Symmetric Ciphers

A Feistel Cipher is a symmetric block cipher design that splits a plaintext block into two equal halves and processes them through several rounds of substitution and permutation using round sub-keys derived from the master key. A block of $2w$ bits is divid...

A block cipher encrypts data in fixed-size blocks. When a message is longer than one block, a mode of operation defines how the cipher is applied repeatedly. Two important modes are described below. --- Definition: In ECB mode, the plaintext is divided into...

A block cipher encrypts a fixed-size block of plaintext into a block of ciphertext using a key. However, most real-world messages are longer than a single block, so different modes of operation define how to apply the block cipher repeatedly to encrypt long...

Subkeys (4-bit each): - $K1 = 1100 = 12$ - $K2 = 1010 = 10$ - $K3 = 0000 = 0$ - $K4 = 1111 = 15$ - $K5 = 0101 = 5$ - $K6 = 1001 = 9$ Input plaintext blocks (4-bit each): - $X1 = 1011 = 11$ - $X2 = 1110 = 14$ - $X3 = 1011 = 11$ - $X4 = 1000 = 8$ Scaled opera...

IDEA (International Data Encryption Algorithm) is a symmetric block cipher that: - Operates on 64-bit plaintext blocks - Uses a 128-bit key - Performs 8 rounds of encryption followed by a final output transformation - Uses three algebraic operations: XOR, a...

--- Monoalphabetic cipher is more vulnerable than polyalphabetic cipher. - Monoalphabetic Cipher: A substitution cipher where each plaintext letter is always replaced by the same fixed ciphertext letter throughout the entire message. Example: Caesar Cipher....

- Element to invert: 95 (hexadecimal), interpreted as an element of $GF(2^8)$. - $95{16} = 1001\,01012$, giving polynomial $$b(x) = x^7 + x^4 + x^2 + 1$$ - AES irreducible (reduction) polynomial: $$m(x) = x^8 + x^4 + x^3 + x + 1$$ Note: The question only st...

A set R with two binary operations (+) and (×) is a Ring if for all a, b, c ∈ R the following axioms hold: Axiom Name ---------------- A1 a + b ∈ R Closure under addition A2 a + (b + c) = (a + b) + c Associativity of addition A3 a + b = b + a Commutativity ...

- Modulus for quadratic residues: $n = 7$ - Tasks: (a) define Galois field with example, (b) explain any two block cipher modes, (c) find quadratic residues of 7. No numeric data is missing. All parts are solvable. --- Definition: A Galois Field (Finite Fie...

- Dividend: $3x^2 + 4x + 3$ - Divisor: $5x + 6$ - Field: $GF(7)$, all arithmetic mod 7. We need $5^{-1} \pmod 7$: since $5 \cdot 3 = 15 \equiv 1 \pmod 7$, we have $$5^{-1} = 3 \text{ in } GF(7)$$ $$\frac{3x^2}{5x} = 3 \cdot 5^{-1} x = 3 \cdot 3 \, x = 9x \e...

--- 2-DES applies the DES algorithm twice with two independent keys $K1$ and $K2$ (each 56 bits, giving 112-bit effective key length). Encryption: $$C = E{K2}(E{K1}(P))$$ Plaintext $P$ is first encrypted with $K1$ to give an intermediate value, which is the...

--- The CIA Triad is the foundational model of information security consisting of three core principles: "Computer Security is the protection afforded to an automated information system in order to attain the applicable objectives of preserving the integrit...

--- A security policy is a set of rules and guidelines that define what is and is not allowed in a system. It is a high-level statement of intent that specifies the security goals an organization wants to achieve. It answers the question: "What needs to be ...

MixColumns is one of the four transformations in each AES round (except the final round). It operates on the state column by column. Each column of the $4 \times 4$ state matrix is treated as a four-term polynomial over $GF(2^8)$ and is multiplied (modulo $...