Private Functional Signatures: Definition and Construction

Paper in proceeding, 2018

In this paper, we introduce a new cryptographic primitive: private functional signatures, where functional signing keys skffor functions f derived from master signing key msk which can be used to sign any message, allow one to sign any message in the range of the underlying function f. Besides, there is an encryption algorithm which takes as input the master secret key msk to produce a ciphertext cxfor message x. And the signing algorithm applies a signing key skfon the ciphertext cxto produce a signature σf(x)on the result f(x). We also formalize the security notions of private functional signatures. Furthermore, we provide a general compiler from any (single-key) symmetric-key predicate encryption scheme into a single-key private functional signature scheme. By instantiating our construction with schemes for symmetric-key predicate encryption, we obtain private functional signature schemes based on a variety of assumptions (including the LWE assumption, simple multilinear-maps assumptions, obfuscation assumptions, and even the existence of any one-way function) offering various trade-offs between security and efficiency.