Abstract
There only exists one deterministic identity-based encryption (DIBE) scheme which is adaptively secure in the auxiliary-input setting, under the learning with errors (LWE) assumption. However, the master public key consists of O(λ) basic matrices. In this paper, we consider to construct adaptively secure DIBE schemes with more compact public parameters from the LWE problem. (i) On the one hand, we gave a generic DIBE construction from lattice-based programmable hash functions with high min-entropy. (ii) On the other hand, when instantiating our generic DIBE construction with four LPHFs with high min-entropy, we can get four adaptively secure DIBE schemes with more compact public parameters. In one of our DIBE schemes, the master public key only consists of ω(logλ) basic matrices.
Highlights
A deterministic identity-based encryption (DIBE) scheme is an identity-based encryption (IBE) scheme [1] whose encryption algorithm is deterministic
In order to construct DIBE schemes, Bellare et al [2] first defined a notion of identity-based lossy trapdoor functions (IB-LTDFs)
To measure the reduction cost, we show the advantage of the learning with errors (LWE) algorithm constructed from the adversary against the corresponding DIBE scheme
Summary
A DIBE scheme is an identity-based encryption (IBE) scheme [1] whose encryption algorithm is deterministic. In SCN12, Xie et al [3] gave a more efficient secure DIBE scheme in the auxiliary-input setting, based on the hardness of the LWE problem In their scheme, there exists only 3 matrices in the master public key. Combining with the result of Zhang et al, we conclude that the adaptively secure and anonymous IBE schemes in [4,5,6,7,8,9,10] naturally imply instantiations of LPHFs with high min-entropy (iii) When instantiating our generic DIBE construction with four LPHFs with high min-entropy in [4, 7, 8], we can get four adaptively secure DIBE schemes with more compact public parameters. In this paper, we present a generic DIBE construction from LPHFs with high min-entropy
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