RESUMEN
Linearly homomorphic signature (LHS) allows the acquisition of a new legal signature using the homomorphic operation of the original signatures. However, the public composability of LHS also prevents it from being used in some scenarios where the combiner needs to be designated. The LZZ22 scheme designates a combiner and preserves the signature structure by having the signer and the designated combiner share a secret. However, LZZ22 is not secure enough because the secret is constant. Here, we first prove that there is a polynomial time adversary that can crack the secret in LZZ22 through multiple signature queries. Then, we propose a new scheme, which realizes all the functions of LZZ22 and fixes the security problem by changing the secret with the message. The proposed scheme is shown to be secure against existential forgery on adaptively chosen subspace attacks under the random oracle model. Finally, we detail how to apply our scheme to the proxy signature and perform it on a personal computer, and the results show that our scheme is efficient.
