# Chapter 1: Computer Security Concepts ## Computer Security The protection afforded to an automated information system in order to attain the applicable objectives of preserving the integrity, availability, and confidentiality of information system resources (includes hardware, software, firmware, information/data, and telecommunications). ## The CIA triad Traditional definitions of information security are based on three information security goals: Confidentiality : Preserving authorized restrictions on information access and disclosure, including means for protecting personal privacy and proprietary information. A loss of confidentiality is the unauthorized disclosure of information. Integrity : Guarding against improper information modification or destruction, including information nonrepudation and authenticity. A loss of integrity is the unauthorized modification or destruction of information. Availability : Ensuring timely and reliable access to and use of information. A loss of availability is the disruption of access to or use of information or an information system. Although the use of the CIA triad to define security objectives is well established, some in the security field feel that additional concepts are needed to present a complete picture. Two of the most commonly mentioned are as follows: Authenticity : The property of being genuine and being able to be verified and trusted; confidence in the validity of a transmission, a message, or message originator. This means verifying that users are who they say they are and that each input arriving at the system came from a trusted source. Accountability : The security goal that generates the requirement for actions of an entity to be traced uniquely to that entity. This supports nonrepudation, deterrence, fault isolation, intrusion detection and prevention, and afteraction recovery and legal action. Because truly secure systems are not yet an achievable goal, we must be able to trace a security breach to a responsible party. Systems must keep records of their activities to permit later forensic analysis to trace security breaches or to aid in transaction disputes. ## Security Attacks Security attacks can be either passive or active. ### Passive attacks Passive attacks are in the nature of eavsdropping on, or monitoring of, transmissions. The goal of the attacker is to obtain information that is being transmitted. Two types of passive attacks are the release of message contents (eavesdropping) and traffic analysis. Eavesdropping : The attacker monitors the communication, for example by sniffing packets or tapping a telephone wire. Traffic analysis : The attacker monitors the amount, source and destination of communication. Passive attacks are very difficult to detect, because they do not involve any alteration of the data. Typically, the message traffic is sent and received in an apparently normal fashion, and neither the sender nor receiver is awere that a third party has read the messages or observed the traffic pattern. however, it is feasible to prevent the success of these attacks, usually by means of encryption. Thus, the emphasis in dealing with passive attacks is on prevention rather than detection. ### Active attacks Active attacks involve some modification of the data stream or the creation of a false stream and can be subdivided into four categories: masquerade, replay, modification of messages, and denial of service. Masquerade : The attacker claims to be a different entity. Replay : The attacker sends a message which has already been sent. Modification of messages : The attacker changes messages during transmission. Denial of service : The attacker prevents legitimate users from accessing resources Active attacks present the opposite characteristics of passive attacks. Whereas passive attacks are difficult to detect, measures are available to prevent their success. On the other hand, it is quite difficult to prevent active attacks absolutely because of the wide variety of potential physical, software, and network vulnerabilities. Instead, the goal is to detect active attacks and to recover from any disruption or delays caused by them. If the detection has a deterrent effect, it may also contribute to prevention. ## Security services A security service is a processing or communication service to give a specific kind of protection to system resources. Peer entity authentication : Provides confirmation of the claimed identity of an entity. Data origin authentication : Provides confirmation of the claimed source (origin) of a data unit (message). Access control : Provides protection