Final answer:
Encrypting a bitstream with recurrence and an initial condition employs an algorithm like a linear feedback shift register to generate a key stream.
The initial state and a recurrence relation are used to produce new bits through operations like XOR, which, when combined with the original bitstream, results in encryption.
The same key stream can be regenerated for decryption using the same initial condition and recurrence relation.
Step-by-step explanation:
Encrypting a sequence of bits or a bitstream using recurrence and an initial condition involves using an algorithm where each bit is encrypted based on the previous bit(s). A simple example could be a linear feedback shift register (LFSR), often used for stream ciphers in cryptography.
To encrypt a bitstream using LFSR, you start with an initial state (the initial condition) and apply a linear recurrence relation to generate subsequent states (bits).
An example of an LFSR recurrence relation might be to take the XOR (exclusive or) operation of the last two bits of the current state. Suppose your initial condition (seed) is 1101, and the recurrence relation is the XOR of the last two bits, your LFSR would output a stream of bits used as a key to encrypt the original bitstream.
If the original bitstream is 101001, you use the XOR operation between the original bitstream and the generated key stream to create the encrypted bitstream.
To decrypt the bitstream, the receiver must know the initial condition and the recurrence relation used in the LFSR. They can then regenerate the same key stream and apply the XOR operation with the encrypted bitstream to retrieve the original bitstream.