I am beginner to pairing-based cryptography. After downloading jpbc library, curve parameters files are seen as properties file. For example, for type A curve, following parameters are given.

type a q 8780710799663312522437781984754049815806883199414208211028653399266475630880222957078625179422662221423155858769582317459277713367317481324925129998224791 h 12016012264891146079388821366740534204802954401251311822919615131047207289359704531102844802183906537786776 r 730750818665451621361119245571504901405976559617 exp2 159 exp1 107 sign1 1 sign0 1

PBC uses elliptic curve.Mostly, as far as I know, most of papers describe pairing $e:G_1\times G_1\rightarrow G_2$, groups are cyclic group of prime order $q$ and $Z_q$ is used.

In typeA pairing,different $q$ and $r$,groups of prime order $q$ and $Z_r$ is used. When random number is generated from $G_1$ group, its length is greater than random number from $Z_r$.

I think previous papers have to combine desired curve and pairing to achieve $q$ size of group and $Z_q$ .How to combine named curve and pairing? May be there will be existing works implementation. Anybody, please explain nature of Type A and other systems. If it is possible, please help me with the link of existing implementations.


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