Introduction to Cryptography
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1 Introduction to Cryptography Jiyou Li lijiyou at sjtu.edu.cn Department of Mathematics, Shanghai Jiao Tong University Sep. 17th, 2013
2 Cryptography Cryptography: the art and science of keeping message secure.
3 Cryptography Cryptography: the art and science of keeping message secure. Confidentiality;
4 Cryptography Cryptography: the art and science of keeping message secure. Confidentiality; Authentication;
5 Cryptography Cryptography: the art and science of keeping message secure. Confidentiality; Authentication; Integrity;
6 Cryptography Cryptography: the art and science of keeping message secure. Confidentiality; Authentication; Integrity; Nonrepudiation; Electronic payment; Anonymity; Electronic votes; Zero-knowledge...
7 The Origins of Cryptography Diplomacy: Zimmerman telegram;
8 The Origins of Cryptography Diplomacy: Zimmerman telegram; War: Enigma machine, Purple;
9 The Origins of Cryptography Diplomacy: Zimmerman telegram; War: Enigma machine, Purple; Individual or corporate privacy;
10 The Origins of Cryptography Diplomacy: Zimmerman telegram; War: Enigma machine, Purple; Individual or corporate privacy; Electronic Commerce...
11 Enigma
12 Cryptanalysis Cryptanalysis: the art and science of breaking cipher systems, recovering the plaintext of a message without access to the key. Attack: a attempted cryptanalysis is called an attack.
13 Cryptanalysis Cryptanalysis: the art and science of breaking cipher systems, recovering the plaintext of a message without access to the key. Attack: a attempted cryptanalysis is called an attack. The n 2 Problem;
14 Cryptanalysis Cryptanalysis: the art and science of breaking cipher systems, recovering the plaintext of a message without access to the key. Attack: a attempted cryptanalysis is called an attack. The n 2 Problem; The Kerckhoffs Principle;
15 Cryptanalysis Cryptanalysis: the art and science of breaking cipher systems, recovering the plaintext of a message without access to the key. Attack: a attempted cryptanalysis is called an attack. The n 2 Problem; The Kerckhoffs Principle; The Moore Law;
16 Cryptanalysis Cryptanalysis: the art and science of breaking cipher systems, recovering the plaintext of a message without access to the key. Attack: a attempted cryptanalysis is called an attack. The n 2 Problem; The Kerckhoffs Principle; The Moore Law; The Murphy Law.
17 Cryptanalytic Attacks Ciphertext-only attack;
18 Cryptanalytic Attacks Ciphertext-only attack; Known plaintext attack ;
19 Cryptanalytic Attacks Ciphertext-only attack; Known plaintext attack ; Chosen plaintext attack;
20 Cryptanalytic Attacks Ciphertext-only attack; Known plaintext attack ; Chosen plaintext attack; Chosen ciphertext attack.
21 Some Cryptographic Protocols Bits Commitment;
22 Some Cryptographic Protocols Bits Commitment; Key Exchange;
23 Some Cryptographic Protocols Bits Commitment; Key Exchange; Secret Sharing Scheme;
24 Some Cryptographic Protocols Bits Commitment; Key Exchange; Secret Sharing Scheme; Digital Signatures;
25 Some Cryptographic Protocols Bits Commitment; Key Exchange; Secret Sharing Scheme; Digital Signatures; Cloud Computing Security...
26 A Cryprtographic Communication Model Plaintext Plaintext Encryption: A key Decryption: A key Ciphertext Channel Eve! Ciphertext
27 The History of Cryptography 1. B.C.?-1949: Classical Cryptography (Substitutions and permutations); : Symmetric Cryptography (Block Dipher and Stream Cipher, based on Shannon s Theorem); present: Modern Cryptography (Public-Key and asymmetric...).
28 Caesar Cipher ABCDEFGHIJKLMNOPQRSTUVWXYZ Key = 3 DEFGHIJKLMNOPQRSTUVWXYZABC Plaintext: JIAOTONGUNIVERSITY Encryption: Shift by KEY = 3 Ciphertext: MLDRWRQJXQLYHUVLWB Decryption: Shift backwards by KEY = 3
29 Vigenere Cipher Plaintext: thi sis adu mmy mes sag e Key: ABC ABC ABC ABC ABC ABC A Ciphertext: TIK SJU AEW MNA MFU SBI E Decryption: "Subtract0the key ABC from ciphertext mod 26.
30 Vernam Ciphers Plaintext: MATHISUSEFULANDFUN Key: NGUJKAMOCTLNYBCIAZ Encryption: /Add0key to message mod 26 Ciphertext: BGO,.. Decryption: /Subtract0key from ciphertext mod 26.
31 Permutation Cipher Example: Plaintext: JIAOTO NGUNIV ERSITY Encryption: Group action by KEY =(135246) Ciphertext: OTJIAO VINGUN YTERSI Decryption: Inverse action by KEY =(164253)
32 Hebern machine
33 Enigma: invented by Arthur Scherbius
34 Rotors
35 Reflector
36 Plugboard
37 Electrical pathway
38 Electrical pathway
39 Mathematics in Enigma E(x i ) = P R i1 M i2 L i3 U L 1 i 3 M 1 i 2 R 1 i 1 P 1 (x i ), where P, R, M, L, U S 26, R i1 = ρ i R ρ i and U is a convolution.
40 Bomber
41 A Cipher 1. A plaintext space M, a ciphertext space C and a key space K; 2. A key generation algorithm; 3. An encryption algorithm E; 4. A decryption algorithm D.
42 Do we have unconditionally secure encryption? Theorem Perfect secrecy is equivalent to H(M C) = H(M) and to the statistic independence between M and C. Theorem (Shannon, 1949) Perfect secrecy implies H(K ) H(M).
43 One-Time Pads: Vernam Ciphers Plaintext: MATHISUSEFULANDFUN Key: NGUJKAMOCTLNYBCIAZ Encryption: /Add0key to message mod 26 Ciphertext: BGO,.. Decryption: /Subtract0key from ciphertext mod 26.
44 One-Time Pads One-Time Pads is unconditionally secure;
45 One-Time Pads One-Time Pads is unconditionally secure; Problem: Exchanging the key;
46 One-Time Pads One-Time Pads is unconditionally secure; Problem: Exchanging the key; There are some clever ways to exchange the key; we will study some of them!
47 Stream Ciphers 1. Making OTP practical; 2. Idea: replace "random" key by "pseudorandom" key; 3. The security depend on specific pseudorandom generators.
48 Public-Key Cryptography (1976-) Discovered by Diffie & Hellman (1976) and now known at GCHQ years before; Uses one-way (asymmetric) functions, public keys, and private keys; Mainly based on two hard problems: Factoring large integers and the discrete logarithm problem.
49 Coding Theory and Cryptography Cryptography needs reliabilityœ
50 Mathematics in Cryptography Linear Algebra Abstract Algebra Number Theory Algebraic Geometry Probability Statistics Combinatorics Computing...
51 References 1. A classical introduction to modern cryptography, S. Vaudenay, Springer, èæú, ¾I ½ Í, ÆÑ, 1999.
52 Exercises 4. Suppose the one time pad encryption of the message "attackatdawn" is "wxtygcjmxenf". What is the one time pad encryption of the message "attackatdusk" under the same key? 5. Let M = C = K = {0, 1,..., 63} and consider the following cipher (M, C, K) defined by: E ( k, x) = x + k mod 64. Does this cipher have perfect secrecy?
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