Modular exponentiation of large number

Question

I'm currently working with a large number for cryptography.

a = 3087646334 

p = 1606938044258990275541962092341162602522202993782792835301611

b = int((p-1)/2).

Euler's Criterion says that

a^b (mod p) = 1 or a^b (mod p) = p-1.

SAGE gives the correct answer and python gives wrong answer. Why is that?

The code is in below.

Sage

a = 3087646334 
p = 1606938044258990275541962092341162602522202993782792835301611
b = int((p-1)/2)

power_mod(a,b,p)

Python

a = 3087646334
p = 1606938044258990275541962092341162602522202993782792835301611
b = int((p-1)/2)

pow(a,b,p)

Please visit the [help], take the [tour] to see what and [ask]. Do some research, search for related topics on SO; if you get stuck, post a [mcve] of your attempt, noting input and expected output. [Post CODE, not PICTURES of code](https://meta.stackoverflow.com/questions/285551/why-not-upload-images-of-code-errors-when-asking-a-question) — mplungjan, Oct 08 '20 at 11:01

score 2 · Accepted Answer · answered Oct 08 '20 at 11:29

2

Because you're using float division, which is inaccurate. Use b = (p-1) // 2 instead.

answered Oct 08 '20 at 11:29

Kelly Bundy

1 Answers1