Cryptography Basics Quiz

Basic Encryption and Decryption (I)

• Cryptography is a branch of mathematics that deals with transforming data.
• Cryptographic algorithms are used in information security and network security to secure data storage, transmission, and interaction between parties.
• Cryptographic algorithms can be categorized as keyless, single-key (symmetric), or two-key (asymmetric).
• Keyless algorithms don't use keys during transformation (e.g., cryptographic hash function).
• Single-key (symmetric) algorithms use a single secret key for both encryption and decryption.
• Two-key (asymmetric) algorithms use distinct but related keys, a public key for encryption and a private key for decryption.
• Plaintext is the original message.
• Ciphertext is the coded message.
• Encryption is the process of transforming plaintext to ciphertext.
• Decryption is the process of transforming ciphertext to plaintext.

Cryptographic Algorithms

• Keyless: No keys are used during cryptographic transformations. Example: Cryptographic Hash Functions.
• Single-key: The result of a transformation is a function of the input data and a single key (secret key).
• Two-key: Two different but related keys (private key and public key) are used at various calculation stages.
• The focus of this chapter is single-key (symmetric encryption or conventional encryption).

Definitions (cont'd)

• Cryptography: The study of various encryption schemes.
• Cryptographic System (Cryptosystem)/Cipher: A scheme for both encryption and decryption.
• Cryptanalysis: Techniques to decipher a message without knowledge of the encryption details. A cryptanalyst is someone who practices cryptanalysis.
• Cryptology encompasses both cryptography and cryptanalysis.
• Cryptographic Hash Function: The most fundamental cryptographic algorithm.
• Its function is a one-way hash algorithm (creates a unique digital fingerprint for a data set—a digest or a hash, not ciphertext). This fingerprint represents the data's content.
• Hashing is used mainly for data comparison as it can't be reversed.
• Encoding: Translates entire words or phrases into other words or phrases.
• Enciphering: Translates individual letters or symbols into other letters or symbols individually.
• Encryption: A comprehensive term encompassing both encoding and enciphering.

Simplified Model of Symmetric Encryption

• Encryption algorithm transforms plaintext into ciphertext.
• Decryption algorithm transforms ciphertext back into plaintext.
• Encryption and decryption algorithms require a shared secret key.
• Security depends on a strong encryption algorithm and secure key management.

Model of Symmetric Cryptosystem

• A model depicts the process of a symmetric cryptosystem with encryption, decryption, a key source, and a secure channel. Data and the key are sent to the destination through the secure channel.

Cryptographic Systems

• Cryptographic systems are characterized by three dimensions: operations, keys, and processing.
• Operations: substitution, transposition, product (e.g., involving multiple substitutions and transpositions).
• Keys: symmetric (single-key), asymmetric (two-key or public-key).
• Processing: block (processes one block of elements at a time—e.g., block cipher), stream (processes elements continuously—e.g., stream cipher).

Cryptanalysis and Brute-Force Attack

• Cryptanalysis aims to recover the encryption key rather than the plaintext using the algorithm's nature and characteristics of the plaintext.
• Brute-force attack tries every possible key until an intelligible translation of ciphertext into plaintext is achieved.
• Knowledge of the expected plaintext and means to distinguish plaintext from gibberish is required.

Types of Attacks on Encrypted Messages

• Ciphertext Only: Only the ciphertext is known to the cryptanalyst.
• Known Plaintext: Some plaintext-ciphertext pairs are known.
• Chosen Plaintext: The cryptanalyst can choose plaintext to encrypt.
• Chosen Ciphertext: The cryptanalyst can choose ciphertext to decrypt.
• Chosen Text: The cryptanalyst can choose both plaintext and ciphertext.

Encryption Scheme Security

• Unconditionally secure: No matter how much time the opponent has, decrypting the ciphertext is impossible because the required information isn't there.
• Computationally secure: The cost of breaking the cipher exceeds the value of the encrypted information/duration of the information’s useful lifetime.

Brute-Force Attack and Strong Encryption

• Brute-force attacks try all possible keys on a piece of ciphertext until an intelligible translation into plaintext is achieved (i.e., requires some knowledge of the expected plaintext).
• Strong encryption makes unauthorized access to plaintext practically impossible.
• Properties of a strong encryption algorithm include: proper algorithm choice, sufficiently long key lengths, appropriate protocols, well-engineered implementation, and absence of deliberate flaws.

