Question

Suppose an LFSR of degree 5 is used as a stream cipher and the following plaintext
m and ciphertext c is known:

m = 00100 11000, c = 10110 01110.

Compute the feedback polynomial, the characteristic polynomial, the period and
the complete keystream.

Answer 1

Stream Cipher

• A stream cipher is a symmetric key cipher where plain text digits are combined with a pseudorandom cipher digit stream(keystream).
• In stream cipher, each plaintext digit is encrypted one at a time with the corresponding digit of keystram to give a digit of cipher text stream.
• stream cipher encrypt one bit at a time.
• Encryption : ciphertext = plaintext XOR keystream
• Decryption : plaintext = ciphertext XOR keystream

Linear Feedback Shift Register (LFSR):

• A LFSR is a shift register whose input bit is a linear function of its previous state.
• The most commonly used linear function of single bits is exclusive-or(XOR).
• LFSR based stream ciphers are popular because of their low hardware implementation cost.
• LFSR is popularly known as Pseudo random number generator. The random numbers repeat itself after 2^n-1 clock cycle ( where n is the number of bits in LFSR)
• A standard ploynomial function : x^8+x^7+x^6+x^4+x^2+1 is used to generate random numbers.
• 8 bit Linear feedback shift register uses 8 D- Flipflops and xor gate and LFSR uses asynchronous reset.

Feedback Polynomial and Characteristic polynomial:

• the ouput sequence of an LFSR is Uniquely determined by its feedback coefficients and its initial state.
• The feedback coefficients c1,c2,...........cL of an LFSR of length L are usually represented by the lfsr feedback polynomial ( connection polynomial) defined by P(X) = 1 - ciXi.