I have a problem with the smallest value of d.
In the whole assignment, there is only one modulus N (6A163), and, except for
the examples on the last page, only two e's, e1 (1E437) and e2 (35A47).
From this information and the factorization of N, I get both (two) d's, d1 and d2.
I am able to verify that both CT's are indeed 57A27, and both PT's are OK.
Since there are only 2 d's, I can easily find the smallest.
I used that value throughout the rest of the assignment and found the PT.
Part 1 explicitely asks to find the smallest value of d, using only N, e1 and e2.
Unless I am mistaken, there is only one value of d corresponding to a given e,
so I only have the 2 values of d.
If I use the process described in the example with the above N, e1/e2, I get:
C = M^e1 mod N, where i = 0:e1-1 (CT's of all possible PT's encrypted with e1)
C = M^e2 mod N, where i = 0:e2-1 (CT's of all possible PT's encrypted with e2)
But the pair N, e1 would only yield to d1 (single value), and N, e2 to d2,
so again only two d's.
Assuming other e values and using the procedure above, I find the corresponding
d values (from the modular inverse), then encode all messages.
In this case,
C[j] = M^e[j] mod N, where i = 0:e[j]-1 and e[j] = 3:lcm(p−1, q−1)-1:2 (all odd values up to the lcm)
Don't know if this makes any sense; I am basing the range for e[j] on the following:
λ(n) = lcm(p−1, q−1), where λ is Carmichael's totient function (the PDF uses lcd?).
e exponents must be chosen such that 1 < e < λ(n) and gcd(e, λ(n)) = 1; i.e., e and λ(n) are coprime.
I take the above into account in my program and find the smallest d in the range 1 < e < λ(n).
I am entering the hex value and the PT (4 parts), all in capital letters and no blanks.
I also tried a few upper values of e, but none of the answers for the smallest d are correct.
Where do I go wrong?
It's probably trivial, but I just don't get it from the wording in the PDF.
Any nudge is appreciated!