Cryptology ePrint Archive: Report 2016/891

Tightly Secure IBE under Constant-size Master Public Key

Jie Chen and Junqing Gong and Jian Weng

Abstract: Chen and Wee [CRYPTO, 2013] proposed the first almost tightly and adaptively secure IBE in the standard model and left two open problems which called for a tightly secure IBE with (1) constant-size master public key and/or (2) constant security loss. In this paper, we propose an IBE scheme with constant-size master public key and tighter security reduction. This (partially) solves Chen and Wee's first open problem and makes progress on the second one. Technically, our IBE scheme is built based on Wee's petit IBE scheme [TCC, 2016] in the composite-order bilinear group whose order is product of four primes. The sizes of master public key, ciphertexts, and secret keys are not only constant but also nearly optimal as Wee's petit IBE. We can prove its adaptive security in the multi-instance, multi-ciphertext setting [PKC, 2015] based on the decisional subgroup assumption and a subgroup variant of DBDH assumption. The security loss is $O(\log q)$ where $q$ is the upper bound of the total number of secret keys and challenge ciphertexts revealed to adversary in each single IBE instance. It's much smaller than those for all known adaptively secure IBE schemes in a concrete sense.

Category / Keywords: identity based encryption; tight security; constant-size public key; composite-order group; Deja Q technique

Original Publication (with minor differences): IACR-PKC-2017

Date: received 12 Sep 2016, last revised 1 Feb 2017

Contact author: S080001 at e ntu edu sg; junqing gong@ens-lyon fr

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Version: 20170201:122951 (All versions of this report)

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