  This paper considers malleable digital signatures, for situations where data
is modified after it is signed. They can be used in applications where either
the data can be modified (collaborative work), or the data must be modified
(redactable and content extraction signatures) or we need to know which parts
of the data have been modified (data forensics). A \new{classical} digital
signature is valid for a message only if the signature is authentic and not
even one bit of the message has been modified. We propose a general framework
of modification tolerant signature schemes (MTSS), which can provide either
location only or both location and correction, for modifications in a signed
message divided into $n$ blocks. This general scheme uses a set of allowed
modifications that must be specified. We present an instantiation of MTSS with
a tolerance level of $d$, indicating modifications can appear in any set of up
to $d$ message blocks. This tolerance level $d$ is needed in practice for
parametrizing and controlling the growth of the signature size with respect to
the number $n$ of blocks; using combinatorial group testing (CGT) the signature
has size $O(d^2 \log n)$ which is close to the \new{best known} lower bound
\new{of $\Omega(\frac{d^2}{\log d} (\log n))$}. There has been work in this
very same direction using CGT by Goodrich et al. (ACNS 2005) and Idalino et al.
(IPL 2015). Our work differs from theirs in that in one scheme we extend these
ideas to include corrections of modification with provable security, and in
another variation of the scheme we go in the opposite direction and guarantee
privacy for redactable signatures, in this case preventing any leakage of
redacted information.
