S-box for byte substitution where the s-box values are multiplicative inverses of 257

The title basically says it. We have a 16 by 16 s-box, $$256$$ entries total. And the first value is the multiplicative inverse of $$257$$, so

$$1 \times k \bmod 257, \space k = 1$$.

$$2 \times k \bmod 257, \space k = 129$$.

$$3 \times k \bmod 257, \space k = 86$$

$$\ldots$$

Would this be secure? and if the value is higher then $$255$$, then we choose the lowest unused number.

• what about the entry of zero ? is it equal to zero? – hardyrama Apr 24 '20 at 10:09
• @hardyrama yes, would that be a problem? – Ömer Enes Özmen Apr 24 '20 at 11:02
• Fixed point . it will be good to calculate the DDT , LAT , BCT and compare it to AES sbox – hardyrama Apr 24 '20 at 11:55
• Okay, But is just the sbox I described above good? – Ömer Enes Özmen Apr 24 '20 at 12:03
• I personally see the question "is this a good sbox" to be similar to the question "is a hammer a good tool" - it rather depends on what you intend to use it for. A hammer is good if you have a nail; it is less good if you're trying to paint a wall (a paintbrush works rather better in that case) – poncho Apr 24 '20 at 15:29