The Diffie-Hellman Algorithm

The Diffie-Hellman Algorithm

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  The Diffie-Hellman Algorithm Er.Jay Nagar(Cyber Security Researcher ) www.jaynagarblog.worpress.com
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  Overview • Introduction • Implementation •Example • Applications • Conclusion J@Y_IT The Diffie-Hellman Algorithm 2
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  Introduction • Discovered byWhitfield Diffie and Martin Hellman – “New Directions in Cryptography” • Diffie-Hellman key agreement protocol – Exponential key agreement – Allows two users to exchange a secret key – Requires no prior secrets – Real-time over an untrusted network J@Y_IT The Diffie-Hellman Algorithm 3
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  Introduction • Security oftransmission is critical for many network and Internet applications • Requires users to share information in a way that others can’t decipher the flow of information “It is insufficient to protect ourselves with laws; we need to protect ourselves with mathematics.” -Bruce Schneier J@Y_IT The Diffie-Hellman Algorithm 4
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  Introduction • Based onthe difficulty of computing discrete logarithms of large numbers. • No known successful attack strategies* • Requires two large numbers, one prime (P), and (G), a primitive root of P J@Y_IT The Diffie-Hellman Algorithm 5
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  Implementation • P andG are both publicly available numbers – P is at least 512 bits • Users pick private values a and b • Compute public values – x = ga mod p – y = gb mod p • Public values x and y are exchanged J@Y_IT The Diffie-Hellman Algorithm 6
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  Implementation Copyright, 2001 byNetIP, Inc. and Keith Palmgren, CISSP.J@Y_IT The Diffie-Hellman Algorithm 7
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  Implementation • Compute shared,private key – ka = ya mod p – kb = xb mod p • Algebraically it can be shown that ka = kb – Users now have a symmetric secret key to encrypt J@Y_IT The Diffie-Hellman Algorithm 8
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  Implementation Copyright, 2001 byNetIP, Inc. and Keith Palmgren, CISSP.J@Y_IT The Diffie-Hellman Algorithm 9
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  Example • Two Internetusers, Alice and Bob wish to have a secure conversation. – They decide to use the Diffie-Hellman protocol J@Y_IT The Diffie-Hellman Algorithm 10
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  Example • Bob andAlice are unable to talk on the untrusted network. –Who knows who’s listening? J@Y_IT The Diffie-Hellman Algorithm 11
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  Example • Alice andBob get public numbers – P = 23, G = 9 • Alice and Bob compute public values – X = 94 mod 23 = 6561 mod 23 = 6 – Y = 93 mod 23 = 729 mod 23 = 16 • Alice and Bob exchange public numbers J@Y_IT The Diffie-Hellman Algorithm 12
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  Example • Alice andBob compute symmetric keys – ka = ya mod p = 164 mod 23 = 9 – kb = xb mod p = 63 mod 23 = 9 • Alice and Bob now can talk securely! J@Y_IT The Diffie-Hellman Algorithm 13
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  Applications • Diffie-Hellman iscurrently used in many protocols, namely: – Secure Sockets Layer (SSL)/Transport Layer Security (TLS) – Secure Shell (SSH) – Internet Protocol Security (IPSec) – Public Key Infrastructure (PKI) J@Y_IT The Diffie-Hellman Algorithm 14
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  Conclusion • Authenticated Diffie-HellmanKey Agreement (1992) – Defeats middleperson attack • Diffie-Hellman POP Algorithm – Enhances IPSec layer • Diffie-Hellman continues to play large role in secure protocol creation J@Y_IT The Diffie-Hellman Algorithm 15
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  Additional Sources • http://www.sans.org/rr/encryption/algorithm .php •http://www.hack.gr/users/dij/crypto/overvie w/index.html • http://WWW.Wikipidia.com J@Y_IT The Diffie-Hellman Algorithm 16