LectureNote18-OtherCrypto

LectureNote18-OtherCrypto - O THER P UBLIC K EY C...

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Unformatted text preview: O THER P UBLIC K EY C RYPTOSYSTEMS P UBLIC K EY C RYPTOGRAPHY I NTRO . TO N UMBER T HEORY D IFFIE-H ELLMAN C RYPTOSYSTEM RSA C RYPTOSYSTEM O THER P UBLIC K EY C RYPTOSYSTEMS M ESSAGE D IGESTS AND C ERTIFICATES CS 556 - Computer Security - c circlecopyrt 2009 Colorado State University 52 / 93 El Gamal Cryptography P UBLIC K EY C RYPTOGRAPHY I NTRO . TO N UMBER T HEORY D IFFIE-H ELLMAN C RYPTOSYSTEM RSA C RYPTOSYSTEM O THER P UBLIC K EY C RYPTOSYSTEMS M ESSAGE D IGESTS AND C ERTIFICATES CS 556 - Computer Security - c circlecopyrt 2009 Colorado State University 53 / 93 A variant of the Diffie-Hellman key distribution scheme, allowing secure exchange of messages Proposed in 1985 by ElGamal in T. ElGamal, A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms, IEEE Transactions on Information Theory, vol IT-31(4), July 1985. Like Diffie-Hellman its security depends on the difficulty of finding discrete logarithms El Gamal Key Generation P UBLIC K EY C RYPTOGRAPHY I NTRO . TO N UMBER T HEORY D IFFIE-H ELLMAN C RYPTOSYSTEM RSA C RYPTOSYSTEM O THER P UBLIC K EY C RYPTOSYSTEMS M ESSAGE D IGESTS AND C ERTIFICATES CS 556 - Computer Security - c circlecopyrt 2009 Colorado State University 54 / 93 Select a large prime p ( 200 digits) and , a small integer Alice chooses a secret number xa Bob chooses a secret number xb Alice and Bob compute y A and y B respectively which are then made public y A = xa mod p (Alices public key) y B = xb mod p (Bobs public key) To Encrypt Message Alice Bob P UBLIC K EY C RYPTOGRAPHY I NTRO . TO N UMBER T HEORY D IFFIE-H ELLMAN C RYPTOSYSTEM RSA C RYPTOSYSTEM O THER P UBLIC K EY C RYPTOSYSTEMS M ESSAGE D IGESTS AND C ERTIFICATES CS 556 - Computer Security - c circlecopyrt 2009 Colorado State University 55 / 93 Alice selects a random number k, 0 k p1 Alice computes a message key K M as K M = y k B mod p Alice computes ciphertext pair C = { C 1 ,C 2 } as C 1 = k mod p C 2 = K M .M mod p, where M is the message to be sent To Decrypt Message...
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This note was uploaded on 05/29/2010 for the course CS 556 taught by Professor Staff during the Spring '08 term at Colorado State.

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LectureNote18-OtherCrypto - O THER P UBLIC K EY C...

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