CSCI6268L06 - Foundations of Network and Foundations of...

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Unformatted text preview: Foundations of Network and Foundations of Network and Computer Security Computer Security J J ohn Black Lecture #6 Sep 9 th 2009 CSCI 6268/TLEN 5550, Fall 2009 Digression on the One-Time Pad Suppose Alice and Bob shared a 10,000 bit string K that was secret, uniformly random Can Alice send Bob a 1KB message M with perfect security? 1KB is 8192 bits; let X be the first 8192 bits of the shared string K Alice sets C = M X, and sends C to Bob Bob computes C X and recovers M Recall that M X X = M Security of the One-Time Pad Consider any bit of M, m i , and the corresponding bits of X and C, (x i , c i ) Then c i = m i x i Given that some adversary sees c i go across a wire, what can he discern about the bit m i ? Nothing! Since x i is equally likely to be 0 or 1 So why not use the one-time pad all the time? Shannon proved (1948) that for perfect security the key must be at least as long as the message Impractical One-Time Pad (cont) Still used for very-top-secret stuff Purportedly used by Russians in WW II Note that it is very important that each bit of the pad be used at most one time! The infamous two time pad is easily broken Imagine C = M X, C = M X Then C C = M X M X = M M Knowing the xor of the two messages is potentially very useful n-time pad for large n is even worse (WEP does this) Counter Mode CTR Blockcipher E under key K, M broken into m blocks of n bits, as usual Nonce N is typically a counter, but not required C = N C i = E K (N++) M i Ciphertext is C = C C 1 C m CTR Mode Again, n bits of ciphertext expansion Non-deterministic encryption Fully parallelizable in both directions Not that widely used despite being known for a long time People worry about counter overlap producing pad reuse Why I Like Modes of Operation Modes are provably secure Unlike blockciphers which are deemed hopefully secure after intense scrutiny by experts, modes can be proven secure like this: Assume blockcipher E is secure (computationally indistinguishable from random, as we described) Then the mode is secure in an analogous black-box experiment The proof technique is done via a reduction much like you did in your NP-Completeness class The argument goes like this: suppose we could break the mode with computational resources X, Y, Z. Then we could distinguish the blockcipher with resources X, Y, Z where these resources arent that much different from X, Y, and Z Security Model Alice and Bob Traditional names Lets us abbreviate A and B Adversary is the bad guy This adversary is passive ; sometimes called eve Note also the absence of side-channels Power consumption, timing, error messages, etc Adversary Alice Key K Key K Bob Various Attack Models Known-Ciphertext Attack (KCA)...
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CSCI6268L06 - Foundations of Network and Foundations of...

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