against unauthorized use of resources. Access control service : Is usually provided in combination with authentication and authorisation services. Data confidentiality : Protects data against unauthorised disclosure. Traffic flow confidentiality : Protects disclosure of data which can be derived from knowledge of traffic flows. Data integrity : Detects any modification, insertion, deletion or replay of data in a message or a stream of messages. Non-repudiation : Protects against any attempt by the creator of a message to falsely deny creating the data or its contents. X.800 talks about nonrepudiation of origin to protect against denial by the sender of a message, and nonrepudiation of receipt to protect against denial by the recipient of a message. Availability service : protects a systems against denial of service. It is not listed in X.800 as a separate service. ## Security mechanisms A security mechanism is a method of implementing one or more security services. Encipherment : Transformation of data in order to hide its information content Digital signature mechanisms: : Cryptographic algorithms which transform data using a signing key. The essential property is that signed data can only be created with the signing key. Access control mechanisms : Access control lists, passwords, or tokens may be used to indicate access rights. Data Integrity mechanisms : "Corruption detection techniques" which can be used with "sequence information". Authentication exchange mechanisms : Protocols which exchange information to ensure identity of protocol participants. We will study examples such as TLS later. Traffic padding : Spurious traffic generated to protect against traffic analysis. Traffic padding is typically used in combination with encipherment. Routing control mechanism : Use of specific secure routes. The notarization mechanism : Uses a trusted third party to assure the source or receipt of data. The trusted third party is sometimes called a notary. ## Risk management A key tool in information security management. 1. Identify threats 2. Classify all threats according to likelihood and severity 3. Apply security controls based on cost benefit analysis # Chapter 2: Number Theory Please feel free to fill this missing chapter. # Chapter 3: Classical Encryption Techniques: ## Symmetric Cipher Model A symmetric encryption scheme has five ingredients: Plaintext : This is the original intelligible message or data that is fed into the algorithm as input. Encryption algorithm : The encryption algorithm performs various substitutions and transformations on the plaintext. Secret key : The secret key is also input to the encryption algorithm. The key is a value independent of the plaintext and of the algorithm. The algorithm will produce a different output depending on the specific key being used at the time. The exact substitutions and transformations performed by the algorithm depend on the key. Ciphertext : This is the scrambled message produced as output. It depends on the plaintext and the secret key. for a given message, two different keys will produce two different ciphertexts. The ciphertext is an apparently random stream of data and, as it stands, is unintelligible. Decryption algorithm : This is essentially the encryption algorith run in reverse. It takes the ciphertext and the secret key and produces the original plaintext. There are two requirements for seccure use of conventional encryption:

# Definitions These are definitions found in course material (mostly exercises) which may prove useful for the exam ##Chapter 1 Availability : ensuring resources are accessible when required by an authorised user Cipher : See own section Confidentiality : preventing unauthorised disclosure of information Data origin authentication : provides confirmation of the claimed source (origin) of a data unit (message) Entity authentication : provides confirmation of the claimed identity of an entity Integrity : preventing unauthorised (accidental or deliberate) modification or destruction of information Kerckhoffs’ principle : the cryptanalyst has complete knowledge of the cipher. The only unknown part is the decryption key. Non-repudiation : Ensures that you cannot hide the source (origin) of a data unit (message). Substitution : each character (or set of characters) is replaced by a different character (or set of characters) Transposition : the characters in the plaintext are mixed up with each other (permuted) ## Chapter 2 Confusion : This involves substitution to make the relationship between the key and ciphertext as complex as possible. Diffusion : This involves