1. Tightly Secure IBE Under Constant-Size Master Public Key
- Author
-
Jian Weng, Jie Chen, and Junqing Gong
- Subjects
Discrete mathematics ,Reduction (recursion theory) ,business.industry ,Open problem ,Order (ring theory) ,020206 networking & telecommunications ,02 engineering and technology ,Upper and lower bounds ,Random oracle ,Public-key cryptography ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,business ,Constant (mathematics) ,Algorithm ,Mathematics ,Standard model (cryptography) - 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 \({\mathcal {O}}(\log q)\) where q is the upper bound of the total number of secret keys and challenge ciphertexts per instance. It’s much smaller than those for all known adaptively secure IBE schemes in a concrete sense.
- Published
- 2017