Algebraic Attacks Against Several Weak Variants of GVW’13 ABE

Abstract

Attribute-based encryption (ABE) is an active research area in the public-key cryptography. Among large amount of ABE schemes, the scheme GVW’13 (STOC13) is an well-known candidate for realizing ABE via lattice mechanism, whose security relies on learning with errors (LWE). This ABE scheme has very exquisite structure, and its crucial component lies in using that two-to-one recoding (TOR) algorithm. However, the main shortcoming of GVW’13 is the use of the huge key-size. Therefore, it encourages people to find out some more simplified variants of GVW’13. In this paper, we first propose three variants of GVW’13 for reducing the size of secret key, which would be the feasible strategies to improve GVW’13 with great possibility. Unfortunately, we can still present three related attacks against these three proposals under the same collusion scenario, respectively.