# Thread: Square root modulo a prime

1. ## Square root modulo a prime

Hello

I hope someone can help me with this.

I have the following equation -

y^2 mod 269 = x^3 + 3*x + 5 mod 269

Let's say x is 64.

So -

y^2 mod 269 = 64^3 + 3*64 + 5 mod 269
y^2 mod 269 = 262144 + 192 + 5 mod 269
y^2 mod 269 = 262341 mod 269
y^2 mod 269 = 66

Now, I happen to know off hand that y is 55, but if I didn't know this, how would I calculate y?

I've been told it's as simple as "square root modulo a prime", but I cannot figure out how to do this.

Can someone please explain this to me in simple steps?

Any help appreciated.

Thanks!

2. Hi,