What are the problems related in using the "normal" ( bigger than N/2) value of the s number in transaction signature and why we use the lower one? Is it about the math behind the ecdsa?
Details are in BIP 146:
We require that the S value inside ECDSA signatures is at most the curve order divided by 2...
A high S value in signature could be trivially replaced by S' = 0xFFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141 - S.
Signatures encode two important values for verification
(r, S) is a valid signature, then so is
(r, -S), which is equivalent to
(r, curver_order -S).