Key Exchange. Secure Software Systems
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1 1 Key Exchange
2 2 Challenge Exchanging Keys &!"#h%&'() & & 1 2 6(6 1) 2 15! $ The more parties in communication, the more keys that need to be securely exchanged " # Do we have to use out-of-band methods? (e.g., phone?) %
3 3 Key Exchange Insecure communica-ons channel Eve can see everything! Alice and Bob agree on a shared secret ( key ) that Eve doesn t know Despite Eve seeing everything!! (alice) " (bob) # (eve)
4 Whitfield Diffie and Martin Hellman, New directions in cryptography, in IEEE Transactions on Information Theory, vol. 22, no. 6, Nov Proposed public key cryptography. Diffie-Hellman key exchange.
5 5 Diffie-Hellman Color Analogy (1) It s easy to mix two colors: + (2) Mixing two or more colors in a different order results in the same color: (3) Mixing colors is one-way (Impossible to determine which colors went in to produce final result)
6 6 Diffie-Hellman Color Analogy! (alice) # (eve) " (bob) + + $ $ Mix (1) Start with public color share across network (2) Alice picks secret color and mixes it to get (3) Bob picks secret color and mixes it to get Mix
7 7 Diffie-Hellman Color Analogy! (alice) # (eve) " (bob) $ $ Mix Eve can t calculate!! (secret keys were never shared) (4) Alice and Bob exchange their mixed colors (, ) (5) Eve will see the mixed colors too (, ) (6) Alice adds her secret color to Bob s mix (7) Bob adds his secret color to Alice s mix Mix
8 8 Diffie-Hellman Color Analogy! # + Mix (alice) (order doesn t matter) " (bob) # Mix +
9 9 Diffie-Hellman Math! ($ % ) '() (*) y is defined as equal to g x modulo p p prime number (modulus) g base integer x random integer Assumption: Computing y is easy! But computing x given y, g, and p is very hard! Discrete Logarithm Problem
10 10 Diffie-Hellman Math! " (alice)! " (% & ')!)* (+)!, (% & -)!)* (+) (bob) + + # # Mix (1) Public color is a large prime number p and base g (2) Alice secret color is random integer r A (3) Bob secret color is random integer r B (4) Alice mixed color is m A (5) Bob mixed color is m B (6) Exchange m A and m B Mix
11 11 Diffie-Hellman Math! # + Mix (alice)! % $ " &. $() (+) " (bob) # Mix +! " $ % & ' $() (+)! %! "
12 12 Diffie-Hellman Math Doesn t have to be modular division Could be elliptic curves Could be supersingular isogeny key exchange Could be <other math words> Secure So/ware Systems
13 13 Public Key Cryptography
14 14 Public Key Cryptography Asymmetric cryptography Sending data to Alice? Use her public Key Alice receives your data? She decrypts it with her private key
15 Ron L. Rivest, Adi Shamir, and Leonard 15 Adleman. A method for obtaining digital signatures and public-key cryptosystems. Communica)ons of the ACM (February 1978) RSA encryption method First public key method
16 16 Public-Key Algorithms Key exchange algorithms Allows two parties to agree on a shared secret across an insecure medium Example: Diffie-Hellman Encryption algorithms Allows sender to encrypt without having to agree first on a shared secret Example: RSA Signature algorithms Allows sender to sign information using sender s private key and receiver to validate using sender s public key
17 17 Public-Key Encryption Public key encryption is awesome! Should we use it everywhere? Secure So/ware Systems
18 18 Caveat Performance Rarely use public key encryption by itself Reasons: Size (RSA can t encrypt anything larger than its modulus, i.e bits) Performance RSA 2048 encryption: 0.08 megacycles/operation (256B) RSA 2048 decryption: 3.25 megacycles/operation AES-GCM: 2-4 cycles per byte Hybrid cryptosystem Use public-key algorithms to coordinate keys, and then use symmetric ciphers (shared key) for bulk operations
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