RSA.lect2 - RSA lect 2.oo3 CS 70 review from Tuesday RSA...

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RSA lect 2.oo3 CS 70, March 10, 2005 review from Tuesday RSA algorithm proof observation: there are enough primes to make it relatively easy to find two of them; there are approximately x/(ln x) primes between 1 and x 1 in 20 SIDs are prime observation: encryption function and decryption function can be applied in either order authentication situation: message isn't necessarily secret, but you want to make sure you know who authored it Alice creates a digital signature S for her message M: S = M^d mod n, where (d,n) is Alice's private key; she then might encrypt it using Bob's public key Bob, on receiving the message, would unencrypt it using his private key, then apply Alice's public key to it to make sure it came from her and wasn't tampered with actually what usually happens is that Alice signs a digest of the message M, formed by applying a hash function h to M, then appends the signed shorter version of the message to the actual M; Bob then applies the same hash function h to M to get the digest, then applies Alice's public key to the signature and compares the result with h(M) note that Alice is essentially signing every message that hashes to the same digest; this is a security risk recently SHA-1, a common hash function for this purpose, was compromised; a simpler function that delivers the same SHA-1 hash value was found a certificate provides assurance that Alice's public key is correct; it adds a signature (e.g.
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