Finite field division

AARRRGH

Hello

I was wondering if anyone could help me with finite field division?

The example I am looking at is this -

Calculations in the field F23

(83) / 7 mod 23 // note: (83) is 8 cubed
= 512 / 7 mod 23
= 6 * 7-1 mod 23 // note: 7-1 is the inverse of 7
= 6 * 10 mod 23
= 14.

I can understand why 7 becomes the inverse of 7, as multiplying by the inverse is the same as dividing by the non-inverse, but why does 512 become 6??

Any help appreciated.

Thanks.

Renny Barrett

512 is congruent to 6 mod 23.

AARRRGH

Thank you for your answer!

Does this mean:

512 mod 23 = 6
6 mod 23 = 6

so both statements are equivalent?

In the above example, do I have to reduce 512 to 6?

Also, is there an easy way to find out if two numbers are congruent?

Thank you!

LeixlipRed

Two numbers (r,s) are congruent mod m if you they have the same remainder mod m. Or equivalently, r-s is congruent to 0(mod m). So in your example above. 512 minus 6 equals 506 which has remainder 0 when divided by 23. ie they're congruent

AARRRGH

Got it, thank you!