A fair offline electronic cash scheme with multiple-bank in standard model

ABSTRACT

Offline electronic cash is a new and well-acknowledged type of e-cash scheme that can release the bank from participating in every spending protocol. However, it is still an unsolved problem to design a secure and efficient fair offline e-cash scheme. Considering this problem, in this paper, we have proposed a fair offline electronic cash scheme with multiple banks in pairing-based instantiation. We adopt Groth–Sahai non-interactive zero-knowledge proof technology in our scheme, to design non-interactive e-cash transactions. Additionally, inspired by Water’s group signature, our solution supports not only multiple users, but also users with accounts in different banks. Moreover, our scheme has efficient double-spending checking and a fair control mechanism. We have formally defined the security properties of the scheme in a standard model, and provided the detailed security proofs of the security properties concerning chosen ciphertext attack (CCA) anonymity, unforgeability and traceability. Analysis and comparison show that our scheme has advantages both in security and in efficiency.

KEYWORDS:

• Offline electronic cash
• multiple bank
• waters signature
• Groth–Sahai proof

Nomenclature

k	=	The secure parameter
CB/LB	=	Central bank/local bank
U	=	User
C/M	=	Customer/merchant
pk	=	The public key used to verify e-cash
msk	=	The master secret key
skO	=	The opening key
PPT	=	Pseudo-polynomial time
$e$	=	A bilinear pairing $G\times G\to G_T$
$F$	=	A bilinear mapping $G^3\times G^3\to G_T^9$;
$Reg[i]$	=	The related value at registry table entry i
HU	=	Honest users
CU	=	Corrupted users

Disclosure statement

The authors reported no potential conflict of interest.

Additional information

Funding

This work was supported in part by the National Science and Technology Major Project under Grant No.2013ZX03002006, the Liaoning Province Science and Technology Projects under Grant No.2013217004, the Liaoning Province Doctor Startup Fund under Grant NO.20141012, the Fundamental Research Funds for the Central Universities under Grant No. N130317002, the Shenyang Province Science and Technology Projects under Grant No. F14-231-1-08, and the National Natural Science Foundation of China under Grant Numbers 61772127, 61472184, 61321491, 61272546.