# Are there any signature algorithms with pseudorandom signatures?

As the title says. My reference point for the "pseudorandom ciphertext" concept is this paper by Möller, which introduces a public-key encryption algorithm with this property. I want to know the analogue for cryptographic signatures; forgive me if this is discoverable somehow via Google, since it is quite hard to get the search engine to understand that "pseudorandom signature" doesn't refer to the random value used in many signature algorithms.

• Every signature algorithm (and most cryptography on general) contains deterministic algorithms with some inputs, and sometimes when you want pseudorandomness you add a single use random value (IV, nonce). Standard ECDSA uses a secret random value unique per signature (repetitions breaks the security). EdDSA is deterministic and do not use such random inputs. There's no inherent need for pseudorandom signatures, it's just a simpler construct compared to the hashing method EdDSA uses. Jul 21 '19 at 13:09
• Depends a bit on what you mean by that. Maybe this is what you're looking for? ia.cr/2011/673 Jul 21 '19 at 15:31
• @Maeher That seems right. Another thing that appears to be what I'm thinking of, and for practical purposes seems to be the same, is "verifiable random functions". Jul 21 '19 at 19:45

A valid signature $$\sigma$$ satisfies the very special property that $$\textsf{Ver}(vk,m,\sigma)=1$$, whereas a random value $$\tilde \sigma$$ will surely not satisfy this property. So a signature simply cannot be indistinguishable from random if $$vk$$ and $$m$$ are known. And if you consider $$vk$$ or $$m$$ to be secret, then you are leaving the standard realm of signatures. The paper mentioned above by Maeher does exactly this.