# American Institute of Mathematical Sciences

November  2019, 13(4): 759-778. doi: 10.3934/amc.2019044

## Identity-based key aggregate cryptosystem from multilinear maps

 Department of Computer Science and Engineering, Indian Institute of Technology Kharagpur, West Bengal 721302, India

Received  October 2018 Revised  March 2019 Published  June 2019

A key-aggregate cryptosystem (KAC) is the dual of the well-known notion of broadcast encryption (BE). In KAC, each plaintext message is encrypted with respect to some identity, and a single aggregate key can be generated for any arbitrary subset $\mathcal{S}$ of identities, such that any ciphertext designated for any identity in $\mathcal{S}$ can be decrypted using this aggregate key. A KAC scheme is said to be efficient if all public parameters, ciphertexts and aggregate keys have polynomial overhead, and can be generated using poly-time algorithms.

A KAC scheme is said to be identity-based if remains efficient even when the number of unique identities supported by the system is exponential in the security parameter $\lambda$. Unfortunately, existing KAC constructions do not satisfy this property. In particular, adopting these constructions to the identity-based setting leads to public parameters with exponential overhead.

In this paper, we propose new identity-based KAC constructions using multilinear maps that are secure in the generic multilinear map model, and are fully collusion resistant against any number of colluding parties. Our first construction is based on asymmetric multilinear maps, with a poly-logarithmic overhead for the public parameters, and a constant overhead for the ciphertexts and aggregate keys. Our second construction is based on the more generalized symmetric multilinear maps, and offers tighter security bounds in the generic multilinear map model. This construction has a poly-logarithmic overhead for the public parameters and the ciphertexts, while the overhead for the aggregate keys is still constant.

Citation: Sikhar Patranabis, Debdeep Mukhopadhyay. Identity-based key aggregate cryptosystem from multilinear maps. Advances in Mathematics of Communications, 2019, 13 (4) : 759-778. doi: 10.3934/amc.2019044
##### References:

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##### References:
Theorem 1: Upper Bounds on Contributions to Length of $L$
 Query Stage Maximum Contribution to $|L|$ SetUp $m+2$ Oracle Query Phase $Q_E+Q_M+Q_P$ Aggregate Key Query Phase (1 and 2) $Q_K$ Challenge $5$ Total $Q_E+Q_M+Q_P+Q_K+m+7$
 Query Stage Maximum Contribution to $|L|$ SetUp $m+2$ Oracle Query Phase $Q_E+Q_M+Q_P$ Aggregate Key Query Phase (1 and 2) $Q_K$ Challenge $5$ Total $Q_E+Q_M+Q_P+Q_K+m+7$
Theorem 2: Upper Bounds on Contributions to Length of $L$
 Query Stage Maximum Contribution to $|L|$ SetUp $2m+1$ Oracle Query Phase $Q_E+Q_M+Q_P$ Aggregate Key Query Phase (1 and 2) $2Q_K$ Challenge $m+5$ Total $Q_E+Q_M+Q_P+2Q_K+3m+6$
 Query Stage Maximum Contribution to $|L|$ SetUp $2m+1$ Oracle Query Phase $Q_E+Q_M+Q_P$ Aggregate Key Query Phase (1 and 2) $2Q_K$ Challenge $m+5$ Total $Q_E+Q_M+Q_P+2Q_K+3m+6$
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