16 Three pass protocol

 

This chapter covers

  • Three pass protocol based on exponentiation
  • Three pass protocol based on matrix multiplication
  • Three pass protocol based on 2-sided matrix multiplication

Sections 2.2 and 2.3 describe how modern cryptography is divided into 3 branches, Secret Key, Public Key and Personal Key. Up to this point, this book has described only methods for Secret Key cryptography. Public Key cryptography is described in many books, so it will not be covered here. This chapter will discuss Personal Key cryptography, the lesser-known third branch of cryptography. Personal Key cryptography is sometimes called keyless cryptography, since the parties do not need to transmit or share any keys.

The basic concept of Personal Key cryptography is that each of the two correspondents, Sandra and Riva, has her own personal key. This key is never transmitted or shared with anyone else, not even with one another, so there is no possibility that Emily can learn any of the personal keys through wire-tapping, intercepting broadcasts, or any other form of eavesdropping. The great advantage of Personal Key cryptography is that you don’t need to set anything up in advance. There does not need to be any secret, secure channel for exchanging keys. The messages can be exchanged on public channels. No key servers or other infrastructure are required.

16.1 Shamir’s method

16.2 Massey-Omura

16.3 Discrete logarithm

16.3.1 Logarithms

16.3.2 Powers of primes

16.3.3 Crash

16.3.4 Factoring

16.3.5 Estimates

16.4 Matrix three pass protocol

16.4.1 Commutative family of matrices

16.4.2 Multiplicative order

16.4.3 Maximum order

16.4.4 Emily attacks

16.4.5 Non-commutative ring

16.4.6 Solving bilinear equations