# System parameters in identity-based encryption

In IBE schemes, the system parameters are $(q, \mathbb{G}, F, \hat{e}, P, Q, T, H_1)$. I don't know $\hat{e}$.

For example, in type A pairing…

type = a

q = 98826429041171753291515535532523512299028170537954154869719707264887274916552228805607584116490046284509883309001532457986879277885241872021906840932513241346999389365188296460009947
h = 32243626948934860887488490158437299489453513352745889246437755713701521031193083418924110592954582395114812811896992400310730276
r = 3064991081731777546575510593831386635550174528483098623

exp2 = 181
exp1 = 127

sign1 = -1
sign0 = -1


Are those system parameters? Does the server share these properties with clients?

The pairing description (type, q, h, r, etc.) is the definition of the field that the elliptic curve of some type operates on. The actual curve is identified by its type and is baked into the framework (e.g. PBC) you're using.

This definition corresponds to $q$ (group order, same as q), $\mathbb{G}, \mathbb{G}_T$ (groups defined by pairing description and curve) and $\hat{e}$ (pairing function $\hat{e}:\mathbb{G}\times\mathbb{G}\rightarrow\mathbb{G}_T$). $\hat{e}$ greatly depends on the actual elliptic curve, because different algorithms or parameters are used. All the other parameters are unique to the scheme that is devised using bilinear pairing.

The pairing description is necessary to have for doing any calculation with the described scheme. It must be known to all participants. Of course, if you're always using the same pairing description, you don't have to send it along with every message of your system. It can be baked into the client software.

Remember to generate a fresh and valid pairing description before you deploy your system into production. This makes it a little harder for attackers to break a system. If every one uses the same defaults, then pre-computation on that single group can break a lot of systems.

• Artjom B. If the user wants to use service from (n) servers, user will have (n) different pairing descriptions. In that cases, if the user wants to send the same message to those servers, does it need to send (n) times? If (n) servers use the same pairing description, broadcast encryption can be done. But the same pairing description of (n) servers will lead to problem?? Commented Jan 24, 2016 at 16:52
• Yes, if every server has different underlying group descriptions, then yes, you would have to encrypt n messages. The thing is that you usually only have one authority/central server, which has only one pairing description and the encryption can be done with the public parameters (public key). There are also multi-authority schemes, but these are bootstrapped after a global setup and use the same pairing description. I don't know what system you're talking about, but I would think that there is something wrong when you have n server. Either way, you can ask a new question with your specifics. Commented Jan 24, 2016 at 16:59
• If there are (n) servers using the same pairing description and hash functions, if a client joins those servers,is there possibility for secret keys generated by those servers will be same? Commented Jan 24, 2016 at 17:12
• Even if all servers use the same pairing description, the groups are usually large enough that there shouldn't be a secret key collision. With different pairing descriptions, you can still get overlapping groups as well as completely different groups. That depends on the curve type Commented Jan 24, 2016 at 17:19
• Thank you very much. Although my questions may be a little wrong, please guide me as I am a new learner to IBE . Commented Jan 24, 2016 at 17:22

The server must give the clients all the necessary information for the clients to be able to compute the pairing. This will differ depending on how pairings are implemented in the system, and what prior knowledge the clients have.

• If there are (n) servers using the same pairing description and hash functions, if a client joins those servers,is there possibility for secret keys generated by those servers will be same? Commented Jan 24, 2016 at 17:09