**Linear Feedback Shift Register (LFSR)** $ k_{m+i}=\sum_{j=0}^{m-1}c_jk_{j+i}\operatorname{mod}2$ can be used to generate a binary keystream where $ i\ge1\:,\:(c_0,c_1,...,c_{m-1})$ are constant bits, and $ (k_1,k_2,...,k_m)$ are the initial bits **Bit Stream**  `p = plaintext, k = key, c = ciphertext` *Consequently:* $ \begin{aligned}\mathrm{p\oplus k=c,c\oplus k=p}\\\\\mathrm{p=(p\oplus k)\oplus k}\end{aligned}$ **Simple Stream Cipher** - Set up a known pattern (sequence) of 1's and 0's as a key - Aply the key to the plaintext bit stream using an XOR function - Recover the plaintext using the same key pattern on the ciphertext bit stream  **Pseudorandom Number Generators** - A (*pseudo-*) *random number generator* (**PRNG**) is an algorithm which produces a long stream of seemingly random numbers in a prescribed range, from a specified initial state, the seed. - A short sequence of key bits would be easy to remember but not very secure - A long sequence of key bits would be secure but hard to remember - Construct a LFSR to solve this issue **Shift Register** - A shift register is a hardware device which - saves bits - shifts bits - For example, a 4-bit shift register looks like:  This is LSFR. It takes in some of the bits in the shift register, then combines them with an XOR, and feedbacks the result as the input  **Example**  **RC4** - RC4 was developed by Ron Rivet of MIT - Ron's Code 4 - RC4 generates a pseudorandom stream of bits (a keystream) which, for encryption, is combined with the plaintext using XOR; decryption is performed the same way.  - Uses an 8-bit keystream to encrypt each byte of plaintext - 3 loops with swaps, are able to produce a keystream with an estimated period of 10¹⁰⁰ - using n = 256, and some arbitrary length *"key"* would generate a valid 8-bit RC4 keystream