Encryption Algorithms: Symmetric vs Asymmetric

• Symmetric encryption: Uses the same key for both encryption and decryption. Common formula: C = E(P, K) and P = D (E(P, K), K).
• Asymmetric encryption: Uses different keys for encryption (public key) and decryption (private key). Common formula: C = E (P, K₁) and P = D (E (P, K₁), KD).

Substitution Technique

• Substitution replaces plaintext letters with other letters, numbers, or symbols (or bit patterns with ciphertext bit patterns).

Caesar Cipher

• A simple substitution cipher where each letter is shifted a fixed number of places down the alphabet (e.g., shift three places down).
• Algorithm: c = E(k, p) = (p + k) mod 26 and decryption: p = D(k, C) = (C – k) mod 26, where k is the shift.
• It has a weakness that is easy to predict the encryption pattern as it is simple.

Caesar Cipher Algorithm

• The Caesar cipher shifts letters a fixed number 'k' positions in the alphabet.

The Caesar Cipher – Examples

• Illustrates how the Caesar cipher works with key values.

Brute-Force Cryptanalysis of Caesar Cipher

• Shows that only 25 possible keys exist for the Caesar cipher.
• Explains how to try every possible key until an intelligible translation into plaintext is obtained.

Monoalphabetic Cipher

• A type of substitution cipher that substitutes each plaintext letter with a single ciphertext letter.
• A drastic increase in the keyspace can be achieved by allowing arbitrary substitution such as permutations of the alphabet.

Cryptanalysis Based on Relative Frequencies of Letters

• The Arabs contributed significantly to cryptanalysis.
• Qalqashandi developed a method for analyzing ciphers.
• Analyzing the relative frequencies of letters in ciphertext helps determine the corresponding letters of the original plaintext from the frequency distribution of the letters from the plaintext.

Relative Frequency of Letters in English Text

• The analyst analyzes the regularities of the language by determining ciphertext letter frequencies (expressed in percentage) and comparing them to a standard frequency distribution in English.
• This comparison helps in determining equivalents to ciphertext letters based on their frequency distribution in the particular language (e.g., given P=13.33% and/or Z = 0.00% frequency from ciphertext, the equivalents in a specific plaintext language can be determined based on the standard frequencies of letters).

Substitution using Key Phrase

• Using a key phrase creates a simple substitution cipher (monoalphabetic) where the key phrase generates the cipher alphabet by substituting the plaintext with letters from the key phrase. The phrase consists of unique letters to avoid redundancies.

Substitution using Key Phrase: Example

• This section demonstrates an example of using the key phrase SPECTACULAR to substitute the plaintext. A better key phrase (e.g., EZRA CORNELL) can be used instead.

Substitution using a Key Phrase and a Matrix

• Using a keyword to substitute letters using a matrix, making the substitution more complex. It does so by transcribing letters from the key phrase as the headings of the column while the remaining letters of the alphabet fill in order in rows below the columns of the key.

Multiplicative Ciphers

• Multiplicative Ciphers (Monoalphabetic Substitutions) substitute letters based on multiplication (f(a) = a*k mod n) where both k and n have no shared factors/GCD (k, n) = 1.
• If k and n are not relatively prime, several plaintext letters will encrypt to the same ciphertext letter, not all letters appearing in the ciphertext.
• Example: if k = 12, Plaintext (ABC…) will be substituted by Ciphertext (AMY… ).

Table of Multiplication modulo 26

• This table provides examples of multiplication modulo 26.
• Only some numbers have multiplicative inverses modulo 26.

Multiplicative Cipher - Encryption example

• Shows a practical step-by-step example of encrypting a message using a multiplicative cipher (where k= 7).

Multiplicative Cipher - Decryption example

• The process of decrypting a message encrypted using the multiplicative cipher using the inverse multiplicative value of the encryption key (k⁻¹) modulo 26.

Cryptanalysis of the Caesar Cipher

• Demonstrates the cryptanalysis process for the Caesar cipher (e.g., recognizing patterns, repetition, and applying these techniques to plaintext and applying ciphertext substitutions).

Polyalphabetic Substitution Ciphers

• Addresses the weakness of monoalphabetic ciphers, which use the same key for every substitution.
• Solutions to flatten the distribution involve using distinct encryption alphabets by using different keys (i.e., polyalphabetic substitution).
• Flatten the frequencies of the letters with polyalphabetic ciphers; combining high and low frequencies in order to avoid the repeated use of encryption alphabet, so as to avoid revealing possible patterns.