Monthly Archives: October 2013

Pseudo-random sequences and finite fields

One way to symmetrically encrypt a message is to generate a sequence of bits of the same length as the message, and perform a bitwise exclusive-or between the message and the sequence. Then the recipent performs the same operation, and recovers the original message. (This is one way to construct a stream cipher.)

Clearly, the security level provided by such an encryption scheme depends entirely on the way in which the sequence was generated. If it is truly random, then we obtain a so-called one time-pad, which, as long as it is used only once, guarantees perfect secrecy. At the other extreme, if the sequence consists of only 0-bits, then the encryption process does nothing at all and an adversary can directly read the message.

Continue reading