Classical Cryptography

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Presentation transcript:

Classical Cryptography The Enigma Rotor machine The Jefferson cylinder Scytale Hieroglyphics

Symmetric Cryptography Uses a single key for both encryption and decryption The encryption and decryption algorithms are inverses of each other

Simple Substitution Ciphers (Monoalphabetic Ciphers) A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Y M I H B A W C X V D N O J K U Q P R T F E L G Z S

Simple Substitution Ciphers (Monoalphabetic Ciphers) A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Y M I H B A W C X V D N O J K U Q P R T F E L G Z S \\COME AT ONCE

Simple Substitution Ciphers (Monoalphabetic Ciphers) A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Y M I H B A W C X V D N O J K U Q P R T F E L G Z S \\COME AT ONCE IKOB YT KJIB

Simple Substitution Ciphers (Monoalphabetic Ciphers) A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Y M I H B A W C X V D N O J K U Q P R T F E L G Z S \\COME AT ONCE IKOB YT KJIB GIVE TO INGE HAVE TO ACHE SECT IN EAST

Methods for decrypting a simple substitution cipher: Brute force attack key space of the substitution cipher = 26! ≈ 288 Letter frequency analysis determine the frequency of every ciphertext letter look at pairs , triples, or quadruples of ciphertext symbols

Letter Frequency The most common digrams (in descending order): th, he, in, en, nt, re, er, an, ti, es, on, at, se, nd, or, ar, al, te, co, de, to, ra The most common trigrams (in descending order): the, and, tha, ent, ing, ion, tio, for, nde, has, nce, edt, tis, oft, sth, men

Polyalphabetic Ciphers Encrypt multiple characters at a time Relationship from plain to ciphertext is one-to-many Thwart statistical attacks

Polyalphabetic Ciphers Vigenère Autokey Playfair Hill One-time pad Rotor Enigma

Vigenère Cipher Let m be a positive integer (the key length) P = C = K = Z26 x ... x Z26 = (Z26) m For k = (k1, ..., km): ek(x1, ..., xm) = (x1 + k1 (mod 26), ..., xm + km (mod m)) dk(y1, ..., ym) = (y1 - k1 (mod 26), ..., ym - km (mod m))

Modern Cryptography AES RSA Rivest, Shamir, and Adleman The Future of Cryptography and Quantum Computing

Average Time Required for Exhaustive Key Search