transformations that dissipate the statistical properties of the plaintext across the ciphertext. (A small change in plaintext should give a completely different ciphertext) Feistel cipher : An iterated cipher in which the round function swaps the two halves of the block and forms a new right hand half Iterated cipher : Most modern ciphers in this category, read more below. Product cipher : A product cipher is a cryptosystem in which the encryption function is formed by applying (or composing) several sub-encryption functions. Substitution-permutation network : An iterated cipher. Takes a block of the plaintext and the key as inputs, and applies several rounds of permutations, known as substitution boxes(S-box) and permutation boxes (P-box). A __S-box__ substitutes sub-blocks of size l bits (its input) by another block of bits (its output). It can be thought of as a substitution cipher. A __P-box__ takes the output from the S-boxes of one round, permutes the bits and feed them into the S-boxes in the next round. It can be thought of as a transposition cipher. At each round, the __round key__ is combined with some operation such as XOR. Group generator : A group generator is a group element g that in the operation __$g^k \mod p$__ represents all the elements that are relatively prime to p. Consider for example the group G $\mathbb{Z}_5$. G consists of the elements {1, 2, 3, 4}. One or several of these group elements may be a group generator for G. A way to check this is to use __$g^k \mod 5$__ for the k group elements and see if they represent all the group elements. Example: $2^1 =2 \mod 5 = 2$ $2^2 =4 \mod 5 = 4$ $2^3 =8 \mod 5 = 3$ $2^4 =16 \mod 5 = 1$ 2 is a group generator for $\mathbb{Z}_5$ because all its elements ({1, 2, 3, 4}) are represented. Finite field : placeholder ## Chapter 3 Electronic Code Book (ECB) Mode : The basic mode of a block cipher. Plaintext block $P$ is encrypted with key $K$ to produce ciphertext block $C_t$. Ciphertext block $C$ is decrypted with key $K$ to produce plaintext block $P_t$.  Cipher Block Chaining (CBC) Mode : A random initialization vector (IV) is chosen and sent together with the ciphertext blocks. $C_t=E(P_t\oplus C_{t-1},K)$ where $C_0=IV$ $P_t=D(C_t,K)\oplus C_{t-1}$ where $C_0=IV$  CTR Mode : CTR is a synchronous stream cipher. The keystream is generated by encrypting successive values of a "counter", initialised using a nonce (randomly chosen value) N: $O_t=E(T_t,K)$, where $T_t=N||t$ is the concatenation of the nonce and block number t. Encryption: $C_t=O_t\oplus P_t$. Decryption: $P_t=O_t\oplus C_t$.  True Random Number Generator (TRNG) : is a physical process which outputs each valid string independently with equal probability Pseudo Random Number Generator (PRNG) : is a deterministic algorithm which approximates a TRNG. Message Authentication Code (MAC) : A message authentication code (MAC) is a cryptographic mechanism used for ensuring message integrity. A MAC tag should at least be of length $\log_2{I/R}$ where $I$ is a limit on how many invalid messages are detected before the key is changed and $R$ is the acceptable probability that a false message is accepted. Stream Cipher : Stream ciphers are characterised by the generation of a keystream using the short key and an initialisation value as input. Each element of the keystream is used successively to encrypt one or more ciphertext characters. Stream ciphers are usually symmetric key ciphers: sender and receiver share the same key and can generate the same keystream given the same initialisation value. Synchronous stream ciphers : The keystream is generated independently of the plaintext. Both sender and receiver need to generate the same keystream and synchronise on its usage. One Time Pad : The key is a random sequence of characters, all of them independently generated. Each character in the key is used one time only. The one-time pad provides perfect secrecy. Linear Feedback Shift Register : A LFSR is a common component in design of stream ciphers. ## Chapter 4 Factorisation problem : Given an integer of *m* bits, find its prime factors. Factorisation by trial division is an exponential time algorithm and is hopeless for numbers of a few hundred bits. A number of special purpose methods exist, which apply if the integer to be factorised has special properties. The best current general method is known as the number field sieve. The number field sieve is a sub-exponential time algorithm. Discrete logarithm problem : Let g be a generator of $\mathbb{Z}_p^*$ for a prime p. The discrete log problem over $\mathbb{Z}_p^*$ is: **given y in $\mathbb{Z}_p^*$ find x with y = $g^x$ mod p.