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Unformatted text preview: CS70: Satish Rao: Lecture 11. Outline. 1. Signature Schemes. 2. Fermat’s Theorem: again. 3. Secret Sharing. 4. Polynomials. RSA reminder RSA reminder Construction: Primes p , q RSA reminder Construction: Primes p , q Find e with gcd ( e , ( p 1 )( q 1 )) = 1 Find d = e 1 ( mod ( p 1 )( q 1 ))) RSA reminder Construction: Primes p , q Find e with gcd ( e , ( p 1 )( q 1 )) = 1 Find d = e 1 ( mod ( p 1 )( q 1 ))) Private Key: k = d Public Key: K = ( N , e ) RSA reminder Construction: Primes p , q Find e with gcd ( e , ( p 1 )( q 1 )) = 1 Find d = e 1 ( mod ( p 1 )( q 1 ))) Private Key: k = d Public Key: K = ( N , e ) Encryption: E ( m , K ) = m e ( mod N ) RSA reminder Construction: Primes p , q Find e with gcd ( e , ( p 1 )( q 1 )) = 1 Find d = e 1 ( mod ( p 1 )( q 1 ))) Private Key: k = d Public Key: K = ( N , e ) Encryption: E ( m , K ) = m e ( mod N ) Decryption: D ( y , k ) = y d ( mod N ) RSA reminder Construction: Primes p , q Find e with gcd ( e , ( p 1 )( q 1 )) = 1 Find d = e 1 ( mod ( p 1 )( q 1 ))) Private Key: k = d Public Key: K = ( N , e ) Encryption: E ( m , K ) = m e ( mod N ) Decryption: D ( y , k ) = y d ( mod N ) Property: D ( E ( m , K ) , k ) = ( m e ) d = m ed ≡ m ( mod N ) Signatures using RSA. Verisign: Browser. Amazon Signatures using RSA. Verisign: Browser. Amazon Certificate Authority: Verisign, GoDaddy, DigiNotar,... Signatures using RSA. Verisign: k v , K v Browser. Amazon Certificate Authority: Verisign, GoDaddy, DigiNotar,... Verisign’s key: K V = ( N , e ) and k V = d ( N = pq .) Signatures using RSA. Verisign: k v , K v Browser. K v Amazon Certificate Authority: Verisign, GoDaddy, DigiNotar,... Verisign’s key: K V = ( N , e ) and k V = d ( N = pq .) Browser “knows” Verisign’s public key: K V . Signatures using RSA. Verisign: k v , K v Browser. K v Amazon Certificate Authority: Verisign, GoDaddy, DigiNotar,... Verisign’s key: K V = ( N , e ) and k V = d ( N = pq .) Browser “knows” Verisign’s public key: K V . Amazon Certificate: C = “I am Amazon. My public Key is K A .” Signatures using RSA. Verisign: k v , K v Browser. K v Amazon [ C , S v ( C )] Certificate Authority: Verisign, GoDaddy, DigiNotar,... Verisign’s key: K V = ( N , e ) and k V = d ( N = pq .) Browser “knows” Verisign’s public key: K V . Amazon Certificate: C = “I am Amazon. My public Key is K A .” Versign signature of C : S v ( C ) : D ( C , k V ) = C d mod N . Signatures using RSA. Verisign: k v , K v Browser. K v Amazon [ C , S v ( C )] [ C , S v ( C )] Certificate Authority: Verisign, GoDaddy, DigiNotar,... Verisign’s key: K V = ( N , e ) and k V = d ( N = pq .) Browser “knows” Verisign’s public key: K V ....
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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.
 Fall '11
 Rau

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