Shared Secret = Trust

Transcription

1 Trust The fabric of life! Holds civilizations together Develops by a natural process Advancement of technology results in faster evolution of societies Weakening the natural bonds of trust From time to time artificial mechanisms need to be introduced eg photo ids Cryptography is a trust building mechanism We are at a point (or about to arrive at a point) where cryptography needs to be part of our day-today lives

2 Shared Secret = Trust At the crux of cryptography is the assumption that TRUST = SHARED SECRET How do we leverage shared secret to build trust? Components of Trust Secrecy, Authentication, Non-repudiation, Integrity, Identity Cryptographic Primitives Encryption/Decryption, Digital Signatures, Hash (oneway) functions, random sequence generators

3 Cryptography Encryption and Decryption Plain Text Encryption Cipher Text Cipher Text Decryption Plain Text Two ways Symmetric Cryptography (shared key) Asymmetric Cryptography (two-key / public-key)

4 An Analogy - Shared Secret as a Key Alice and Bob share a key to a lock Handling messages Put them in a box Secure the box with the lock Alice knows only Bob has a key (and viceversa) Shared key enables trust Modern cryptography uses bits and computer programs (algorithms)

5 Paper and Pencil Cryptography Read Sections 2.1 through 2.3 of text Evolution of Cryptography First documented use by Julius Caesar Caesar Cipher (Enciphering and Deciphering) MEET YOU TOMORROW (Plain Text) RJJY DTZ YTRTWWTB (Cipher Text) 26 possible keys (0-25, key 5 used in example above) Vignere Cipher (26 x m keys) M E E T Y O U T O M O R R O W D O G D O G D O G D O G D O G (4,15,7), m=3 P S K W M U X H U P C X U C C

6 More P&P Ciphers Auto-key Vignere Cipher MEET YOU TOMORROW (Plain Text) HIYA (key) Extended key H I Y A M E E T Y O U T O M O Cipher M E E T Y O U T O M O R R O W H I Y A M E E T Y O U T O M O T M C T K S Y M M A I K F A K

7 Even More Ciphers! A more complex substitution Cipher Each letter substituted by an arbitrary letter Full Vignere. Key generation NETWORKSECURI TY ANDCRYPTOGRAPHYBIZ NETWORKSCU IYA DPGHBZFJ LMQVX ABCD EFGHI J KLMNOPQRSTUVWXYZ 26! ( ) keys Permutation Ciphers Text length M AND -> (2,3,1) -> NDA M! possible permutations Modern Ciphers Combination of substitution and permutation Repeated application many rounds

8 Brute-force Attacks on Ciphers A good cipher is only susceptible to brute-force attacks C = E(P,K). How do we get P from C? Without the knowledge of K Try every possible key K P i = D(C,K i ) How do we know when to stop? Under any key there will be a corresponding P i How do we know that a particular P i is the correct plaintext? Does this mean brute force attacks are not possible?

9 Entropy of Plain Text Think of all possible 100 character strings that make sense For example, say a billion books, each with 1 billion strings that make sense - still makes it only possible phrases! How many total strings of length 100? That is more than 3 x ! Say we encrypt a meaningful string with a 64 bit key, the ciphertext is decrypted with another key What is the probability that the wrong key results in a string that makes sense? 2 64 * /(3* ) < 6 * Which is good news for the attacker...

10 Vernam Cipher The Ultimate Cipher? What if we make the number of possible keys the same as the number of possible plain text messages? One-time pad Vernam Cipher Cannot try out keys any more! There is always a key which maps cipher text to every possible plain text No way an attacker can eliminate any message all messages are equally likely The attacker learns NOTHING! Perfect Secrecy

11 Establishing shared secrets Alice and Bob Have no a priori common secrets Can they establish a secret over an open channel? Oscar can listen to all exchanges between Alice and Bob Can Alice and Bob establish a secret not privy to Oscar?

12 Asymmetric Key Cryptography Encrypt with public key Decrypt with private key Private key is secret, public key is not (could be entered in some on-line public directory) Used for Secrecy and Digital Signatures Plain Text Encryption Cipher Text Plain Text Encryption Signed Text Cipher Text Decryption Plain Text Signed Text Decryption Plain Text

13 Asymmetric Key Cryptography Alice, Bob and Oscar - have never met before no shared secret Alice announces her public key to Bob (Oscar also listens) Bob chooses a secret randomly and encrypts it with Alice's public key Alice can decrypt Bob's message and determine Bob's chosen secret Oscar cannot (he does not have access to Alice's Private key) Now Alice and Bob have a shared secret! Notion of Public key cryptography is definitely not intuitive!

14 Illustration of Asymmetric Key Cryptography Simple box with a lock won't work - need a more sophisticated contraption! Message box (locker) with trapdoors Encryption and Digital Signatures Front door opened with public key to drop messages for Alice and collect documents signed by Alice Back door can be opened only by Alice with her private key. Only an analogy. Need trapdoor one-way functions to realize asymmetric cryptography.