
320 Cryptography with Open-Source Software
Some basic protocols
Tri partite key exchange. One of the simplest protoco ls involving pairings
is Joux’s three-way Diffie Hellman key exchange [42]. This is a method for
three people to agree on a single key to be used between all of them. This can
be do ne without pairings, but r e quires three steps. In the first step, Alice,
Bob and Charlie agree on an elliptic curve E and a point P on it. Each
produces a secret integer a, b, c respectively. Alice computes aP , Bob bP and
Charlie cP . In the s e c ond step, Alice passes her result to Bob, Bob passes
his to Charlie, and Charlie passes his to Alice. Then Alice ...