Threshold Cryptosystem Using Pell´s Equation

This paper analyzed the basic principles of secret sharing in threshold cryptosystem and its superiority considering its application in key management. Combining secret sharing and key management, we present a threshold key management scheme based on PEC(Pell´s Equation based Cryptosystem). By utilizing secret sharing and probabilistic encryption algorithm in key generating and distributing, the scheme achieves threshold management of symmetric key and public key certificate. The scheme avoids the misuse of certificate generating and tracing by CA (Certificate Agency) members, renders effective supervision on key management. It prevents coalition attack, intruder-in-middle attack and generalized certificate forgery. We also provide an application case of the threshold key management scheme in key managing and certificate supervision, it further justify the scheme´s brevity, security, high efficiency regarding its application in such circumstances as with restricted computation ability, integrated space and limited bandwidth yet requiring for high-speed operation.