Classical CryptographyThe Jefferson cylinder The Enigma Rotor machine

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 ZY 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 ZY 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 ZY 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 ONCEIKOB 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 ZY 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 ONCEIKOB 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, raThe 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))

• AES• RSA

•The Future of Cryptography and Quantum Computing

Rivest, Shamir, and Adleman

Modern Cryptography

Average Time Required for Exhaustive Key Search