Introduction to Cryptography
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1 T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A Introduction to Cryptography EECE 412 1
2 Module Outline Historical background Classic ciphers One-time pad The Random Oracle model Random functions: Hash functions Random generators: stream ciphers Random Permutations: block ciphers 2
3 learning objectives each student should be able to: explain classic ciphers covered in the lectures encrypt and decrypt using these classic cyphers break classic ciphers (home assignment #2) explain one-time-pad and encrypt/decrypt wit it explain the Random Oracle Models for hash function, stream cipher, and block cipher 3
4 Crypto Cryptology! The art and science of making and breaking secret codes Cryptography! making secret codes Crypto! all of the above (and more) Cryptanalysis! breaking secret codes 4
5 How to Speak Crypto A cipher or cryptosystem is used to encrypt the plaintext The result of encryption is ciphertext We decrypt ciphertext to recover plaintext A key is used to configure a cryptosystem A symmetric key cryptosystem uses the same key to encrypt as to decrypt A public key cryptosystem uses a public key to encrypt and a private key to decrypt 5
6 Crypto as Black Box key key plaintext encrypt decrypt plaintext ciphertext a generic use of crypto 6
7 basic assumptions in crypto assumptions 1. The system is completely known to the attacker 2. Only the key is secret Also known as Kerckhoffs Principle Crypto algorithms are not secret 7
8 Kerckhoff s Principle The security of a cryptosystem must not depend on keeping secret the crypto-algorithm. The security depends only on keeping secret the key Auguste Kerckhoff von Nieuwenhof Dutch linguist
9 basic assumptions in crypto assumptions 1. The system is completely known to the attacker 2. Only the key is secret Also known as Kerckhoffs Principle Crypto algorithms are not secret Why do we make this assumption? Experience has shown that secret algorithms are weak when exposed Secret algorithms never remain secret Better to find weaknesses beforehand 9
10 Historical Background To read: 10
11 two types of ciphers substitution transposition 11
12 Letter Indices in English Alphabet 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
13 Caesar Cipher Plaintext is HELLO WORLD Change each letter to the third letter following it (X goes to A, Y to B, Z to C) Key is 3, usually written as letter D C = P + K mod 26 Ciphertext: KHOOR ZRUOG Plain! HELLOWORLD Key DDDDDDDDDD! Cipher!KHOORZRUOG 13
14 a simple attack how to attack Caesar Cipher? exhaustive/brute-force (key) search with 26 keys, how many attempts on average? Trudy can try 2 40 candidates/second hours months how to increase key space for substitution cipher? 14
15 Monoalphabetic Substitution Invented by Arabs in 8th or 9th centuries A B C D E F G H I J K L M N.. Z F T W S G M P A Z C L V O D.. B Plain! HELLOWORLD Key!! Cipher Cipher! AGVVYEYZVS 15
16 Frequency Analysis of English Letters 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 16
17 Polyalphabetic Vigenère Cipher proposed by Blaise de Vigenere from the court of Henry III of France in the sixteenth century Like Cæsar cipher, but use a phrase Example Message: TO BE OR NOT TO BE THAT IS THE QUESTION Key:! RELATIONS Encipher using Cæsar cipher for each letter: Plain TO BE OR NOT TO BE TH AT I S THE QUESTION Key RE LA T I ONS RE LA T I ON SR ELA T I ONSREL Cipher KS ME HZ BBL KS ME MPOG AJ XSE J CSF LZSY 17
18 T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A Playfair Cipher 18
19 background encrypts pairs of letters (digraphs), instead of single letters ~600 possible digraphs rather than the 26 possible monographs was used for tactical purposes by British forces in the Second Boer War (in South Africa) and in World War I the Australians and Germans during World War II 19
20 anecdotal history invented in 1854 by Charles Wheatstone rejected by the British Foreign Office when it was developed because of its perceived complexity Wheatstone offered to demonstrate that three out of four boys in a nearby school could learn to use it in 15 minutes the Under Secretary of the Foreign Office responded: "That is very possible, but you could never teach it to attachés." named after Lord Playfair who promoted the use of the cipher source: wikipedia.org 20
21 setting up the cipher 5 x 5 table example key: playfair example drop any duplicate letters fill the remaining of the letters from the English alphabet / one letter (J or Q) source: wikipedia.org 21
22 encryption overview 1. break the plain text into digraphs 1. split double letters with X, e.g., EE -> EXE 2. append X if odd number of characters. 3. "Hide the gold in the tree stump" becomes "HI DE TH EG OL DI NT HE TR EX ES TU MP" 2. map each digraph out using the table 22
23 mapping rules If a pair forms a rectangle, replace it with letters from the opposite corners on the same row. source: wikipedia.org 23
