Research On Techniques Securing Mobile Code Based On Homomorphic Encryption

Mobile code is a new design paradigm fitting for large scale applications. It has a broad prospect of being used in active network, mobile agent, ecommerce, and so on. It is desiderated to solve its security problems. The difficult of the research is how to protect the mobile code no being tampered by malicious host and the information carried by the mobile code no leaking.The security threats of mobile code include confidentiality attacks, integrity attacks, availability refusals and authentication risks. The techniques to protect confidentiality and integrity of mobile code are important. They can solve the problems of tampering and information leaking.Tamper resistant hardware (TRH) is the earliest method to protect mobile code. There were few people making research on pure software protection based on cryptograph. The essential of TRH is data encryption. TRH has many disadvantages, namely bad system expansibility, difficulty of securely exchanging key, host must invoke driver module of hardware and trusted software protection module, corrupted hardware leaking the secret user information, must trust the hardware manufacture.Encryption theory and method to protect mobile code is an important direction of research on pure software protection. It includes secure circuit computing, obfuscating algorithm, homomorphic encryption.Secure circuit computing is a blind computing scheme based on the complexity of Boolean circuit. It can protect confidentiality of code and secret information and is base of many secure schemes. Its shortcoming is multiple rounds of interactive between the two communicators.Obfuscating algorithm is a program transformation technique to protect mobile code and software intellectual property rights. It makes the transformed program or disassembly result elusive. The measurement of performance and security of obfuscating algorithm bases on the complexity of time and memory space of the software. It is difficult to estimate the time of resistant attacks and can not efficiently protect the carried information.Homomorphic encryption is cryptographic technique base on the computing complexity theory of math puzzle. It is different from conventional data encryption. It allows operations on encrypted data without the decryption algorithm and key and the decrypted result is equal to that of operations on plaintext.The scheme to protect mobile code based on homomorhpic encryption is an important direction of research on pure software protection. Two research directions and resolving schemes have been formed under two premises, 1) coarse granularity premise supposes that mobile code is composed of functions. Secure mobile code computing would succeed if all kinds of functions could be computed with encrypted functions. The kinds of functions are so large that it is difficult and big challenge to find a universal scheme to encrypt functions. 2) fine granularity premise supposes that mobile code is composed of arithmetic operations (+, -,×,÷), compare operations (<, >, =), Boolean calculations(and, or, not), bit operations (and, or, not, shift). Accordingly, secure mobile code computing would succeed if all kinds of the operations could be encrypted and computed. It is difficult to find a homomorphic algorithm which can encrypt all the operations.The research on homomorphic encryption and mobile code security scheme based on homomorphic encryption is beginning not long ago. The disadvantages are listed as follows: homomorphic encryption is limited to integer ring; only rational polynomial functions can be encrypted; the polynomial skeletons of encrypted functions are plaintext; the encryption of arithmetic operation over real number has many secure issues such as known plaintext attacks, decimal fraction information leaking, positive and negative information leaking, restricting in encrypted subtractive, being incapable of non-interactive encrypted evaluation, the expensive overhead of computation and communication for encrypted compare operations, integrity checking to be deleted easily and to be constructed difficultly.This paper makes research on the above disadvantages as follows: theories and techniques about homomorphic encryption over real number; non-interactive evaluation with encrypted elementary functions; how to hide polynomial skeletons; secure evaluation with encrypted arithmetic operations over real number; fare, efficient and secure evaluation with encrypted comparing operations; integrity checking protocol and algorithm based on cryptograph.The major innovations of this research include:1) Public key homomorphic encryption algorithm over real number domain based on modified ElGamal is proposed. The algorithm can resist known plaintext attacks, not leak the decimal fraction and sign information, not restrict the encrypted subtractive, can be used in non-interactive evaluation with encrypted functions.2) The kinds of encrypted functions are expanded from rational polynomial over integer number domain to elementary functions over real number domain. Non-interactive evaluation with encrypted elementary functions is implemented based on the above homomorphic encryption algorithm and Taylor series.3) Two schemes to hide polynomial skeletons are proposed and implemented. The first is to add encrypted redundancy terms. The second is the concept of power homomorphic encryption and algorithm.4) Arithmetic homomorphic encryption over real number domain based on Fermat's Little Theorem is proposed. The algorithm can resist known plaintext attacks, not leak the decimal fraction and sign information, not restrict the encrypted subtractive, can be used in non-interactive evaluation with encrypted functions.5) Fare, efficient and secure comparing protocol and algorithm over real number is proposed. They have lower cost at computing and communication of evaluation with encrypted comparing operations.6) Encrypted functions embedding algorithm is proposed to check the integrity of mobile code. The check is apt to be constructed and implemented. This scheme couples the check functions with the normal computed function, so that deleting the check functions would destroy the normal computing function.