Deriving a signature without the signer

Adam54

7/13/24, 3:46 PM

Say we have an element $g=H(m)$ in a group (this element may or may not be a generator of the group).

Are there signature schemes that enable to sign this element, and then to be able to derive a signature of $g^a$ for a chosen $a$ without the presence of the signer?

Thank you for your help.

1 + 0

homomorphic-signatures

Score:1

Crypto

poncho

7/13/24, 4:00 PM

Are there signature schemes that enable to sign this element, and then to be able to derive a signature of $g^a$ for a chosen $a$ without the presence of the signer?

If you mean "without access to the private key", and you prohibit $a \equiv 1 \pmod q$ (where $q$ is the group order), no, there's not such standard signature mechanism.

For a signature system, we expect that the attacker (without access to the private key) who can get a number of values signed (for example, $g$) is still unable to generate a valid signature for any other message (including $g^a$).

+ 3

Mark

7/13/24, 4:53 PM

It's worth mentioning that a common way to stop someone with a signature of $m$ from creating a signature of $f(m)$ is by signing hashes $H(m)$ rather than messages $m$ directly. A scheme may support signing $g = H(m)$, and support creating valid signatures of $g^a := H(m)^a$ while still being secure, as it would be unclear how to find $m'$ such that $H(m') = H(m)^a$, which would be required for a break.

Adam54

7/13/24, 5:45 PM

@Mark Thank you for the remark. I have added the precision about $g=H(m)$.

Adam54

7/13/24, 5:46 PM

@poncho Yes I understand your remark. Thank you for your answer.

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EN: Deriving a signature without the signer

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