Attribute-based key-insulated signature for boolean formula

Abstract

In order to minimize the impact of secret signing key exposure in attribute-based signature scenario, we construct an attribute-based key-insulated signature (ABKIS) scheme for expressive monotone boolean function access structures utilizing only four pairing operations in verification process and making the signature length constant, that is, the number of pairings required for signature verification and the size of signature are independent of the size of attribute set participated in the respective process. The (strong) key-insulated selective security of our ABKIS scheme is reduced to the computational Diffie–Hellman Exponent problem without using any random oracles. The proposed construction attains signer privacy, which is a fundamental requirement of the signature schemes in the attribute-based setting.

Keywords:

• attribute-based signature
• key-insulation mechanism
• monotone boolean function
• constant-size signature

2010 AMS Subject Classifications:

• 94A60
• 94A62

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Monotone boolean function means that $\mathrm{{\rm Y}}\left(W\right)=1$ and $W\subset W^{\prime }$ implies $\mathrm{{\rm Y}}\left(W^{\prime }\right)=1.$

2. We consider $U=\{0,1{\}}^{\ast }$ is the attribute universe, i.e. each arbitrary string is treated as an attribute. Using a collision resistant hash function $f:\{0,1{\}}^{\ast }\to {\mathbb{Z}}_p^{\ast }$, we can map each attribute string to an element of ${\mathbb{Z}}_p^{\ast }$. For simplicity, we consider all elements of ${\mathbb{Z}}_p^{\ast }$ as attribute universe, i.e. $U={\mathbb{Z}}_p^{\ast }$.