Public‐Key Cryptography and Key Management
Jie Wang, Zachary A. Kissel · 2015
This chapter first introduces the basic concepts of public-key cryptography (PKC). It then describes several concrete public-key cryptosystems, including Diffie-Hellman key exchange, Elgamal public-key cryptosystem, RSA public-key cryptosystem, and elliptic-curve PKC. These methods use several results in number theory. The chapter also discusses several common attacks on RSA that take advantage of inappropriately selected parameters. This will serve as a guideline for choosing correct RSA parameters. The security of elliptic-curve cryptography (ECC) rests on the difficulty of solving the elliptic-curve logarithm problem, which has not been studied as intensively as the discrete logarithm problem. However, the requirements of ECC parameters are not as rigid as those of RSA. Finally, the chapter discusses how to transmit secret keys using PKC without sharing prior secrets and how to manage keys. To use PKC to encrypt or authenticate data, one must first obtain the receivers' public keys.