信息论教学中的若干问题补遗

Supplements to Several Issues in Information Theory Teaching

信息论是基于信息熵概念对信源编码、信道编码和密码学进行理论分析的学科.对一次一密的对称密码系统的完善性也多采用概率机制阐明,且对非对称密码系统的安全性则以单向函数为凭据,这些都没有使用信息熵概念来作理论分析.采用信息熵对算术编码的熵最优收敛性、一次一密的完善性和非对称密码系统的安全性进行论证或分析.

Information theory is a discipline that theoretically analyzes source coding,channel coding,and cryptography based on the concept of information entropy.In the classical literature,the asymptotic entropy optimality proofs of arithmetic coding are mostly heuristics,lacking the rigor of mathematical proofs.The perfection of one-time one-dense symmetric cryptosystems is also clarified with probability mechanisms,and for asymmetric cryptosystems Security is based on a one-way function,which does not use the concept of information entropy for theoretical analysis.This paper uses information entropy to demonstrate or analyze the optimal convergence of arithmetic coding,the completeness of one-time density,and the security of asymmetric cryptosystems.