# Since it gives negative power, how is rcon(0) calculated in AES?

I'm trying to calculate Rijndael key schedule "Rcon" values manually. I know how to calculate each value with the equation rcon(i) = x^(i-1) mod x^8 + x^4 + x^3 + x^1 + 1, for example:

recon(10) = x^(10-1) mod x^8 + x^4 + x^3 + x^1 + 1
x^(9) mod (x^8 + x^4 + x^3 + x^1 + 1)
=> x^5 + x^4 + x^2 + x
=> 0011 0110
=> 0x36 (10th number in RCON Table)


But if i equals to 0 then

rcon(0) = x^(-1) mod x^8 + x^4 + x^3 + x^1 + 1


According to "Wikipedia: Rijndael key schedule ~ Rcon", the first value in Rcon table is 0x8d, which most probably is the value for rcon[0]. I would like to know how it is calculated.

I know how to calculate the mod on paper and this is exactly how I calculated the 0x36 above. But since the power of x is -1 in this case, I am stuck with it. How is rcon[0] calculated in AES?

-

It is essentially caulcated by division of 0x01 within the finite field.