** Big O-notation : placeholder Fermat test : *if* a number p is prime then $a^{p−1}$ mod p = 1 for all a with gcd(a, p) = 1. If we examine a number n and find that $a^{n−1}$ mod n $\neq$ 1 then we know that n is not prime. Miller-Rabin test : placeholder RSA Encryption equation : placeholder RSA Decryption equation : placeholder RSA Padding : placeholder Prime number theorem : placeholder Håstad's attack : placeholder ## Chapter 5 Generator of $\mathbb{Z}_p^*$ : placeholder Diffie-Hellman key exchange : placeholder Elgamal cryptosystem : placeholder Collision resistance : placeholder Second preimage resistance : placeholder One-wayness : placeholder Birthday paradox : placeholder HMAC : placeholder GCM Mode : placeholder ## Chapter 6 Digital signature : placeholder Existential forgery : placeholder Selective forgery : placeholder Digital Signature Algorithm (DSA) : placeholder Key predistribution : placeholder Session key distribution : placeholder Key agreement : placeholder Needham-Schroeder protocol : placeholder Kerberos : placeholder TODO: Scrape definitions from all exercises (currently they are just from exercise 1-6) # Ciphers ## Symmetric cipher (secret key cipher) encryption and decryption keys known only to sender and receiver. (DES) ## Asymmetric cipher (public key cipher) each participant has a public key and a private key, may allow both encryption and signatures. (RSA) ## Attacks ### Ciphertext only attack the cryptanalyst has available only the intercepted cipher text. ### Known plaintext attack the cryptanalyst knows a small amount of plaintext and its cipher text equivalent ### Chosen plaintext attack The cryptanalyst can obtain the cipher text equivalent of some plaintext which can be selected by the attacker, i.e the attacker has an "inside encryptor” available ### Chosen cipher text attack The cryptanalyst can obtain the plaintext equivalent of some cipher text which can be selected by the attacker, i.e. the attacker has an “inside decryptor” available. ## Historical ciphers - Caesar - Substitution - Vigenère. Caesar, but also uses a key in order to choose how many steps to shift the alphabet for each letter ## Stream ciphers ## Block ciphers ### DES #### Triple-DES To increase the security of DES, the algorithm may be run multiple times. Two times would be the simplest, but is vulnerable to a _meet-in-the-middle_ attack. To counter this, three runs are needed. This is often implemented as Encrypt-Decrypt-Encrypt. This allows backwards compatibility with normal DES, by using the same key for all three steps: $$ E(K_1, D(K_1, E(K_1, X))) = E(K_1, X) $$ While 3DES takes three keys as parameters, using it with only two keys is enough to stop the meet-in-the-middle attack, and often good enough: $$ E(K_1, D(K_2, E(K_1, X))) $$ Some applications, like PGP and S/MIME, still use three keys with 3DES. ### AES Consists of four stages: Substitute bytes : Uses an S-box to perform a byte-by-byte substitution of the block ShiftRows : A simple permutation MixColumns : A substitution that makes use of arithmetic over $GF(2^8)$ AddRoundKey : A simple bitwise XOR of the current block with a portion of the expanded key Only the `AddRoundKey` stage makes use of the key. The other three stages provides confusion, diffusion and non-linearity, but no security in themselves. When decrypting with AES, the inverses of the three first stages are used. The `AddRoundKey` stage is the same, because $ A \oplus B \oplus B = A $. #### Key expansion Input : 16-byte key. Output : 176 bytes (44 words) The first four words are used in the initial AddRoundKey step. The next ten word-groups are used in the ten rounds of the cipher. ### RSA # Iterated ciphers - Encryption process divided into _r_ similar rounds - the sub encryption functions _g_ are the same for all rounds - Each key $K_i$ is derived from the overall master key K. The keys $K_i$ are called round keys or subkeys and are derived from K using a process called the key schedule. ## Encryption Given a plaintext block, P, a round function g and round keys $K_1, K_2, . . . ,K_r$ , the ciphertext block, C, is derived through r rounds as follows. $$W_{0} = P$$ $$W_{1} = g(W_{0}, K_{1})$$ $$W_{2} = g(W_{1}, K_{2})$$ $$.$$ $$.$$ $$.$$ $$W_{r} = g(W_{r−1}, K_{r})$$ $$C = W_{r}$$ # Pseudorandom number generation Generated numbers should be as random as possible. This is defined by two criteria: Uniform distribution : The frequency of occurence of ones and zeros should be approximately equal. Independence : It should not be possible to infer a subsequence from any other.