A homomorphic signature scheme (also malleable signature scheme) is a digital signature scheme that allows computations on signed data (without access to the secret signing key) while preserving the authenticity of the data.

A homomorphic signature scheme (also malleable signature scheme) is a digital signature scheme that allows computations on signed data (without access to the secret signing key) while preserving the authenticity of the data.

A simple example of a homomorphic signature scheme is the textbook RSA signature scheme, where given two signatures $\sigma_1=m_1^d \pmod N$ and $\sigma_2=m_2^d \pmod N$ under private key $d$ anyone without having access to the signing key $d$ can obtain $\sigma=\sigma_1\cdot\sigma_2 \pmod N$, which represents a valid signature for message $m_1\cdot m_2 \pmod N$. This is a very simple example of an insecure multiplicatively homomorphic signature scheme and there are various types supporting various homomorphic operations today, e.g., redactable (quotable) signatures, linearly homomorphic signatures, which fall under the more general framework of P-homomorphic signatures.