I just read
S.S. Al-Riyami and K.G. Paterson, Certificateless public key cryptography 2003
https://web.archive.org/web/20181222114112/http://eprint.iacr.org/2003/126.pdf
The math is not too complicated, but I find the notation a pain.
Also, all the fuss over the group operation being additive in G_1 and multiplicative in G_2 seems such a faff.