The Answer to the Previous Post's Question...

[syncategorematic]

...is no.

If I understood my notes and textbook correctly.

Do you really want to know why?

Comments

[snowfox090.livejournal.com]

I wanna know why!

[indicolite.livejournal.com]

Alright, darling - you asked for it!

Why does the elliptic curve y^2 = x^3 + 10x +5 not define a group over Z_17?

By Equation 10-2 in Stallings Cryptography and Network Security Principles and Practices 4th ed.:

It can be shown that a group is defined based on the set E(a,b)= {x,y | y^2 = x^3 + ax + b} if the following condition is met:

4a^3 + 27b^2 != 0 (in the finite field being Z modulo p, p a prime)

Now, 4(10^3) + 27(5^2) = 4675
= 275(17)
=- 0 mod 17

Therefore E(10,5) does NOT define a group over Z_17. QED

This is actually way neater than in my homework, and my homework does not have references either. But unlike you, my professor knows what I am talking about, hopefully.