Public-Key Ciphers

Abstract

But how is it possible that you can encrypt, but you cannot decrypt even with the help of the largest and most modern computers? The keyword we want to explore in this chapter is public-key ciphers, where you can make the key publicly known. RSA is based on the difficulty of decomposing large natural numbers into factors in a reasonable time, Diffie-Hellman and ElGamal use the problem that one cannot compute so-called discrete logarithms efficiently enough. Here we do not get into trouble with ECDH, but we do get onto elliptic curves. Since public-key ciphers need much more computing time than symmetric ciphers, they are usually only used for secret key exchange for e.g. Triple-DES or AES. Even with public-key ciphers, of course, there are constant efforts to crack the methods. Here, we learn Pollard’s methods for efficiently factorizing large natural numbers in many cases to attack RSA. We also try to use baby-step-giant-step and Pohlig-Hellman to solve the discrete logarithm in reasonable computation time. In the practical examples, we take a closer look at working securely on the Internet, wireless WLAN and the Bluetooth radio interface.