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Introduction to Block Ciphers

Introduction to Block Ciphers. Liam Keliher Dept . Mathematics and Computer Science Mount Allison University. Terminology. Cryptography : Study of mathematical techniques to provide information security

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Introduction to Block Ciphers

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  1. Introduction to Block Ciphers Liam Keliher Dept. Mathematics and Computer Science Mount Allison University

  2. Terminology • Cryptography: Study of mathematical techniques to provide information security • Cryptanalysis: Analysis of cryptographic methods, either to expose weaknesses or to prove strengths • Cryptology: Cryptography + Cryptanalysis • Primitive: Cryptographic building block – typically a mathematical function of some kind, e.g., • hash function • digital signature scheme • block cipher

  3. ke kd plaintext (p) plaintext (p) ciphertext (c) encryption algorithm decryption algorithm Attacker A block cipher is an encryption/decryption algorithm ► parameterized by a (master) key known only to communicating parties ► input (plaintext) / output (ciphertext) are n-bit strings (n = block size)

  4. Round R Round 2 Round 3 Round 1 subkeys k Most Block Ciphers are Product Ciphers plaintext (p) k1 k2 master key k3 kR ciphertext (c)

  5. n/2 bits n/2 bits kr f n/2 bits n/2 bits Feistel Network ► Standard block cipher structure ► Consists of multiple rounds (simpler encryption steps) ► One round:  input is split in half  left input half copied to right half of output  left input half forms input to round function, which depends on subkey for current round  round function output is XORed with right half of input to produced left half of output

  6. SPN-Based Block Ciphers Substitution-Permutation Network (SPN): ►Consists of multiple encryption rounds ► one round = three layers  Subkey mixing (XOR)  Substitution (s-boxes)  Linear transformation

  7. Well-known Block Ciphers • Data Encryption Standard (DES) • standardized by U.S. government in 1977 • Feistel network with 64-bit block and 56-bit key • extensivelycryptanalyzed (led to many new attacks) • Advanced Encryption Standard (AES) • selected as winner of NIST competition in 2001 • SPN structure with 128-bit block and 128/192/256-bit key • Camellia • successor to Japanese AES candidate E2 • Feistel network in which the round function is a mini SPN

  8. Advanced Encryption Standard (AES) • Originally called Rijndael(“Rhine-doll”) from names of designers, Vincent Rijmen and Joan Daemen • Number of rounds is based on key size: • 128 bits  10 rounds • 192 bits  12 rounds • 256 bits  14 rounds • Widely adopted since 2001 • arguably the most implemented block cipher today • used in Mount Allison’s wireless network

  9. Camellia • Block cipher introduced by NTT and Mitsubishi in August 2000 • used in Sony PSP, WinZIP, OpenSSH, etc. • Incorporated into numerous international standards (e.g., ISO/IET, IETF) • Considered competitive with the Advanced Encryption Standard (AES) for security and speed • Based on variation of Feistel network design above

  10. S S S S S S S S Camellia Specifics • Block size: N=128 bits • Possible key sizes: 128, 192, 256 bits • Number of rounds depends on key size: 128  18 rounds / 192 or 256  24 rounds • Subkeys are same size as input block (128 bits) • Round function:  kr 64-bit linear transformation

  11. Breakdown of Camellia Round Function = XOR operation (bitwise addition modulo 2) = substitution box (s-box): invertible mapping {0,1}8  {0,1}8 [needs to be nonlinear] = linear transformation; fast way to combine s-box outputs S

  12. Differential Cryptanalysis (DC) • Based on probability that a plaintext pair with a fixed XOR “difference” will produce an intermediate pair after (R-1) rounds with a fixed XOR difference • called differential probability (DP) • depends on (unknown) key, but average values can be used • Given fixed input/output differences with high DP, and enough captured plaintext-ciphertext pairs, attack can extract some or all of the key • DC was first successful attack on the Data Encryption Standard (an ancestor of Camellia) • Discovered in 1990 by Biham and Shamir

  13. input (plaintext) difference Δp rounds 1 … (R-1) View this as a big s-box: Want to find (Δx, Δy) such that DP (Δx, Δy) is maximized Reason: data complexity (number of p-c pairs required for successful attack) is proportional to inverse of this DP value Δq round R Δc output (ciphertext) difference

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