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Lecture 7 - Class Notes RSA – one way function Easy to...

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Unformatted text preview: Class Notes September 30, 2008 RSA – one way function- Easy to compute, hard to invert- Probability it can be inverted with today’s computers is almost zero- Factoring of the product of two large primes Plaintext P E(P) = p e mod n Public key (e,n) Private key: d D(p e mod n) = pe d mod n = P N = pq (p, q primes) E relatively prime to (p-1)(q-1) E*d = 1 mod(p-1)(q-1) Hard-Core predicate for RSA Least significant bit of P is a hard-core predicate for RSA Given E(P) = p e mod n we cannot compute the lsb(p) least significant bit with a probability different from (1/2 – E) – about the same as guessing. Example: P = 1101 Compute a random string until s until lsb(s) = 1. Now encrypt s with RSA. Now the recipient decrypts and retrieves the lsb. The least significant bit is a hardcore predicate for RSA. 4 Main applications 1. (Cryptographic hash functions) Cryptographic hash functions is used to compute the digest of files. The digest depends on all bits in the given file. The digest is stored with file. The digest is stored with file....
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Lecture 7 - Class Notes RSA – one way function Easy to...

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