Shrinking generator explained

In cryptography, the shrinking generator is a form of pseudorandom number generator intended to be used in a stream cipher. It was published in Crypto 1993 by Don Coppersmith, Hugo Krawczyk and Yishay Mansour.[1]

The shrinking generator uses two linear-feedback shift registers. One, called the sequence, generates output bits, while the other, called the sequence, controls their output. Both and are clocked; if the bit is 1, then the bit is output; if the bit is 0, the bit is discarded, nothing is output, and the registers are clocked again. This has the disadvantage that the generator's output rate varies irregularly, and in a way that hints at the state of S; this problem can be overcome by buffering the output. The random sequence generated by LFSR can not guarantee the unpredictability in secure system and various methods have been proposed to improve its randomness [2]

Despite this simplicity, there are currently no known attacks better than exhaustive search when the feedback polynomials are secret. If the feedback polynomials are known, however, the best known attack requires less than • bits of output.[3]

A variant is the self-shrinking generator.

An implementation in Python

This example uses two Galois LFRSs to produce the output pseudorandom bitstream. The Python code can be used to encrypt and decrypt a file or any bytestream.

  1. !/usr/bin/env python3

import sys

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class GLFSR: """Galois linear-feedback shift register."""

def __init__(self, polynom, initial_value): print "Using polynom 0x%X, initial value: 0x%X." % (polynom, initial_value)

self.polynom = polynom | 1 self.data = initial_value tmp = polynom self.mask = 1

while tmp != 0: if tmp & self.mask != 0: tmp ^= self.mask

if tmp

0: break

self.mask <<= 1

def next_state(self): self.data <<= 1

retval = 0

if self.data & self.mask != 0: retval = 1 self.data ^= self.polynom

return retval

class SPRNG: def __init__(self, polynom_d, init_value_d, polynom_c, init_value_c): print "GLFSR D0: ", self.glfsr_d = GLFSR(polynom_d, init_value_d) print "GLFSR C0: ", self.glfsr_c = GLFSR(polynom_c, init_value_c)

def next_byte(self): byte = 0 bitpos = 7

while True: bit_d = self.glfsr_d.next_state bit_c = self.glfsr_c.next_state

if bit_c != 0: bit_r = bit_d byte |= bit_r << bitpos

bitpos -= 1

if bitpos < 0: break

return byte

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def main: prng = SPRNG(int(sys.argv[3], 16), int(sys.argv[4], 16), int(sys.argv[5], 16), int(sys.argv[6], 16),)

with open(sys.argv[1], "rb") as f, open(sys.argv[2], "wb") as g: while True: input_ch = f.read(1)

if input_ch

"": break

random_ch = prng.next_byte & 0xFF g.write(chr(ord(input_ch) ^ random_ch))

if __name__

See also

Notes and References

  1. D. Coppersmith, H. Krawczyk, and Y. Mansour, “The shrinking generator,” in CRYPTO ’93: Proceedings of the 13th annual international cryptology conference on Advances in cryptology, (New York, NY, USA), pp. 22–39, Springer-Verlag New York, Inc., 1994
  2. Poorghanad, A. et al. Generating High Quality Pseudo Random Number Using Evolutionary methods IEEE, DOI: 10.1109/CIS.2008.220.
  3. Caballero-Gil, P. et al. New Attack Strategy for the Shrinking Generator Journal of Research and Practice in Information Technology, Vol. 1, pages 331–335, Dec 2008.