Compact hierarchical identity-based encryption based on a harder decisional problem

Abstract

We generalize the decisional problem that was used to prove the security of a well-known hierarchical identity-based encryption scheme by Boneh, Boyen and Goh. We argue that our new problem is strictly harder than the original problem, and thus the security of the aforementioned cryptographic primitive is laid on even stronger foundations.

Keywords:

• hierarchical identity-based encryption
• hard problems
• decisional assumptions
• standard model
• generic model

2010 AMS Subject Classifications:

• 94A60
• 68P25
• 68Q17

1998 ACM Computing Classification System Codes:

• E.3
• F.2.2

Notes

1. Notice that for ℓ=1, the maximum appearance degree of the variable X equals 1 in both inputs. This is why the impossibility argument does not hold for ℓ=1, and indeed we have proven that .