SPCABS: Signature-Policy Comparable Attribute-Based Signatures

Table 1

Summary of existing works.

Scheme	Access structure	Type	Assumption	Model
Maji et al. [1]	LSSS	KP	CDH	GGM
Jin and Kim [2]	Threshold	KP	CDH	ROM
Jin et al. [3]	Threshold	SP	CDH	ROM&SM
Shahandashti and Safavi-Naini [4]	Threshold	KP	CDH	SM
Gagné et al. [5]	Threshold	KP	CDH	ROM
Maji et al. [6]	Threshold	SP	CDH&DLIN	GGM
Gu et al. [7]	LSSS	SP	CDH	SM
Okamoto and Takashima [8]	Threshold	KP	DLIN	GGM
Okamoto and Takashima [9]	LSSS	SP	DLIN	GGM
Herranz et al. [10]	Threshold	SP	DLIN	GGM
Chen et al. [11]	LSSS	SP	CDHE	ROM
Su et al. [12]	Threshold	SP	CDH	ROM
Wang and Chen [13]	Threshold	SP	SIS	ROM
Escala et al. [14]	LSSS	SP	SIS	SM
Tang et al. [15]	Circuit	KP	MCDH	ROM
Sakai et al. [16]	Circuit	KP	CDH	ROM
Kaafarani and Ghadafi [17]	Circuit	SP	DDH	GGM
Datta et al. [18]	LSSS	SP	DLIN	SM
Cao et al. [19]	Threshold	SP	CDH	SM
Cao et al. [20]	Threshold	KP	CDH	ROM
El Kaafarani et al. [21]	LSSS	SP	DDH	ROM
Okamoto and Takashima [22]	LSSS	SP	DLIN	ROM
El Kaafarani et al. [23]	LSSS	SP	DLIN&CDH	ROM&SM
Ghadafi [24]	LSSS	SP	DDH&DLIN	SM

LSSS = linear secret sharing scheme, SP=signature-policy, KP=key-policy, DLIN = decisional linear assumption, SIS=short integer solution, CDH=computational Diffie–Hellman assumption, MCDH = multilinear CDH, DDH = decisional DH, CDHE=computational Diffie–Hellman exponent assumption, GGM = generic group model, ROM = random oracle model, and SM=standard model.