Question

polynomial bo bit + b2 t2 +b3 t3 a) A binary string bobib2b3 is converted to a and is then coded by multiplying by the polynomial1+t2+t3. The resulting polynomial is then converted back to a binary string of length seven then transmitted. This string is received as 1011010, with bit order being lower powers to the left. Assume that at most one of these seven been corrupted in the transmission process (Ensure that you have determined the correct order of bits in any correspond- ing polynomial calculations that you perform.) 7. [15 Marks] (7) and (7) bits has (i Show that indeed an error has occurred in one of the bits. (ii) What was the correct transmitted string? (iii) Correct the error and recover the original message bobib2b3 b) In an RSA Public Key system, Eve's modulus is 707137, which is the product of two primes; her encoding key is 13. Bob wants to send Eve a message, represented by the number 11. (i) What is the encoded message that Bob actually sends to Eve? (ii) Eve's decoding key is 379861. Use this information to determine the two primes p and q such that px q = 707137.

Answer 1

AS FOR GIVEN DATA..

A binary string bobibzb3 is converted to a polynomial b3 t3 + b2 t2 +b1t + bo and is then coded by multiplying by the polynomial t3 + t2 +1. The resulting polynomial is then converted back to a binary string of length seven (7) and then transmitted This string is received as 1100011, with bit order being higher powers of t to the left. Assume that al most one of these seven (7) bits has been corrupted in the transmission process. (Ensure that you have appreciated the correct order of bits in any corresponding polynomial calculations that you perform.

EXPLANATION ::-

(i) Show that indeed an error has occurred in one of the bits

SOL::-

A binary string is converted to polynomial b₀ + b₁t+ b₂t³ . So the operation here are in modulo 2.

1) Let the original string was b₁ b₂ b₃ are assume that no error was done during transmission.

=

Hence the output will be

0 1 0 1 0

      

   

As there is almost one error happend ,error surves happend

(ii What was the correct transmitted string?

SOL::-

Put then  

all other equations takes right position so, that string output is 0 1 0 1 1 1 0.

(iii) Correct the error and recover the original message bob1b2b3.

SOL::-

Original message is 0110.