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17 ../../principles/security.rst:245
	English ↹ ↵ NBS … “ ” ‘ ’ ﹙-﹚ ‐ – — Cryptographic primitives 24/10000 · 24
18 ../../principles/security.rst:247
	English ↹ ↵ NBS … “ ” ‘ ’ ﹙-﹚ ‐ – — Cryptography techniques have initially been defined and used by spies and armies to exchange secret information in manner that ensures that adversaries cannot decode the information even if they capture the message or the person carrying the message. A wide range of techniques have been defined. The first techniques relied on their secrecy to operate. One of the first encryption schemes is attributed to Julius Caesar. When he sent confidential information to his generals, he would encode each message by replacing each letter with another letter that is :math:`n` positions after this letter in the alphabet. For example, the message `SECRET` becomes `VHFUHW` when encoded using Caesar's cipher. This technique could have puzzled some soldiers during Caesar's wars, but today even young kids can recover the original message from the ciphered one. 852/10000 · 852
19 ../../principles/security.rst:261
	English ↹ ↵ NBS … “ ” ‘ ’ ﹙-﹚ ‐ – — The security of the Caesar cipher depends on the confidentiality of the algorithm, but experience has shown that it is impossible to assume that an algorithm will remain secret, even for military applications. Instead, cryptographic techniques must be designed by assuming that the algorithm will be public and known to anyone. However, its behavior must be controlled by a small parameter, known as the key, that will only be known by the users who need to communicate secretly. This principle is attributed to Auguste Kerckhoff, a French cryptographer who first documented it : 579/10000 · 579
20 ../../principles/security.rst:270
	English ↹ ↵ NBS … “ ” ‘ ’ ﹙-﹚ ‐ – — `A cryptographic algorithm should be secure even if the attacker knows everything about the system, except one parameter known as the secret key.` 146/10000 · 146
21 ../../principles/security.rst:279
	English ↹ ↵ NBS … “ ” ‘ ’ ﹙-﹚ ‐ – — This principle is important because it remains the basic assumption of all cryptographers. Any system that relies on the secrecy of its algorithm to be considered secure is doomed to fail and be broken one day. 210/10000 · 210
22 ../../principles/security.rst:287
	English ↹ ↵ NBS … “ ” ‘ ’ ﹙-﹚ ‐ – — With the Kerckhoff principle, we can now discuss a simple but powerful encryption scheme that relies on the `XOR` logic operation. This operation is easily implemented in hardware and is supported by all microprocessors. Given a secret, :math:`K`, it is possible to encode a message `M` by computing :math:`C_M = K \oplus M`. The receiver of this messages can recover the original message as since :math:`M = K \oplus (K \oplus M)`. This `XOR` operation is the key operation of the perfect cipher that is also called the Vernam cipher or the one-time pad. This cipher relies on a key that contains purely random bits. The encrypted message is then produced by XORing all the bits of the message with all the bits of the key. Since the key is random, it is impossible for an attacker to recover the original text (or plain text) from the encrypted one. From a security viewpoint, the one-time-pad is the best solution provided that the key is as long as the message. 965/10000 · 965
23 ../../principles/security.rst:301
	English ↹ ↵ NBS … “ ” ‘ ’ ﹙-﹚ ‐ – — Unfortunately, it is difficult to use this cipher in practice since the key must be as long as the message that needs to be transmitted. If the key is smaller than the message and the message is divided into blocks that have the same length as the key, then the scheme becomes less secure since the same key is used to decrypt different parts of the message. In practice, `XOR` is often one of the basic operations used by encryption schemes. To be usable, the deployed encryption schemes use keys that are composed of a small number of bits, typically 56, 64, 128, 256, ... 574/10000 · 574
24 ../../principles/security.rst:310
	English ↹ ↵ NBS … “ ” ‘ ’ ﹙-﹚ ‐ – — A secret key encryption scheme is a perfectly reversible functions, i.e. given an encryption function `E`, there is an associated decryption function `D` such that :math:`\forall k \forall M : D(K, E(M,K))=M`. 209/10000 · 209
