# AES S-Box: How is value for 01 mapped to 7c?

If irreducible polynomial $m(x) = x^8+x^4+x^3+x+1$ is chosen, or even for any other value, the multiplicative inverse will not exist for $01$, as $0000 0001$ will perfectly divide $m(x) = 100011011$ leaving remainder zero.

So then how it the value for $01$ mapped to $7c$ in AES S-box?

• The inverse of $1$ is $1$ (in any ring). – yyyyyyy Mar 10 '18 at 8:09

$00000001$ is its own inverse in the Rijndael field, because polynomial multiplication by itself gets $00000001$ and is unchanged by the modulo operation. This will always be true in any ring, as noted in a comment above.