Internet Infrastructure Security

In summary, the Affine Cipher uses an encryption function that cannot use all values in {0, 1, · · · , 25} for a, such as in the case of a = 10. The Chinese Remainder Theorem (CRT) can be used to reduce the computational complexity of RSA by breaking a number from a large modulus into smaller moduli. For RSA with p = 7 and q = 11, e = 5 and 7 are legitimate values and the corresponding d is 7. The steps for generating the public and private keys for RSA include selecting primes, computing phi and e, and finding d such that ed ≡ 1 (mod phi).
  • #1
anthonyhk7
2
0
urgent 《Internet Infrastructure Security》

1. (Affine Cipher) Recall that the encryption function for the Affine Cipher is EK(m) = (a ×
m + b) mod 26. Moreover, not all values in {0, 1, · · · , 25} can be used for a. To illustrate
it, consider a = b = c = 10. Explain why a = 10 cannot be used. (Note: do not use
multiplicative inverse for the explanation).

2. (The Chinese Remainder Theorem, CRT) The CRT is very useful for reducing the computational complexity of RSA by decomposing a number from a large modulus into several
numbers coming from smaller moduli (a plural of modulus). For example, given a number
3000 from Z5797 (5797 = 11 × 17 × 31), decompose it into numbers from smaller moduli.

3. (RSA) Consider RSA with p = 7 and q = 11. Are 5 and 7 legitimate values for e and why?
If any of the two values is legitimate, find the corresponding d.

thanks for help!:frown:
i need the steps for my revision! Really Thanks all!
 
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  • #2


OK, what have you tried?
 
  • #3


i have try my best to read the notes and google,
but until some steps don't know how to process the following parts
such as step 4...

1. Select primes p=11, q=3.
2. n = pq = 11.3 = 33
phi = (p-1)(q-1) = 10.2 = 20
3. Choose e=3
Check gcd(e, p-1) = gcd(3, 10) = 1 (i.e. 3 and 10 have no common factors except 1),
and check gcd(e, q-1) = gcd(3, 2) = 1
therefore gcd(e, phi) = gcd(e, (p-1)(q-1)) = gcd(3, 20) = 1
4. Compute d such that ed ≡ 1 (mod phi)
i.e. compute d = e-1 mod phi = 3-1 mod 20
i.e. find a value for d such that phi divides (ed-1)
i.e. find d such that 20 divides 3d-1.
Simple testing (d = 1, 2, ...) gives d = 7
Check: ed-1 = 3.7 - 1 = 20, which is divisible by phi.
5. Public key = (n, e) = (33, 3)
Private key = (n, d) = (33, 7).
 

FAQ: Internet Infrastructure Security

What is internet infrastructure security?

Internet infrastructure security refers to the measures and protocols put in place to protect the network and systems that make up the internet, such as servers, routers, and other hardware and software components.

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