Basic Encryption and Decryption

### Basic Encryption and Decryption
- Cryptography is a branch of mathematics dealing with data transformation.
- Cryptographic algorithms are used in information and network security.
- Cryptography is essential for secure data storage, transmission and interaction.

### Cryptographic Algorithms
- These can be keyless, single-key, or two-key.
- Keyless algorithms do not use keys during cryptographic transformations such as Cryptographic Hash Functions.
- Single-key algorithms use a single key, known as a secret key.
- Two-key algorithms use two different but related keys: a private key and a public key.
- This chapter covers single-key algorithms, such as symmetric or conventional encryption.

### Definitions in Cryptography
- Encryption encodes a message to make its meaning not obvious.
- Plaintext is the original message.
- Ciphertext is the coded message.
- Encryption is converting plaintext to ciphertext, also called enciphering.
- Decryption restores plaintext from ciphertext, also called deciphering.
- Cryptography is the study of encryption schemes.
- A cryptographic system (or cipher) is a scheme for encryption and decryption.
- Cryptanalysis uses techniques for deciphering a message without knowledge of the enciphering details.
- A person practicing cryptanalysis is called a cryptanalyst.
- Cryptology includes the areas of cryptography and cryptanalysis.

### Cryptographic Hash Function
- Cryptographic Hash Functions are basic cryptographic algorithm that is one-way.
- Hash algorithms create a unique "digital fingerprint," called hashing.
- A digest (or message digest/hash) represents the contents of the data.
- Hashing algorithms do NOT create ciphertext that can later be decrypted.
- Hashing is "one-way", where the contents can't be used to reveal the original data.
- Hashing is used for comparison purposes.
- A secure hash that is created from a set of data cannot be reversed.
- A secure hashing algorithm is fixed size, unique, original, and secure.

### Simplified Symmetric Encryption Model
- There are two requirements for secure conventional encryption: a strong encryption algorithm and having the sender and receiver obtain copies of the secret key in a secure fashion, keeping it secure.

### Cryptographic Systems
- Cryptographic Systems can be characterized along three independent dimensions: the type of operations used for transforming plaintext to ciphertext, the number of keys used, and the way in which the plaintext is processed
- The type of operations used for transforming plaintext to ciphertext are substitution, transposition, and product.
- Number of Keys can be symmetric (i.e., single-key, secret-key, conventional encryption ) or asymmetric encryption (i.e. two-key, or public-key encryption).
- The way Plaintext is processed can be via block cipher (processes the input one block of elements at a time, producing an output block for each input block) or stream cipher (processes the input elements continuously, producing output one element at a time, as it goes along).

### Cryptanalysis and Brute-Force Attack
- The objective of attacking an encryption system is to recover the key rather than recovering the plaintext with two general approaches: Cryptanalysis or Brute-force attack.
- Cryptanalysis relies on the nature of the algorithm plus some knowledge of the characteristics of the plaintext.
- The brute-force attack tries every possible key on a piece of ciphertext until an intelligible translation into plaintext is obtained with half of all possible keys being tried to achieve success.

### Types of Attacks
- Ciphertext Only Attack requires the Cryptanalyst to know the Encryption algorithm and Ciphertext.
- Known Plaintext Attack requires the Cryptanalyst to know the Encryption algorithm, Ciphertext and there’s One or more plaintext-ciphertext pairs formed with the secret key.
- Chosen Plaintext Attack requires the Cryptanalyst to know the Encryption algorithm, Ciphertext and possesses a Plaintext message, together with its corresponding ciphertext generated with the secret key
- Chosen Ciphertext Attack requires the Cryptanalyst to know the Encryption algorithm, Ciphertext and requires a Ciphertext chosen with it's corresponding decrypted plaintext generated with the secret key
- Chosen Text Attack requires the Cryptanalyst to know the Encryption algorithm, Ciphertext and possesses a Plaintext message together with its corresponding ciphertext generated with the secret key, plus having a Ciphertext chosen by cryptanalyst together with its corresponding decrypted plaintext generated with the secret key

### Encryption Scheme Security
- Unconditionally secure encryption can't be decrypted even if an opponent has lots of time.
- Computationally secure encryption means the cost of breaking the cipher exceeds the value of the encrypted information and the time required to break the cipher exceeds the useful lifetime of the information.

### Brute-Force Attack Details
- The brute-force attack involves trying every possible key of ciphertext into plaintext to try to get a intelligible message.
- Half of all possible keys must be tried to achieve success.
- Some degree knowledge about the expected plaintext, and some means of automatically distinguishing plaintext from garble may supplement this attack.