24 mapping rules If the letters appear on the same column of your table, replace them with the letters immediately below respectively. source: wikipedia.org 24
25 P L A Y F I R E X M B C D G H K N O Q S T U V W Z HI DE TH EG OL DI NT HE TR EX ES TU MP BM OD??... 25
26 P L A Y F I R E X M B C D G H K N O Q S T U V W Z HI DE TH EG OL DI NT HE TR EX ES TU MP BM OD ZB??... 26
27 P L A Y F I R E X M B C D G H K N O Q S T U V W Z HI DE TH EG OL DI NT HE TR EX ES TU MP BM OD ZB XD??... 27
28 P L A Y F I R E X M B C D G H K N O Q S T U V W Z HI DE TH EG OL DI NT HE TR EX ES TU MP BM OD ZB XD NA??... 28
29 P L A Y F I R E X M B C D G H K N O Q S T U V W Z HI DE TH EG OL DI NT HE TR EX ES TU MP BM OD ZB XD NA BE??... 29
30 P L A Y F I R E X M B C D G H K N O Q S T U V W Z HI DE TH EG OL DI NT HE TR EX ES TU MP BM OD ZB XD NA BE KU??... 30
31 P L A Y F I R E X M B C D G H K N O Q S T U V W Z HI DE TH EG OL DI NT HE TR EX ES TU MP BM OD ZB XD NA BE KU DM??... 31
32 P L A Y F I R E X M B C D G H K N O Q S T U V W Z HI DE TH EG OL DI NT HE TR EX ES TU MP BM OD ZB XD NA BE KU DM UI??... 32
33 If the letters appear on the same row of your table, replace them with the letters immediately to right, respectively. Wrap to left, if needed. source: wikipedia.org 33
34 P L A Y F I R E X M B C D G H K N O Q S T U V W Z HI DE TH EG OL DI NT HE TR EX ES TU MP BM OD ZB XD NA BE KU DM UI XM??... 34
35 P L A Y F I R E X M B C D G H K N O Q S T U V W Z HI DE TH EG OL DI NT HE TR EX ES TU MP BM OD ZB XD NA BE KU DM UI XM MO??... 35
36 P L A Y F I R E X M B C D G H K N O Q S T U V W Z HI DE TH EG OL DI NT HE TR EX ES TU MP BM OD ZB XD NA BE KU DM UI XM MO UV??... 36
37 HIDE THE GOLD IN THE TREE STUMP HI DE TH EG OL DI NT HE TR EX ES TU MP BM OD ZB XD NA BE KU DM UI XM MO UV IF How to decrypt it with the key? What betrays Palyfair? How can one break it? 37
38 Double Transposition Permute rows and columns! Plaintext: attackxatxdawnx! Ciphertext: xtawxnattxadakc! Key: matrix size and permutations (3,5,1,4,2) and (1,3,2) 38
39 Cryptanalysis: Terminology Cryptosystem is secure if best known attack is to try all keys Cryptosystem is insecure if any shortcut attack is known By this definition, an insecure system might be harder to break than a secure system! Why? 39
40 T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A one-time pad (OTP) 40
41 One-Time Pad A Vigenère cipher with a random key at least as long as the message Provably unbreakable Why? Plain text D O I T D O N T Key A J I Y A J D Y Cipher text D X Q R D X Q R! Warning: keys must be random, or you can attack the cipher by trying to regenerate the key 41
42 Little Bit of History about 95 years ago, January 19,
43 Literally, a book filled with codewords Zimmerman Telegram encrypted via codebook!! Februar!!! 13605!! fest!!! 13732!! finanzielle!! 13850!! folgender!! 13918!! Frieden!!! 17142!! Friedenschluss! Codebook!!! :!! : Modern block ciphers are codebooks! 43
44 Zimmerman Telegram Arthur Zimmermann ( ) German Foreign Secretary One of most famous codebook ciphers ever Led to US entry in WWI Ciphertext shown here 44
45 Zimmerman Telegram Decrypted! British had recovered partial codebook! Able to fill in missing parts 45 45
46 T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A Random Oracle Model Read: Anderson
47 What is Random Oracle Model? Queries Responses source of randomness infinite storage 47
48 Random Function as Random Oracle In: string of any length Queries Responses Out: random string of fixed length Applications: One-way functions Hash functions Message digests Time stamping Properties efficiency -- easy to compute h(x) for any x. one-way -- given any y, it s infeasible to find x, s.t., h(x) = y weak collision resistance -- given x and h(x), it s infeasible to y!= x, s.t. h(y) == h(x) strong collision resistance -- infeasible to find any x!= y, s.t., h(x) == h(y) 48
49 Random Generator (Stream Cipher) as Random Oracle In: short string (key) length of the output Queries Responses Out: long random stream of bits (keystream) Properties! Should not reuse Use seed Applications: Communications encryption Storage encryption 49
50 Example: A5 stream cipher for GSM From: Alex Biryukov, Adi Shamir, David Wagner 50 Real Time Cryptanalysis of A5/1 on a PC 50
51 Random Permutation (Block Cipher) as Random Oracle In fixed size short string (plaintext) M, DES bits Key K Queries Responses K 1 K 2 Out same fixed size short string (ciphertext) C 51 Notation! C = { M } K! M = { C } K Properties! Invertible 51
52 Summary Historical background Caesar, Vigenère, Palyfair, and Double Transpositionciphers One-time pad One-way functions Asymmetric cryptosystems The Random Oracle model Random functions: Hash functions Random generators: stream ciphers Random Permutations: block ciphers Queries Responses 52
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