crypto-slides-02-shannon.1x1

crypto-slides-02-shannon.1x1 - Shannon’s Theory of...

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Unformatted text preview: Shannon’s Theory of Secrecy Systems See: C. E. Shannon, Communication Theory of Secrecy Systems , Bell Systems Technical Journal, Vol. 28, pp. 656–715, 1948. c circlecopyrt Eli Biham - August 18, 2010 53 Shannon’s Theory of Secrecy Systems (2) Notation Given a cryptosystem, denote M a message (plaintext) C a ciphertext K a key E be the encryption function C = E K ( M ) D be the decryption function M = D K ( C ) For any key K , E K ( · ) and D K ( · ) are 1-1, and D K ( E K ( · )) =Identity. c circlecopyrt Eli Biham - August 18, 2010 54 Shannon’s Theory of Secrecy Systems (2) Shannon’s Theory of Secrecy Systems (1949) Let { M 1 ,M 2 ,...,M n } be the message space. The messages M 1 ,M 2 ,...,M n are distributed with known probabilities p ( M 1 ) ,p ( M 2 ) ,...,p ( M n ) (not necessarily uniform). Let { K 1 ,K 2 ,...,K l } be the key space. The keys K 1 ,K 2 ,...,K l are dis- tributed with known probabilities p ( K 1 ) ,p ( K 2 ) ,...,p ( K l ). Usually (but not necessarily) the keys are uniformly distributed: p ( K i ) = 1 /l . Each key projects all the messages onto all the ciphertexts, giving a bipartite graph: c circlecopyrt Eli Biham - August 18, 2010 55 Shannon’s Theory of Secrecy Systems (2) † Shannon’s Theory of Secrecy Systems (1949) (cont.) p 1 =p(M 1 ) p 2 =p(M 2 ) p 3 =p(M 3 ) p n =p(M n ) M 1 M 2 M 3 M n C 1 C 2 C 3 C n K 1 K 2 K 3 K 4 c circlecopyrt Eli Biham - August 18, 2010 56 Shannon’s Theory of Secrecy Systems (2) Perfect Ciphers Definition : A cipher is perfect ( íìùî ) if for any M,C p ( M | C ) = p ( M ) (i.e., the ciphertext does not reveal any information on the plaintext)....
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This note was uploaded on 04/14/2011 for the course CS 236506 taught by Professor Yanivcarmeli during the Spring '11 term at Technion.

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crypto-slides-02-shannon.1x1 - Shannon’s Theory of...

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