x33, 0x88, 0x07, 0xc7, 0x31, 0xb1, 0x12, 0x10, 0x59, 0x27, 0x80, 0xec, 0x5f,
+    0x60, 0x51, 0x7f, 0xa9, 0x19, 0xb5, 0x4a, 0x0d, 0x2d, 0xe5, 0x7a, 0x9f, 0x93, 0xc9, 0x9c, 0xef,
+    0xa0, 0xe0, 0x3b, 0x4d, 0xae, 0x2a, 0xf5, 0xb0, 0xc8, 0xeb, 0xbb, 0x3c, 0x83, 0x53, 0x99, 0x61,
+    0x17, 0x2b, 0x04, 0x7e, 0xba, 0x77, 0xd6, 0x26, 0xe1, 0x69, 0x14, 0x63, 0x55, 0x21, 0x0c, 0x7d,
+];
+
+fn calculate_models(ciphertexts: &[[u8; 16]]) -> Vec<[[u8; 16]; 256]> {
+    ciphertexts
+        .iter()
+        .map(|c| {
+            let mut row = [[0; 16]; 256];
+
+            for i in 0..256 {
+                for j in 0..16 {
+                    row[i][j] = RSBOX[(c[j] ^ (i as u8)) as usize];
+                }
+            }
+
+            row
+        })
+        .collect()
+}
+
+fn read_msgs(path: impl AsRef<Path>) -> Vec<[u8; 16]> {
+    let file = std::fs::File::open(path).unwrap();
+
+    let mut bufreader = std::io::BufReader::new(file);
+
+    let mut line = [0; 66];
+
+    let mut r = Vec::new();
+    while bufreader.read_exact(&mut line).is_ok() {
+        let mut key = [0; 16];
+        let mut msgs = [0; 16];
+
+        for i in 0..16 {
+            key[i] = u8::from_ascii_radix(&line[2 * i..2 * i + 2], 16).unwrap();
+            msgs[i] = u8::from_ascii_radix(&line[33 + 2 * i..33 + 2 * i + 2], 16).unwrap();
+        }
+
+        let key = GenericArray::from(key);
+        let mut block = GenericArray::from(msgs.clone());
+        let cypher = Aes128::new(&key);
+
+        cypher.encrypt_block(&mut block);
+
+        r.push(*block.as_ref());
+    }
+
+    r
+}
+
+const TRACES: usize = 87;
+
+fn read_traces(path: impl AsRef<Path>) -> Vec<[u8; TRACES]> {
+    let file = std::fs::File::open(path).unwrap();
+
+    let bufreader = std::io::BufReader::new(file);
+
+    bufreader
+        .lines()
+        .map(|l| {
+            let l = l.unwrap();
+
+            let mut trace = [0; TRACES];
+
+            for (i, t) in l
+                .trim()
+                .split(',')
+                .map(|t| t.parse::<u8>().unwrap())
+                .enumerate()
+            {
+                trace[i] = t;
+            }
+
+            trace
+        })
+        .collect()
+}
+
+fn correlation(
+    bit: usize,
+    key_hypothesis: usize,
+    trace_index: usize,
+    cyphtertext: &[[[u8; 16]; 256]],
+    traces: &[[u8; TRACES]],
+) -> f64 {
+    let mut x = 0i64;
+    let mut y = 0i64;
+    let mut xy = 0i64;
+    let mut xsqr = 0i64;
+    let mut ysqr = 0i64;
+
+    for i in 0..traces.len() {
+        let xi = (cyphtertext[i][key_hypothesis][bit / 8] & (1 << (bit % 8))) as i64;
+        let yi = traces[i][trace_index] as i64;
+
+        x += xi;
+        y += yi;
+        xy += xi * yi;
+        xsqr += xi * xi;
+        ysqr += yi * yi;
+    }
+
+    let n = traces.len() as i64;
+    let num = (n * xy - x * y) as f64;
+    let denom = f64::sqrt((n * xsqr - x * x) as f64) * f64::sqrt((n * ysqr - y * y) as f64);
+
+    num / denom
+}
+
+fn main() {
+    let start = std::time::Instant::now();
+    let cyphertext = read_msgs("./alan/Task-3-example_traces/test_msgs.csv");
+    println!("read msgs: {:?}", start.elapsed());
+
+    let start = std::time::Instant::now();
+    let models = calculate_models(&cyphertext);
+    println!("calculate models: {:?}", start.elapsed());
+
+    let start = std::time::Instant::now();
+    let traces = read_traces("./alan/Task-3-example_traces/test_traces.csv");
+    println!("read traces: {:?}", start.elapsed());
+
+    let start = std::time::Instant::now();
+    for bit in 0..128 {
+        let (max_index, max) = (0..256)
+            .into_par_iter()
+            .map(|key_hypothesis| {
+                let m = (0..traces[0].len())
+                    .map(|trace_index| {
+                        correlation(bit, key_hypothesis, trace_index, &models, &traces).abs()
+                    })
+                    .reduce(f64::max)
+                    .unwrap_or(0.0);
+                (key_hypothesis, m)
+            })
+            .reduce(
+                || (0, 0.0),
+                |a, b| {
+                    if a.1 > b.1 { a } else { b }
+                },
+            );
+        println!("bit: {bit}, key_hypothesis: {max_index}, max: {max}");
+    }
+    println!("calculate correlations: {:?}", start.elapsed());
+}