### Strong Encryption
- Strong Encryption makes it difficult for persons or systems to gain access to plaintext that has been encrypted and there are several properties that increase algorithm strength: appropriate choice of cryptographic algorithm, sufficiently long key lengths, choice of protocols, engineered implementation and absense of hidden flaws

### Encryption Algorithm Types
- Encoding translates entire words or phrases to other words or phrases.
- Enciphering translates letters or symbols individually.
- Encryption is the group of term that covers both encoding and enciphering.
- Symmetric Encryption uses the same key for encryption and decryption, following C = E(P, K) for encryption and P = D (E(P,K), K) for decryption.
- Asymmetric Encryption uses different keys for encryption and decryption, following  C = E (P, KE) for encryption and P = D (E (P, KE), KD) for decryption.

### Substitution Technique
- The Substitution Technique replaces letters of plaintext with other letters or by numbers or symbols.
- If the plaintext is viewed as a sequence of bits, it substitutes plaintext bit patterns with ciphertext bit patterns.

### Caesar Cipher
- Caesar Cipher is a substitution cipher and replaces each letter with the letter standing three places further down the alphabet, wrapping around so the letter following Z is A.
- Benefit: easy to remember.
- Disadvantage: easy to predict pattern of encryption.

### Caesar Cipher Algorithm
- Letters can be defined as numbers, starting with A assigned to 0.
- The shift may be of any amount, so the general Caesar algorithm is: "C = E(k, p ) = (p + k ) mod 26". "k" takes a value in the range of 1 to 25.
- The decryption algorithm is: "p = D(k, C ) = (C − k ) mod 26".

### Caesar Cipher - Decryption
- Decryption can be performed by following "p = D(k, C ) = (C − k ) mod 26"

### Brute-Force Cryptanalysis of the Caesar Cipher
- Has only 25 possible ciphers being that maps A to B,C,...,Z.
- This cipher could be simply tried to search until an intelligible translation into plaintext is obtained.
- Cipher Analysis is a given ciphertext where one has to just try all shifts of letters and do be need to recognize when have plaintext,
- This can be used to break ciphertext.

### Monoalphabetic Cipher
- With only 25 possible keys, the Caesar cipher isn't secure.
- Substitution achieves dramatic key space increase, like permutations of the alphabet.
- The permutation of a finite set S is an ordered sequence of all elements of that set, with each element appearing exactly once.
- If there are n! permutations of a set of n elements then it follows with n, there are over twenty six factorial possible keys.
- This approach is referred to as a monoalphabetic substitution cipher because a single cipher alphabet is used per message which always uses the same letter of the alphabet for the ciphertext letter.

### Cryptanalysis Based on Relative Frequencies
- Arabic author Qalqashandi wrote down a technique to solve ciphers which is used today.
- The line of attack is based on characteristics of the plaintext.
- The ciphertext letters are written down and counted to get the frequency of each symbol.
- The average frequency of each letter of language has plaintext which can be written out.
- Ciphertext can thus be solved.

### Key Phrase Substitution
- A Key Phrase, which is a keyword, is a simple substitution cipher, monoalphabetic cipher that mixes the letters using key phrase to generate the cipher alphabet.
- The plaintext retaining word divisions happens with each letter substituted by the letter in given key phrase.
- Key Phrase must contain unique letters and its redundancies removed before encrypting.
- Key phrase substitutions the same strength as the previous simple substitution ciphers.

### Key Phrase/Matrix Substitution
- To strengthen a key phrase substitution, apply a matrix to help identify which columns and rows will be used for its remaining sets of letters which fill order in said rows below.

### Multiplicative Ciphers
- In these ciphers, encryption uses f(a) = a*k mod n, where k and n are relatively prime so the letters of the alphabet produced a complete set of residues.
- If k and n are not relatively prime, several plaintext will encrypt to the same ciphertext letter and not all letter will appear in the ciphertext alphabet and e.g. if k = 12 and n =26.
- Decryption requires the ciphertext number to be multiplied by the multiplicative inverse of the key mod 26.
- Only 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, and 25 have multiplicative inverses mod26
- Here you can identify the numbers and Multiplicative inverses in this scenario:
    - 1=>1, 3=>9, 5=>21, 7=>15, 9=>3, 11=>19, 15=>7 , 17=>23, 19=>11, 21=>5, 23=>17, 25=>25

### Caesar Cipher Analysis
- Weaknesses: Blank translates to itself, English has relatively few short words, known short words can be subbed, repetition of patterns exposed.

### Polyalphabetic Substitution Ciphers
- They flatten the the frequency of the cypher alphabet where E1 (T) = a and E2 (T) = b and E1 (X) = a and E2 (X) = b.
- They combine two distributions by using two separate encryption alphabets.
- The first applies to all characters in odd positions while the second applies to even positions.