A Postquantum Linkable Ring Signature Scheme from Coding Theory

Algorithm 3

Our LRS scheme.

(1)	Public parameters:.
(2)	KeyGen: User :
	(i) Samples as private key.
	(ii) Calculates the public key and sets as .
(3)	Sign: performs the following steps:
	(i) Calculates .
	(ii) Repeats Algorithm2 with the input times such that the soundness error is negligible and then obtains .
	(iii) Sets as .
	(iv) Sets the corresponding responses according to the step 6 of Algorithm2.
	(v) Sets the transcript .
	(vi) Outputs the linkable ring signature .
(4)	Ver: Given a signature , the verifier
	(i) Calculates ;
	(ii) According to Algorithm2 with the input to check if is a valid transcript.
	(iii) If the above condition holds, it returns 1; otherwise, it returns 0.
(5)	Link: When two signatures are received, the verifier parses and
	(i) Checks if and are correct.
	(ii) Checks if .
	(iii) If the above two conditions hold, it outputs 1; otherwise, it outputs 0.