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Lecture23

# Lecture23 - Algorithms in Systems Engineering IE170 Lecture...

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Algorithms in Systems Engineering IE170 Lecture 23 Dr. Ted Ralphs

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IE170 Lecture 23 1 References for Today’s Lecture Required reading CLRS Chapter 31 References Koblitz, A Course in Number Theory and Cryptography , Second Edition (1999).
IE170 Lecture 23 2 RSA Public Key Encryption Algorithm The RSA algorithm is used almost universally to encrypt data on the Internet. If you have ever visited a secure site on the Internet, you have used RSA encryption. Procedure for creating public and private keys. Randomly choose two large prime numbers p and q such that p 6 = q . Compute n = pq . Select an odd integer e that is relatively prime to φ ( n ) = ( p - 1)( q - 1) = n + 1 - p - q . Compute d as the multiplicative inverse of e modulo φ ( n ) . The pair ( e, n ) is the public key . The pair ( d, n ) is the private key . The encoding function is f E ( P ) = P e mod n . The decoding function is f D ( C ) = C d mod n .

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IE170 Lecture 23 3 Some Questions Does the RSA algorithm actually yield a cryptosystem (are the encoding and encoding functions really inverses)? How secure is this system, i.e., is the encoding key really a trap door function? Can we compute the keys efficiently? Can we find large prime numbers efficiently? Does d always exist and can we compute it? Can we encode and decode efficiently?
IE170 Lecture 23 4 How Secure is RSA Encryption?

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