Assymetric Key Encryption - Public Key Cryptosystems The magic words are squeamish ossifrage Plaintext of the message encoded in RSA-129 given in Martin

Assymetric Key Encryption - Public Key Cryptosystems The...

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“The magic words are squeamish ossifrage.” Plaintext of the message encoded in RSA-129, given in Martin Gardner’s 1977 “Mathematical Games” column about RSA. Public Key Cryptosystems
Problem: distributing secret keys is Difficult: eavesdroppers are everywhere Expensive: hard to secure channels Can two people communicate securely without having to meet first and establish a key? Who needs public key encryption? 2
Trust a third party 3 Alice Bob E (K AB , K A ) E (K AB , K B ) Keys Я Us knows K A , K B , ....
Trust a third party 3 Alice Bob E (“Bob”, K A ) E (K AB , K A ) E (K AB , K B ) Keys Я Us knows K A , K B , ....
Trust a third party 3 Alice Bob E (“Bob”, K A ) E (K AB , K A ) E (K AB , K B ) Generates random K AB Keys Я Us knows K A , K B , ....
Trust a third party 3 Alice Bob E (“Bob”, K A ) E (K AB , K A ) E (K AB , K B ) Generates random K AB Keys Я Us knows K A , K B , ....
Trust a third party 3 Alice Bob E (“Bob”, K A ) E (K AB , K A ) E (K AB , K B ) E (M, K AB ) Generates random K AB Keys Я Us knows K A , K B , ....
Trust a third party 3 Alice Bob E (“Bob”, K A ) E (K AB , K A ) E (K AB , K B ) E (M, K AB ) Generates random K AB E (“Alice” || K AB , K B ) Keys Я Us knows K A , K B , ....
How much do you trust a third party? Third party knows everyone’s keys! Third party can read any message! Big Brother is watching you… Is this scalable? Problem: limited number of all-knowing oracles Problem: need to involve a third party for all transactions Other, more secure protocols We’ll cover these in a bit… General principle: include as much information as needed to ensure that messages are self-contained Don’t assume anything in the message! Trusting a third party: issues 4
Alice generates 2 20 messages: “This is puzzle x . The secret is y .” ( x and y are random numbers) Encrypts each message using symmetric cipher with a different key Sends all encrypted messages to Bob Bob chooses random message, performs brute-force attack to recover plaintext and key k Bob sends x (clear) to Alice Alice and Bob use k to encrypt messages Merkle’s puzzles (1974) 5
Alice generates 2 20 messages: “This is puzzle x . The secret is y .” ( x and y are random numbers) Encrypts each message using symmetric cipher with a different key Sends all encrypted messages to Bob Bob chooses random message, performs brute-force attack to recover plaintext and key k Bob sends x (clear) to Alice Alice and Bob use k to encrypt messages Alice: uses DES symmetric cipher ~2 55 expected brute force work to break DES Or perhaps uses a weakened form of AES Eve: has to break the 2 20 to find which one matches x ~ 2 19 × 2 55 expected work Alice and Bob change keys frequently enough since it is less work to agree to a new key Merkle’s puzzles (1974) 5
1969: ARPANet born with 4 sites Whitfield Diffie starts thinking about strangers sending messages securely 1974: Whitfield Diffie gives talk at IBM lab Audience member mentions that Martin Hellman (Stanford professor) had spoke about key distribution That night, Diffie starts driving 5000 km to Palo Alto Diffie, Hellman and Ralph Merkle work on key distribution problem Birth of public key cryptosystems 6
Secret paint mixing 7 Analogy from The Code Book (S. Singh) Alice Bob Yellow paint (public)
Secret paint mixing 7 Analogy from The Code Book (S. Singh) Alice Bob Yellow paint (public)

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