PTC Protocol Working Group

1
The Diffie-Hellman Algorithm

• PTC Protocol Working Group
• Gagan Puranik
• March 25, 2004

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• It is insufficient to protect ourselves with
  laws we need to protect ourselves with
  mathematics.
• -Bruce Schneier

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Contents

• Introduction
• Implementation
• Example
• Applications
• PWG approved specs

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Introduction

• Discovered by Whitfield Diffie and Martin Hellman
• Allows two users to agree on symmetric key
• Requires no prior secrets
• Although, AUTHENTICATION is required to address
  man-in-the-middle attack
• Real-time over an untrusted network (e.g.
  wireless)
• Based on the difficulty of computing discrete
  logarithms of large numbers
• Requires
• two large numbers
• one prime (P)
• and (G) a primitive root of P

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Implementation
Source NetIP, Inc. and Keith Palmgren, CISSP.
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Example

• Alice and Bob agree on DH parameters
• P 23, G 2
• Alice
• Private key x 9
• Public key X 29 mod 23 512 mod 23 6
• Bob
• Private key y 5
• Public key Y 25 mod 23 32 mod 23 9
• Alice and Bob exchange public keys
• Alice compute symmetric key using Private Key x
  and Public Key Y
• ka Yx mod P 99 mod 23 2
• Bob compute symmetric key using Private Key y and
  Public Key X
• kb Xy mod P 65 mod 23 2

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Applications

• Diffie-Hellman is currently used in many
  protocols, namely
• Secure Sockets Layer (SSL)/Transport Layer
  Security (TLS)
• Secure Shell (SSH)
• Internet Protocol Security (IPSec)
• Public Key Infrastructure (PKI)
• In the future,
• Secure Paging (1Way and/or 2Way). ?

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PWG approved specs

• RFC 41 ANSI X9.63 EC key agreement protocol
• Establish keys using
• EC large number generator
• EC-DH to establish symmetric keys
• ECDSA for authentication
• SHA-1 for data integrity
• RFC 30 AES
• Symmetric key encrypted messaging
• follows the U.S. Governments FIPS 197
  recommendation
• Excerpts from NISTs AES fact sheet
  (http//csrc.nist.gov/CryptoToolkit/aes/aesfact.ht
  ml)
• Assuming that one could build a machine that
  could recover a DES key in a second (i.e., try
  255 keys per second), then it would take that
  machine approximately 149 thousand-billion (149
  trillion) years to crack a 128-bit AES key. To
  put that into perspective, the universe is
  believed to be less than 20 billion years old.
• "Barring any attacks against AES that are faster
  than key exhaustion, then even with future
  advances in technology, AES has the potential to
  remain secure well beyond twenty years."