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# Puncturable signature

Puncturable digital signature schemes are a variant of digital signatures, which allow the signing key to be 'punctured'. Puncturing a signing key at a specific message ${\displaystyle m^{*}}$ allows the owner of the punctured signing key to produce signatures for all other messages except ${\displaystyle m^{*}}$. They were introduced by Mihir Bellare, Igors Stepanovs and Brent Waters at Eurocrypt 2016.[1]

Blockchain proof-of-stake consensus protocols are a possible application of these signature schemes.[2]

## References

1. "New Negative Results on Differing-Inputs Obfuscation". EUROCRYPT 2016: Advances in Cryptology.
2. Zhang, Zhenfeng; Wang, Yuchen; Fan, Xiong; Xu, Jing; Li, Xinyu (2019-09-09). "Puncturable Signatures and Applications in Proof-of-Stake Blockchain Protocol".

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