The Mathematics of the RSA PublicKey （RSA PublicKey的数学）.pdf

The Mathematics of the RSA Public-Key Cryptosystem Burt Kaliski RSA Laboratories ABOUT THE AUTHOR: Dr Burt Kaliski is a computer scientist whose involvement with the security industry has been through the company that Ronald Rivest, Adi Shamir and Leonard Adleman started in 1982 to commercialize the RSA encryption algorithm that they had invented. At the time, Kaliski had just started his undergraduate degree at MIT. Professor Rivest was the advisor of his bachelor’s, master’s and doctoral theses, all of which were about cryptography. When Kaliski finished his graduate work, Rivest asked him to consider joining the company, then called RSA Data Security. In 1989, he became employed as the company’s first full-time scientist. He is currently chief scientist at RSA Laboratories and vice president of research for RSA Security. Introduction Number theory may be one of the “purest” branches of mathematics, but it has turned out to be one of the most useful when it comes to computer security. For instance, number theory helps to protect sensitive data such as credit card numbers when you shop online. This is the result of some remarkable mathematics research from the 1970s that is now being applied worldwide. Sensitive data exchanged between a user and a Web site needs to be encrypted to prevent it from being disclosed to or modified by unauthorized parties. The encryption must be done in such a way that decryption is only possible with knowledge of a secret decryption key. The decryption key should only be known by authorized parties. In traditional cryptography, such as was available prior to the 1970s, the encryption and decryption operations are performed with the same key. This means that the party encrypting the data and the party decrypting it need to share the same decryption key. Establishing a shared key between the parties is an interesti