Say I generate the following private ECDSA key :
07b8fd762ccec1a071245c4b4798b6f78eac4cbe2cad227c325e01c6c9a1ef73
Is there anything wrong with creating derivatives by just adding 1? e.g.
07b8fd762ccec1a071245c4b4798b6f78eac4cbe2cad227c325e01c6c9a1ef74
07b8fd762ccec1a071245c4b4798b6f78eac4cbe2cad227c325e01c6c9a1ef75
07b8fd762ccec1a071245c4b4798b6f78eac4cbe2cad227c325e01c6c9a1ef76
07b8fd762ccec1a071245c4b4798b6f78eac4cbe2cad227c325e01c6c9a1ef77
07b8fd762ccec1a071245c4b4798b6f78eac4cbe2cad227c325e01c6c9a1ef78
07b8fd762ccec1a071245c4b4798b6f78eac4cbe2cad227c325e01c6c9a1ef79
07b8fd762ccec1a071245c4b4798b6f78eac4cbe2cad227c325e01c6c9a1ef7a
07b8fd762ccec1a071245c4b4798b6f78eac4cbe2cad227c325e01c6c9a1ef7b
etc.
Mathematically I can't think of any. Means if the seed is discovered, screwed - but isn't that always the case with deterministic ??
If there is a concept I am not understanding, where can I read more about it?
Thank you.