Ingemarsson Requires N-1 rounds and O(N2) exponentiations
Burmester-Desmedt Requires 2 rounds but full broadcast
GDH (Steiner et al.) Requires N rounds and O(N) exp.
9 Butterfly Group Diffie-Hellman Example u1 u2 u3 u4
Can be extended to arbitrary radix b using Ingemarsson as the basic building block.
Optimal radix in both cases is 2.
u5 u6 u7 u8 10 The Conference Tree
Group key formation procedure is described by
Communication flow diagram
Conference tree describes the subgroups and subgroup keys.
u1 u2 u3 u4 u5 u6 u7 K101 K001 K011 K100 K110 K000 K010 K111 u8 11 Making Primes
Fact Let n be an odd prime and let where r is odd. Let a be any integer such that gcd(an)1. Then either or for some .
Definition Let n be an odd composite with . Let
. If either or for some then n is a strong pseudoprime base a and a is a strong liar for n.
Fact If n is an odd composite integer then at most 1/4 of the numbers a are strong liars for n.
We can use this in a Monte-Carlo algorithm to produce primes
Test t different as.
Probability of falsely identifying a prime is
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