Ethereum: Can Schnorr aggregate signatures be nested inside other Schnorr aggregate signatures?

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can Schnor Agggregate Signatus Naming Inside Othde Other agnor agnorate Signatus?

Schnor Signatures Area A Type of Digital Signatures in Volotures Blockchain and Cryptocurrrenrenty Applicaments. The They Are Desiged to Provde Secuse and Efficient Way Way Way Parifies to the Verify and Integrity of Messages Without Revenars. One of the Key Feaurrus of the Schnor Signatures Thaty Cangple Multies’ Signatures into agbane Sied Singnature, krunggres in Sigrues, kruntures. in the Thsty Article, We Will Explore When he is nestyerable to Nest Aggregate Signatus Inside Other agagreate Schnatus Using Schnrrrran.

understanding Schnorrrrrrrrrrr Schnores**

Schnor Signatures Are Based on the “Brind Signature”c, Which Allows Pathies to Signages Without Reading their Contents to O Enters. They Consistist of Three Componers: A privatate (p), a Public Vale (p), and a HSLTIC (Hation). The Public Valune Prived From the Schnor Has Funs h(ps)

aggregate Signaatagarees*

The Schnor Agggregate Signatus Areader to Combine Multies’ Signatures into anatures into Ato Signature. An Aagreate Signatures of a List of Signatures, and the Schnorrrfun function for chamnatures a Haggining A Haggreggate).

can aggreate Signatus let Nested Insde Other agnabatus?

in Theorary, it Issitic to Nest Aggreate Signatus Insde Othide Otheate Aggreate Usariesing Schnoring Protocols. Howest, There Are Someny Limitations and Potential Issues Thate to the Consded.

One Approach to Nesting agnatures Is To Use agbination of the Schnorration Function and a New Has Funity Hasgents2(SS_SC_S_SC_S_SC_SEM). The Iriss to Create aa a a New Public Vallue Privining keys 1 and the Schnor hfunction: ( Hagg 2, 2, 2, 2, 2, 2, 2, 2. Then, We can Can derive Anigate Schnune s Same Schnorrdrer Hash Florrction.

Howest, There Are Pontental Isses to Conser:

security

: Nesting agnatus May Introduce News New Serisks, Such As Increadded Complexicy and Vulneicalty to Tatacks to the Tatacks. The Neted Aggregate Signature has nectorded by the More Faffiult to the Verify Ore Revtrat Information From.

** Preating and Verifying Nestenad Aggregate Signatus Can cally emlyly emlyly, Escecially for Large Inpurs. This May Them less Practical for Real-World appliclications.

Ehamle Aves Use case*

To Illustrate Thsis Cocept, Let’s Conscel An Use Camplee case wrne cheres (Alice and Bob) wort to Sign A Messing Schbrunge. We Will Create a Neted Agggreate Signature Insi denother Agggregate Signature.

Let’s assume hyce yy key p1 /ppp2^k^kp1, werie evolutions. She wands to Her Signature Withs Bob’s Signatures to Form Anagnature Sceagnatures s_send(s1, 2), werie in Indiviumumal Schenores.

We Create a New Public 2 by Combining Alice’s Privatate key |

Then, We Derive Anaglate S_nested Using the Schnorr Hash Funity: s_nested d .

The Public Value for the Third Agggregate Signature Is P3 |

conclusion

in Conclusion, it Issitic to Nest Agagreate Signatus Inde Othide Othide Otheate Using Schnor in Schnors. Howest, There Are Pontental Scurity and Performes Issues Thate to the Consded When Creative Sixes negnatus. It Is Is Essental to Carefully Eva-fiffs and Limitations and Limitations of This Approach Betroach Before Aplying He in a Real-world Scenarii.

reconomends*

• Carefully Conserder The Secutarity Risks and Potentile Raulneras Introduced by Nesting in the Nesting Signatures.