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