Threshold Encryption Research Based On ECC Without A Trusted Party

Secret sharing is an important branch of modern cryptography, and it haschanged the mode of single encryption, signature and authentication, which can notonly decentralize responsibility, but also improve the security and reliability ofsystem. In traditional secret sharing, the existence of the trusted party will lead to“authority deception” and “single point of failure”, and the secret sharing without atrusted party tries to solve these two problems fundamentally. Currently, theresearch of secret sharing without a trusted party has mainly focused on thresholdsignature, and the study of threshold encryption without a trusted party is rare.Elliptic Curve Cryptosystem (ECC) is a classic public key cryptosystem, which hasthe following advantages, such as short key, high efficiency and safety.This dissertation introduces the related theories and mathematical knowledgeabout Elliptic Curve Cryptosystem, makes an intensive study of threshold secretsharing, analyzes some classic threshold secret sharing schemes, and lays emphasison the study of threshold secret sharing without a trusted party. To improve thetraditional ECC algorithm, a threshold encryption scheme without a trusted party isproposed and the scheme has the following characteristics:(1) Without a trusted party, participants generate their own secret shares andsystem public key cooperatively, which improves the security and reliability ofsystem.(2) Anyone can encrypt with the system public key, any t participants candecrypt by employing deception factors, and the system private key is unexposed indeception stage, which guarantees the safty and reusability of system private key.(3) In traditional ECC, plaintexts are mapped onto the x value of a point (x, y)on elliptic curve. In the dissertation, plaintexts can be parallelly encrypted with xand y value of a point (x, y)on elliptic curve simultaneously, which improvesencryption efficiency of the system.At last, this dissertation introduces the generation algorithm of large primenumbers and its core functions of large numbers’ computation. Each functionalmodule of the scheme is analyzed in detail, and the prototype system is realized byVC++6.0. It can be proved that the scheme is correct and feasible by experiments.