Understanding_Cryptography_Chptr_8---Discrete_Logarithm

Understanding_Cryptography_Chptr_8---Discrete_Logarithm -...

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Understanding Cryptography by Christof Paar and Jan Pelzl www.crypto-textbook.com These slides were prepared by Christof Paar and Jan Pelzl Chapter 8 – Public-Key Cryptosystems Based on the Discrete Logarithm Problem ver. February 22, 2010
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s The slides can used free of charge. All copyrights for the slides remain with Christof Paar and Jan Pelzl. s The title of the accompanying book “Understanding Cryptography” by Springer and the author’s names must remain on each slide. s If the slides are modified, appropriate credits to the book authors and the book title must remain within the slides. s It is not permitted to reproduce parts or all of the slides in printed form whatsoever without written consent by the authors. U Some legal stuff (sorry): Terms of Use 2/19 Chapter 8 of Understanding Cryptography by Christof Paar and Jan Pelzl
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s Diffie–Hellman Key Exchange s The Discrete Logarithm Problem s Security of the Diffie–Hellman Key Exchange s The Elgamal Encryption Scheme U Content of this Chapter 3/19 Chapter 8 of Understanding Cryptography by Christof Paar and Jan Pelzl
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s Proposed in 1976 by Whitfield Diffie and Martin Hellman s Widely used , e.g. in Secure Shell (SSH), Transport Layer Security (TLS), and Internet Protocol Security (IPSec) s The Diffie–Hellman Key Exchange (DHKE) is a key exchange protocol and not used for encryption (For the purpose of encryption based on the DHKE, ElGamal can be used.) U Diffie–Hellman Key Exchange: Overview 4/19 Chapter 8 of Understanding Cryptography by Christof Paar and Jan Pelzl
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U Diffie–Hellman Key Exchange: Set-up 1. Choose a large prime p. 2. Choose an integer α {2,3, . . . , p-2}. 3. Publish p and α . 5/19 Chapter 8 of Understanding Cryptography by Christof Paar and Jan Pelzl
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Alice U Diffie–Hellman Key Exchange Bob Choose random private key k prA =a {1,2,…, p -1} Choose random private key k prB =b {1,2,…, p -1} Compute corresponding public key k pubA = A = α a mod p Compute correspondig public key k pubB = B = α b mod p Compute common secret k AB = B a = ( α a ) b mod p Compute common secret k AB = A b = ( α b ) a mod p A B y y = AES kAB (x) x = AES -1 kAB (y) 6/19 Chapter 8 of Understanding Cryptography by Christof Paar and Jan Pelzl We can now use the joint key k AB for encryption, e.g., with AES
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Alice U Diffie–Hellman Key Exchange: Example Bob Choose random private key k prA = a = 5 Choose random private key k prB =b = 12 Compute corresponding public key k pubA
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This note was uploaded on 04/01/2011 for the course MA C taught by Professor Anario during the Spring '11 term at Universitat Politècnica de Catalunya.

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Understanding_Cryptography_Chptr_8---Discrete_Logarithm -...

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