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7. It is well known that banking transaction require authentication. Every authentication requires some computations. Suppose it is observed that for these computations, the required time grows as the square of the size of the number Currently, the 32 bit computations take 5 ms time for authentication. The computers are expected to authenticate in no more than 100 ms. What is the largest sized numbers that can be processed to support strong authentication? 8. Some prime numbers appear with a difference of 2. For instance (5, 7) and (11, 13) are such pairs. Find a smallest such pair which is greater than 150 9. In cryptography RSA requires computation of the form a raised to the power of b modulo m. Suppose we have an integer 5. What is the value of 5 raised to the power of 238 modulo 31 (Hint: 5 raised to the power is 1 modulo 31) Show transcribed image text
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