Implementing-cryptography-using-python

146 Chapter 5 ■ Stream Ciphers and Block Ciphers
In Chapter 4, you first learned about pseudorandomness. A linear-feedback
shift register (LFSR) is an algorithm for generating pseudorandom numbers.
The sequence of pseudorandom numbers generated by an LFSR can be used as
the one-time pad for an encryption algorithm. However, it has a major weakness:
the numbers generated are periodic, and an attacker can figure out the key
using a known plaintext attack. In the previous section, you used a PRNG to
make a stream cipher. The next level of complexity that you can utilize would
be something similar to the Trivium stream cipher, which uses a CSPRNG that
generates one bit at a time. It tries to make the LFSR idea more secure by having
multiple registers that interfere with each other. The intuitive notion is that
LFSRs yield to linear algebra, so let’s add just enough complexity to be nonlinear.
Figure 5.1 represents a schematic of a three-register Trivium implementation.
Cell 1
1
66 69
Cell 93
91 92 93
Cell 1
1
Cell 84
69 78 82 83 84
Output
Cell 1 Cell 111
1 66
87 109110111
Figure 5.1: Three-register representation of Trivium
When looking at Figure 5.1, you see it as three separate registers that each
produce their own output. The final output bit is the XOR of all three output bits.
The output of each register is also used to help form the input of another register.
For the initialization, to kick-start Trivium, it accepts two inputs: an 80-bit
key and an 80-bit IV. The 80-bit key is loaded into the leftmost 80 bits of the first
register. The 80-bit IV is loaded into the leftmost 80 bits of the second register.
Finally, the final 3 bits of the third register are set to 1 (the rightmost bits).
The stream is then run 4 × 288 times with the output discarded; this is now
the opening state.
Let’s do the first (tossed-out) run using an all 1 key and an all 1 IV, to show the
idea. Bits 1−80 are all 1, bits 94−173 are all 80, and bits 286−288 are all 1; everything
else is 0. The first output bit is an XOR of three different bits, so let’s look