Classical cryptography

Classical Cryptography •Shift cipher •Substitution cipher •Affine cipher •Vigenère Cipher •Hill Cipher References • Douglas Stinson, Cryptography: Theory and Practice, 3rd, Chapman & Hall CRC, 2006 – Chapter Secure communication scheme The set of integers modulo m: • Remarks: – Congruences – – is a ring • Examples: We will always consider (a mod b) >= – = {0, 1, 2, …, 25} – 14 + 20 = in – 5*7 = in Lab computing: try operators + and * modulo m in Python The Shift Cipher For the particular key K = 3, the cryptosystem is often called the Caesar Cipher, which was purportedly used by Julius Caesar Caesar cipher (K = 3) • x = “NGUYENTHANHNHUT” • y = “QJXBHQWKDQKQKXW” The Shift Cipher Encryption example The Shift Cipher Encryption example The Shift Cipher Decryption example ow Cryptool it! 10 The Permutation Cipher 32 33 34 1.16 35 1.17 36 The Permutation Cipher is a special case of the Hill Cipher Short break! 37 Stream ciphers • The encryption of all previous cryptosystems using the same key K for each block of the plaintext: • block cipher • Stream cipher uses keystream z = z1z2… 38 Stream ciphers • Periodic stream cipher with period d – zi+d = zi for all i > – Vigenere is a periodic stream cipher with period m • Some basic stream cipher: (self-reading) – Linear feedback shift register (LFSR) – Autokey Cipher 39 The Vigenère cipher is a stream cipher • We define the keystrean as follow: • This generate the keystream Short break! 40 Cryptanalysis • The goal of the adversary/the opponent: – Determine the key K • General assumption (Kerckhoff’s principle): – Oscar knows the cryptosystem being used • Four attack models: – – – – Ciphertext only Known plaintext Chosen plaintext Chosen ciphertext More difficult Less difficult 41 Basic tool for cryptanalysis • Statistical properties of language (English) – Beker and Piper partition 42 Digrams and trigrams in English • The 30 most common digrams 43 Cryptanalysis example of Affine Cipher • 1st Guess: –R –D e t – gcd(6,26) > 44 Cryptanalysis of Affine Cipher • Next guess R e, E t: – we obtain a = 13 (13|26) • Next guess R e, H t: – we obtain a = (gcd(8,26)>1) • Next guess R e, K t: – we obtain a = 3, b = (maybe correct) 45 Exercises • Big problem: – Statistical properties of Vietnamese language • Cryptanalyses of: (self-reading) – Substitution Cipher – Vigenere Cipher – Hill Cipher – LFSR Cipher 46 ...References • Douglas Stinson, Cryptography: Theory and Practice, 3rd, Chapman & Hall CRC, 2006 – Chapter Secure communication