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# CSS is introduced in 1996- It is a 40 bit stream cipher that uses 2 li.docx

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# CSS is introduced in 1996- It is a 40 bit stream cipher that uses 2 li.docx

CSS is introduced in 1996. It is a 40 bit stream cipher that uses 2 linear feedback shift registers (LFSRs) of 17-bit and 25-bit and denoted by R 1 and R 2. The feedback polynomials for R 1 and R 2 are respectively:
C 1 (x) = x 17 + x 2 +1 and C 2 (x) =x 25 + x 21 + x 20 + x 10 + 1
The LFSRs are initialized with the 40-bit key. One bit of each LFSR is set to 1 to prevent the 0 state which generate only 0 keystream. A byte of the keystream is generated by 8 shifts of both registers and the use of an 8-bit adder with carry.
Encryption and decryption are done by bit-xor input bytes with keystream bytes. Write an application implement CSS with given specifications to do both encrypt and decrypt of any binary file.
Write a report to document your CSS application. Also, discuss the possible attacks on this cryptosystem
Solution
Ans;
FOLLOW THIS ou have two vectors r(t) .- Each one defines a space curve , r1 = (t , (1-t) ,(3+t^2) ) r2 = ( (3-s), (s-2), s^2 ) they intercept when r1=r2 , ie , t= 3-s (1-t) = s-2 3+t^2 = s^2 s+t= 3 s+t= 3 ( coupled) t= 3-s 3+(3-s)^2 =s^2 3+9-6s+s^2 =s^2 6s= 12 s=2 t=1 plug in r1 Point is P(1,0,4) The angle , dr1/dt = (1,-1, 2t) at t=1 dr1/dt = (1,-1,2) = U dr2/ds = (-1,1,2s ) at s= 2 dr2/ds = (-1,1,4) = V U dot V = IUI IVI cos T (-1 -1+8) = (2)(sqrt18) cos T = 6 sqrt 2 cos T cos T = 1/sqrt2 = (1/2) sqrt2 T= pi/4
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CSS is introduced in 1996. It is a 40 bit stream cipher that uses 2 linear feedback shift registers (LFSRs) of 17-bit and 25-bit and denoted by R 1 and R 2. The feedback polynomials for R 1 and R 2 are respectively:
C 1 (x) = x 17 + x 2 +1 and C 2 (x) =x 25 + x 21 + x 20 + x 10 + 1
The LFSRs are initialized with the 40-bit key. One bit of each LFSR is set to 1 to prevent the 0 state which generate only 0 keystream. A byte of the keystream is generated by 8 shifts of both registers and the use of an 8-bit adder with carry.
Encryption and decryption are done by bit-xor input bytes with keystream bytes. Write an application implement CSS with given specifications to do both encrypt and decrypt of any binary file.
Write a report to document your CSS application. Also, discuss the possible attacks on this cryptosystem
Solution
Ans;
FOLLOW THIS ou have two vectors r(t) .- Each one defines a space curve , r1 = (t , (1-t) ,(3+t^2) ) r2 = ( (3-s), (s-2), s^2 ) they intercept when r1=r2 , ie , t= 3-s (1-t) = s-2 3+t^2 = s^2 s+t= 3 s+t= 3 ( coupled) t= 3-s 3+(3-s)^2 =s^2 3+9-6s+s^2 =s^2 6s= 12 s=2 t=1 plug in r1 Point is P(1,0,4) The angle , dr1/dt = (1,-1, 2t) at t=1 dr1/dt = (1,-1,2) = U dr2/ds = (-1,1,2s ) at s= 2 dr2/ds = (-1,1,4) = V U dot V = IUI IVI cos T (-1 -1+8) = (2)(sqrt18) cos T = 6 sqrt 2 cos T cos T = 1/sqrt2 = (1/2) sqrt2 T= pi/4
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### CSS is introduced in 1996- It is a 40 bit stream cipher that uses 2 li.docx

1. 1. CSS is introduced in 1996. It is a 40 bit stream cipher that uses 2 linear feedback shift registers (LFSRs) of 17-bit and 25-bit and denoted by R 1 and R 2. The feedback polynomials for R 1 and R 2 are respectively: C 1 (x) = x 17 + x 2 +1 and C 2 (x) =x 25 + x 21 + x 20 + x 10 + 1 The LFSRs are initialized with the 40-bit key. One bit of each LFSR is set to 1 to prevent the 0 state which generate only 0 keystream. A byte of the keystream is generated by 8 shifts of both registers and the use of an 8-bit adder with carry. Encryption and decryption are done by bit-xor input bytes with keystream bytes. Write an application implement CSS with given specifications to do both encrypt and decrypt of any binary file. Write a report to document your CSS application. Also, discuss the possible attacks on this cryptosystem Solution Ans; FOLLOW THIS ou have two vectors r(t) .- Each one defines a space curve , r1 = (t , (1-t) ,(3+t^2) ) r2 = ( (3-s), (s-2), s^2 ) they intercept when r1=r2 , ie , t= 3-s (1-t) = s-2 3+t^2 = s^2 s+t= 3 s+t= 3 ( coupled) t= 3-s 3+(3-s)^2 =s^2 3+9-6s+s^2 =s^2 6s= 12 s=2 t=1 plug in r1 Point is P(1,0,4) The angle , dr1/dt = (1,-1, 2t) at t=1 dr1/dt = (1,-1,2) = U dr2/ds = (-1,1,2s ) at s= 2 dr2/ds = (-1,1,4) = V U dot V = IUI IVI cos T (-1 -1+8) = (2)(sqrt18) cos T = 6 sqrt 2 cos T cos T = 1/sqrt2 = (1/2) sqrt2 T= pi/4