When Bob Met Alice Who Met Carol

Using Cryto Pairing and Key Sharing With MIRACL Golang

I love receiving a new crypto library, and diving in to discover its hidden secrets. The latest one is MIRACL [here], and where we are collaborating with Professor Michael Scott, and who is one of the founding fathers of crypto pairs. As we share a passion for crypto pairing too, it is an easy collaboration for us. So let’s look at implementing a scheme where Bob, Alice and Carol can share a secret key, and to showcase the wonderful features of crypto pairing.

Tripartite Diffie-Hellman algorithm

Elliptic curves are used fairly extensively in public key encryption (such as in Bitcoin and Tor). A BN-curve (Barreto-Naehrig curve) [paper] defines an elliptic curve which can be used for pairings that allow for a high security and efficiency level.

So how do we generate a shared key between three parties? This page implements the tripartite Diffie-Hellman algorithm [Paper] and what Bob (B), Alice (A) and Carol (C ) share their key pairings and then can calculate a shared secret key. In this case a, b and c are the private keys generated by Alice, Bob and Carol, respectively. Bob, Alice and Carol then generate key public keys from curves G1 and G2. In this case we show the keys for Alice, which are pa…