Lec-10 - CS70 Satish Rao Lecture 10 Outline 1 Cryptography 2 Public Key Cryptography 3 RSA system 3.1 Efficiency Repeated Squaring 3.2 Correctness

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Unformatted text preview: CS70: Satish Rao: Lecture 10. Outline. 1. Cryptography 2. Public Key Cryptography 3. RSA system 3.1 Efficiency: Repeated Squaring. 3.2 Correctness: Fermat’s Theorem. 3.3 Construction. 4. Warnings. Cryptography ... Bob Alice Eve Cryptography ... Bob Alice Eve Secret s Cryptography ... Bob Alice Eve Secret s Message m Cryptography ... Bob Alice Eve Secret s Message m E ( m , s ) Cryptography ... Bob Alice Eve Secret s Message m E ( m , s ) Cryptography ... Bob Alice Eve Secret s Message m E ( m , s ) m = D ( E ( m , s ) , s ) Cryptography ... Bob Alice Eve Secret s Message m E ( m , s ) m = D ( E ( m , s ) , s ) Example: Cryptography ... Bob Alice Eve Secret s Message m E ( m , s ) m = D ( E ( m , s ) , s ) Example: One-time Pad: secret s is string of length | m | . Cryptography ... Bob Alice Eve Secret s Message m E ( m , s ) m = D ( E ( m , s ) , s ) Example: One-time Pad: secret s is string of length | m | . E ( m , s ) – bitwise m ⊕ s . Cryptography ... Bob Alice Eve Secret s Message m E ( m , s ) m = D ( E ( m , s ) , s ) Example: One-time Pad: secret s is string of length | m | . E ( m , s ) – bitwise m ⊕ s . D ( x , s ) – bitwise x ⊕ s . Cryptography ... Bob Alice Eve Secret s Message m E ( m , s ) m = D ( E ( m , s ) , s ) Example: One-time Pad: secret s is string of length | m | . E ( m , s ) – bitwise m ⊕ s . D ( x , s ) – bitwise x ⊕ s . Works because m ⊕ s ⊕ s = m ! Cryptography ... Bob Alice Eve Secret s Message m E ( m , s ) m = D ( E ( m , s ) , s ) Example: One-time Pad: secret s is string of length | m | . E ( m , s ) – bitwise m ⊕ s . D ( x , s ) – bitwise x ⊕ s . Works because m ⊕ s ⊕ s = m ! ...and totally secure! ...given E ( m , s ) any message m is equally likely. Cryptography ... Bob Alice Eve Secret s Message m E ( m , s ) m = D ( E ( m , s ) , s ) Example: One-time Pad: secret s is string of length | m | . E ( m , s ) – bitwise m ⊕ s . D ( x , s ) – bitwise x ⊕ s . Works because m ⊕ s ⊕ s = m ! ...and totally secure! ...given E ( m , s ) any message m is equally likely. Disadvantages: Cryptography ... Bob Alice Eve Secret s Message m E ( m , s ) m = D ( E ( m , s ) , s ) Example: One-time Pad: secret s is string of length | m | . E ( m , s ) – bitwise m ⊕ s . D ( x , s ) – bitwise x ⊕ s . Works because m ⊕ s ⊕ s = m ! ...and totally secure! ...given E ( m , s ) any message m is equally likely. Disadvantages: Shared secret! Cryptography ... Bob Alice Eve Secret s Message m E ( m , s ) m = D ( E ( m , s ) , s ) Example: One-time Pad: secret s is string of length | m | . E ( m , s ) – bitwise m ⊕ s . D ( x , s ) – bitwise x ⊕ s . Works because m ⊕ s ⊕ s = m !...
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This note was uploaded on 02/29/2012 for the course COMPSCI 70 taught by Professor Rau during the Fall '11 term at University of California, Berkeley.

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Lec-10 - CS70 Satish Rao Lecture 10 Outline 1 Cryptography 2 Public Key Cryptography 3 RSA system 3.1 Efficiency Repeated Squaring 3.2 Correctness

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