论文标题:一种基于门限方案和椭圆曲线密码体制的数据加密方案
A Scheme of Data Encryption Based on Threshold Scheme and Elliptic Curve Cryptosystem
论文作者 唐晓东
论文导师 黄穗,论文学位 硕士,论文专业 计算机软件与理论
论文单位 暨南大学,点击次数 81,论文页数 73页File Size3227k
2003-04-01论文网 http://www.lw23.com/lunwen_416140172/ (m,n)-门限方案,数据加密方案,椭圆曲线密码体制,LaGrange插值公式,椭圆曲线离散对数问题
(m,n)-threshold scheme,scheme of data encryption,elliptic curve cryptosystem,LaGrange interpolation formula,elliptic curve"s discrete logarithm problem
本文提出了一种基于(m，n)-门限方案和椭圆曲线密码体制的数据加密方案。在该方案中，用户分为单人用户和群组用户两种类型。群组用户是指由多个(不妨设为n个)参与者组成的一个集体，他们共同分享一个私钥，每个参与者只拥有一个与其他用户不同的私钥的影子。他们中至少有m个(m≤n)才能重构出私钥。单人用户是指个人用户，其私人密钥为个人所有。在加密和解密的过程中，群组用户都需要进行密钥(私钥)的恢复和认证。方案实现了以下几个方面的功能：①基于(m，n)-门限方案的多人加密，单人解密。②单人加密，基于(m，n)-门限方案的多人解密。③单人加密，单人解密。④基于(m，n)-门限方案的多人加密，基于(m，n)-门限方案的多人解密。加密方案利用有限域中的多项式方程(基于LaGrange插值公式)来构造(m，n)-门限方案，该门限方案和一次一密乱码本一样安全。加密方案中没有使用超奇异椭圆曲线及异常椭圆曲线，椭圆曲线上基点的阶为大素数(长度≥160比特)，保证了椭圆曲线离散对数问题的难解性，从而最终保证了整个方案的安全性。
This thesis proposes a scheme of data encryption based on the (m,n)-threshold scheme and elliptic curve cryptosystem in which users are handled as an individual-user and a group-user. A group-user is a group made up of many (may be n) participants, each of whom holds a shadow of a common key (private key) different from one another. The key can be recovered by the minimum of m (m≤n) participants in the group. An individual-user is one who holds the key all by himself. The functions of this scheme are as follows: ①The encryption of plaintext based on the (m,n)-threshold scheme by a group-user and the decryption of ciphertext by an individual-user; ②The encryption of plaintext by an individual-user and the decryption of ciphertext based on the (m,n)-threshold scheme by an group-user; ③The encryption of plaintext and the decryption of ciphertext by individual-users; ④ The encryption of plaintext and the decryption of ciphertext based on the (m,n)-threshold scheme by group-users. The (m,n)-threshold scheme, which is constructed on polynomial equation over finite field (based on LaGrange interpolation formula), is secure as one-time pad"s. Its security is ensured by the difficulty of elliptic curve"s discrete logarithm problem by means of the exclusion of supersingle and anomalous elliptic curves and the adoption of a big prime (more than 160 bits) for the order of base-point in elliptic curve in this scheme of data encryption.
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