E0 is a

stream cipher stream cipher is a symmetric key cipher where plaintext digits are combined with a pseudorandom cipher digit stream ( keystream). In a stream cipher, each plaintext digit is encrypted one at a time with the corresponding digit of the keystream ...

used in the

Bluetooth Bluetooth is a short-range wireless technology standard that is used for exchanging data between fixed and mobile devices over short distances and building personal area networks (PANs). In the most widely used mode, transmission power is limit ...

protocol. It generates a sequence of

pseudorandom A pseudorandom sequence of numbers is one that appears to be statistically random, despite having been produced by a completely deterministic and repeatable process. Background The generation of random numbers has many uses, such as for random ...

numbers and combines it with the data using the

XOR Exclusive or or exclusive disjunction is a logical operation that is true if and only if its arguments differ (one is true, the other is false). It is symbolized by the prefix operator J and by the infix operators XOR ( or ), EOR, EXOR, , , ...

operator. The

key length In cryptography, key size, key length, or key space refer to the number of bits in a key used by a cryptographic algorithm (such as a cipher). Key length defines the upper-bound on an algorithm's security (i.e. a logarithmic measure of the fastes ...

may vary, but is generally 128 bits.

Description

At each iteration, E0 generates a bit using four

shift register A shift register is a type of digital circuit using a cascade of flip-flops where the output of one flip-flop is connected to the input of the next. They share a single clock signal, which causes the data stored in the system to shift from one lo ...

s of differing lengths (25, 31, 33, 39 bits) and two internal states, each 2 bits long. At each clock tick, the registers are shifted and the two states are updated with the current state, the previous state and the values in the shift registers. Four bits are then extracted from the shift registers and added together. The algorithm XORs that sum with the value in the 2-bit register. The first bit of the result is output for the encoding. E0 is divided in three parts: # Payload key generation # Keystream generation # Encoding The setup of the initial state in Bluetooth uses the same structure as the random bit stream generator. We are thus dealing with two combined E0 algorithms. An initial 132-bit state is produced at the first stage using four inputs (the 128-bit key, the Bluetooth address on 48 bits and the 26-bit master counter). The output is then processed by a polynomial operation and the resulting key goes through the second stage, which generates the stream used for encoding. The key has a variable length, but is always a multiple of 2 (between 8 a