On Threshold Signatures from MPC-in-the-Head

We initiate the study of (n out of n) threshold signatures built from MPC-in-the-Head signatures. While recent impossibility results (Doerner, Kondi and Rosenbloom, CRYPTO'24) show that any such construction must have a signature size that grows with the number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> </mml:math> of users (or else require a prohibitive non-black-box use of cryptography), we outline a general strategy to confine the dependency in the number of users to a term of the form <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>λ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mi>O</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> , where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>λ</mml:mi> </mml:mrow> </mml:math> is a security parameter and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> a constant that depends on the signature scheme. We provide a concrete instantiation of our strategy by building a threshold signature on top of the scheme of (Carozza, Couteau, and Joux, EUROCRYPT'23).