What are the implications of BLS signature verification without checking the elements are in the prime subgroup?

Jack Lloyd

8/31/24, 2:52 PM

Consider a BLS signature verification using BLS12-381 where signatures are in $G_1$ and public keys are in $G_2$. Verification is performed by checking that

$e(sig, G2) = e(H(m), pk)$

or equivalently (by taking advantage of the bilinearity property to avoid one of the final exponentiations) that

$e(sig, -G2) * e(H(m), pk)$ is the $G_t$ identity element.

If an implementation fails to check that $sig$ is within the prime order subgroup of $G_1$, what are the implications? This seems obviously a bad situation, but can it lead directly to signature forgery?

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forgery

bls-signature

Elon Musk

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EN: What are the implications of BLS signature verification without checking the elements are in the prime subgroup?

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