一种新的可实现安全公钥密码体制——4次同余方程的应用

A Novel Security-Ensured Public Key Cryptosystem——A Quartic Congruential Equation Approach

提出了一种新的、可实现安全的公钥密码体制,在采用原有的公钥、私钥的基础上,增加数量庞大、开销极低的公开参数集合;在每加密一批数据时选择一组新的不重复公开参数。提出了判断4次同余方程解结构及其求解的线性时间快速算法,以实现公开参数集合的操作。该安全方案可以主动抵御选择明文攻击与各种选择密文攻击,包括IND-CCA2,并且可以达到类似一次一密的安全效果。对于大批量数据的加密解密,计算和存储开销集中于第一个数据,自第二个之后只需要简单的异或操作;可应用于如RFID标签的低端产品或如无线网络等计算、存储、带宽等资源受到极大限制的设备中。

For improving the efficiency and the potential for actively protecting against attacks, a novel security-ensured public key cryptosystem is proposed. The idea is that a large set of published parameters, which are generated with almost no more overheads, is taken into account in addition to the original public and private keys. A new set of published parameters will be chosen when a group of data to be encrypted each time. The linear time quick algorithms for deciding the solution structure and computing the solution of the quartic congruential equations are proposed for implementing the operations on the published parameters. This cryptosystem can actively protect against the chosen plaintext and the various chosen ciphertext attacks including IND-CCA2 attacks. It achieves the same security like One-Time-Pad. For the repeated encryption/decryption for a set of data the requirements for computation and memory size are deeply decreased because only a series of XOR operations are needed after first data item has been encrypted/decrypted. Due to this reason, this cryptosystem may be used in very low-end devices, such as RFID tags, sensor networks, where the computation, memory and bandwidth are very limited.