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Threshold Cryptosystem Based Fair Off-Line E-cash

The paper analyzed the security threats and system flaws of present e-cash schemes. Combining (t,n) threshold cryptography and e-cash, we present a threshold fair off-line e-cash scheme based on ECC ( Elliptic Curve Cryptosystem) . The scheme can trace the user identity and e-cash by embedding identity mark in e-cash generating and exchanging, and thus effectively prevents such illegal usage of e-cash as bribery and blackmailing, etc. By utilizing secret key sharing and probabilistic encryption algorithm, the scheme achieves threshold management of private key, avoids the misuse of identity tracing and currency tracing in fair e-cash scheme. The scheme achieves effective supervision on identity and e-cash tracing for fair electronic commerce, it also prevents coalition attack, intruder-in-middle attack and generalized e-cash forgery. Further analyses and comparison with other e-cash schemes also justify the scheme's brevity, security, high efficiency, and thus considerable improvement on system efficiency regarding software and hardware application.