Provably Secure Lattice-Based Self-Certified Signature Scheme

Algorithm 2

Extract.

	Input: with an identity , .
	Output: the user’s key .
(1)	selects a random uniform matrix from as the secret key, where .
(2)	Computes , and sends to CA.
(3)	Upon receiving the , CA performs as follows:
(i)	computes .
(ii)	uses the algorithm SampleMAT to output .
(iii)	sends to through a secure channel.
(4)	checks the authenticity of by verifying and . If so, output as their partial private key. Otherwise, reject it.