# Key-Policy Attribute-Based Encryption for General Boolean Circuits from Secret Sharing and Multi-linear Maps

## Abstract

We propose a Key-policy Attribute-based Encryption (KP-ABE) scheme for general Boolean circuits, based on secret sharing and on a very particular and simple form of leveled multi-linear maps, called *chained multi-linear maps*. The number of decryption key components is substantially reduced in comparison with the scheme in [7], and the size of the multi-linear map (in terms of bilinear map components) is less than the Boolean circuit depth, while it is quadratic in the Boolean circuit depth for the scheme in [7]. Moreover, the multiplication depth of the chained multi-linear map in our scheme can be significantly less than the multiplication depth of the leveled multi-linear map in the scheme in [7]. Selective security of the proposed scheme in the standard model is proved, under the decisional multi-linear Diffie-Hellman assumption.

## Keywords

Attribute-based encryption Multi-linear map Boolean circuit## References

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