Type 2 Structure-Preserving Signature Schemes Revisited

At CRYPTO 2014, Abe, Groth, Ohkubo and Tibouchi presented genericsigner structure-preserving signature schemes using Type 2 pairings. The schemes were claimed to enjoy the smallest number of group elements in signatures and the fastest signature verification. By properly accounting for the concrete structure of the underlying group and subgroup membership testing of group elements in signatures, we show that the schemes are not as efficient as claimed. We present natural Type 3 analogues of the Type 2 schemes, and show that the Type 3 schemes are superior to their Type 2 counterparts in every aspect. We also formally establish that all Type 2 structure-preserving signature schemes can be converted to the Type 3 setting without any penalty in security or efficiency, and show that the converse is false.