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lec-11 - CS70 Satish Rao Lecture 11 Outline 1 Signature...

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CS70: Satish Rao: Lecture 11. Outline. 1. Signature Schemes. 2. Fermat’s Theorem: again. 3. Secret Sharing. 4. Polynomials.

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RSA reminder
RSA reminder Construction: Primes p , q

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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 )

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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 )

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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

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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 .)

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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 .”

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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 . 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 .

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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 . 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 . Browser receives: [ C , y ]
Signatures using RSA. Verisign: k v , K v Browser. K v Amazon [ C , S v ( C )] [ C , S v ( C )] C = E ( S V ( C ) , k V )? Certificate Authority: Verisign, GoDaddy, DigiNotar,...

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