G22.3033-003 Introduction to Cryptography
نویسنده
چکیده
This lecture begins with a discussion on secret-key and public-key cryptography, and then discusses One-Way Functions (OWF), and their importance in cryptography. Essentially, an OWF is easy to compute, but difficult to invert. A One-Way Permutation (OWP) is an OWF that permutes elements from a set. A Trap-Door Permutation (TDP) is essentially an OWP with certain information, that if disclosed, allows the function to be easily inverted. No OWF is known to exist, since showing the existence of a function that is truly difficult to invert hasn’t been proven yet. However, there exists good candidates for OWF, OWP, and TDP. I’ll describe Prime Product as an example of an OWF candidate, Modular Exponentiation as an example of an OWP candidate, and RSA as an example of a TDP candidate. And, I’ll back up certain proofs with the appropriate number theory. Then, I’ll go on to discuss how the assumption of the existence of OWF leads to a secure password-authentication system. And, I’ll show that S/Key System (an example of password-authentication where the information stored and used for authentication keeps changing) is secure using any OWP. Next, I’ll describe the criticisms made against OWF, OWP, and TDP in practical applications, and give suggestions of how to overcome these criticisms.
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