25 ../../principles/security.rst:316
	English ↹ ↵ NBS … “ ” ‘ ’ ﹙-﹚ ‐ – — Various secret key cryptographic functions have been proposed, implemented and deployed. The most popular ones are : 116/10000 · 116
26 ../../principles/security.rst:319
	English ↹ ↵ NBS … “ ” ‘ ’ ﹙-﹚ ‐ – — DES, the Data Encryption Standard that became a standard in 1977 and has been widely used by industry. It uses 56 bits keys that are not considered sufficiently secure nowadays since attackers can launch brute-force attacks by testing all possible keys. Triple DES combines three 56 bits keys, making the brute force attacks more difficult. 340/10000 · 340
27 ../../principles/security.rst:324
	English ↹ ↵ NBS … “ ” ‘ ’ ﹙-﹚ ‐ – — RC4 is an encryption scheme defined in the late 1980s by Ron Rivest for RSA Security. Given the speed of its software implementation, it has been included in various protocols and implementations. However, cryptographers have identified several weaknesses in this algorithm. It is now deprecated and should not be used anymore :rfc:`7465`. 339/10000 · 339
28 ../../principles/security.rst:329
	English ↹ ↵ NBS … “ ” ‘ ’ ﹙-﹚ ‐ – — AES or the Advanced Encryption Standard is an encryption scheme that was designed by the Belgian cryptographers Joan Daemen and Vincent Rijmen in 2001 [DR2002]_. This algorithm has been standardized by the U.S. National Institute of Standards and Technology (NIST). It is now used by a wide range of applications and various hardware and software implementations exist. Many microprocessors include special instructions that ease the implementation of AES. AES divides the message to be encrypted in blocks of 128 bits and uses keys of length 128, 192 or 256 bits. The block size and the key length are important parameters of an encryption scheme. The block size indicates the smallest message that can be encrypted and forces the sender to divide each message in blocks of the supported size. If the message is larger than an integer number of blocks, then the message must be padded before being encrypted and this padding must be removed after decryption. The key size indicates the resistance of the encryption scheme against brute force attacks, i.e. attacks where the attacker tries all possible keys to find the correct one. 1133/10000 · 1133
29 ../../principles/security.rst:354
	English ↹ ↵ NBS … “ ” ‘ ’ ﹙-﹚ ‐ – — AES is widely used as of this writing, but other secret key encryption schemes continue to appear. ChaCha20, proposed by D. Bernstein is now used by several internet protocols :rfc:`7539`. A detailed discussion of encryption schemes is outside the scope of this book. We will consider encryption schemes as black boxes whose operation depends on a single key. A detailed overview of several of these schemes may be found in [MVV2011]_. 435/10000 · 435
30 ../../principles/security.rst:363
	English ↹ ↵ NBS … “ ” ‘ ’ ﹙-﹚ ‐ – — In the 1970s, Diffie and Hellman proposed in their seminal paper [DH1976]_, a different type of encryption : `public key cryptography`. In public key cryptography, each user has two different keys : 198/10000 · 198
31 ../../principles/security.rst:367
	English ↹ ↵ NBS … “ ” ‘ ’ ﹙-﹚ ‐ – — a public key (:math:`K_{pub}`) that he can distribute to everyone 65/10000 · 65
32 ../../principles/security.rst:368
	English ↹ ↵ NBS … “ ” ‘ ’ ﹙-﹚ ‐ – — a private key (:math:`K_{priv}`) that he needs to store in a secure manner and never reveal to anyone 101/10000 · 101
33 ../../principles/security.rst:371
	English ↹ ↵ NBS … “ ” ‘ ’ ﹙-﹚ ‐ – — These two keys are generated together and they are linked by a complex mathematical relationship that is such that it is computationally difficult to compute :math:`K_{priv}` from :math:`K_{pub}`. 196/10000 · 196
34 ../../principles/security.rst:375
	English ↹ ↵ NBS … “ ” ‘ ’ ﹙-﹚ ‐ – — A public key cryptographic scheme is a combination of two functions : 69/10000 · 69
35 ../../principles/security.rst:377
	English ↹ ↵ NBS … “ ” ‘ ’ ﹙-﹚ ‐ – — an encryption function, :math:`E_{p}`, that takes a key and a message as parameters 83/10000 · 83
36 ../../principles/security.rst:378
	English ↹ ↵ NBS … “ ” ‘ ’ ﹙-﹚ ‐ – — a decryption function, :math:`D_{p}`, that takes a key and a message as parameters 82/10000 · 82