| Summary: | 博士 === 國立成功大學 === 電機工程學系碩博士班 === 93 === In the past, we made a signature by signing a name or affixing a seal on a document to establish the corresponding rights and duties. However since we are now in the age with Electronic Commerce and Electronic Government, the usage of digital signatures is very important. Learning how to use digital signatures is also significant. In addition, since the law of digital signature has been passed in October 31 2001, the security of digital signature schemes should not be ignored.
A completed digital signature scheme should achieve the functions of “Integrity”, “Identification” and “Non-repudiation.” In general, a digital signature scheme can be achieved by a public key cryptosystem or by a special algorithm. For different security assumptions, we can divide digital signature algorithms into two categories. One is a digital signature scheme based on the discrete logarithm problem. Under the assumption that the discrete logarithm problem cannot be broken, this kind of digital signature scheme is secure. In other words if the discrete logarithm problem can be broken, this kind of digital signature scheme will become insecure. The other is a digital signature based on the factoring problem. Similarly under the assumption that the factoring problem cannot be broken, this kind of digital signature scheme is secure. That is, if the factoring problem can be broken, this kind of digital signature scheme will also be broken.
The discrete logarithm problem and the factoring problem are two hard-solved mathematical problems, and the two problems are believed unsolved in a reasonable time-period in the world. However if any one of the two problems is solved in the future, the digital signature schemes based on this hard-problem assumption will become insecure. Hence if there is a digital signature algorithm of which the security is based on both the discrete logarithm problem and the factoring problem, the digital signature scheme will be still secure under the situation that any one of the two problems is solved. Therefore for the enhancement of system security, the adoption of the digital signature algorithm based on both assumptions is very important.
In the dissertation, we specially have some researches and discussions on the digital signature algorithms based on both the discrete logarithm problem and the factoring problem. We also propose another digital signature scheme. Firstly aiming at the digital signature algorithms based on the discrete logarithm problem and the ones based on the factoring problem, we introduce some well-known and representative digital signature systems. Next focus on the digital signature algorithms based on two-hard-problem assumption, we have a detailed review on them and on their cryptanalysis methods. We also summarize the attacking methods and discuss the insecure reasons. Finally, we propose a digital signature scheme based on two assumptions and also list its all generations. Of course, we also proof that the security of the proposed scheme is based on both the discrete logarithm problem and the factoring problem.
|
|---|
