Research on treatment to prevent loss of cryptographic key

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We construct efficient secret sharing scheme (SSS) (including "1-out-of-n" cryptosystem) and consider the treatment against the loss of cryptographic key. To make more concretely, we propose Hybrid P2P network model which does not access to the root server in case the system preserves or gathers the share of SSS. Our scheme can give some guarantee for the data integrity even when the system loses both terminal machines (e.g. mobile PC) and removable cryptographic key (e.g. USB key). We solve the above problem mainly using the following two methods : (1) The system uses the work key (not master key) to encrypt the data in mobile PC ; (2) The system uses the authentication code from the root server, which decrypts the encrypted data. Consequently, our system realizes the share's generation and the data recovery related to the (k, n) threshold scheme. The system gives the data integrity for the authentication code between server and client machines. Profitable performance evaluation is al … More so obtained from implementation point of view.We also propose fast software/hardware implementation to calculate the paring on elliptic curve. Nowadays there are so many applications in the pairing based cryptosystem, e.g. ID-based cryptosystem, short signature, broadcast encryption, etc. However there exist some drawbacks in pairing calculation. This means that the amount of work to calculate the pairing is very large compared to the conventional calculation method. We propose some efficient pairing algorithms for calculation. One of them is a proposal of an efficient (twisted) Ate pairing. The twisted Ate pairing is faster than the conventional Tate pairing. We give the loop-shorten technique of the Eta T pairing. This pairing can be applied to the twisted Ate pairing and computational cost is reduced by 25 to 50 % in terms of software implementation. In addition, we show that the improvement of the twisted Ate pairing is theoretically faster than the Ate pairing when parameter rho is approximately 2. In the same way, we also proposed other efficient pairings and estimate them compared to conventional pairings. Less