Schnorr-based multi-signature schemes support offline preprocessing of nonce commitments to reduce online signing to a single round. However, preprocessing is inherently bounded: each preprocessed nonce pair consumes signer-side storage, and once exhausted, an interactive commitment round is required to refill. This limitation is particularly severe for TPM~2.0 devices, where usable NVRAM is typically 6--16\,KB and connectivity is intermittent. This paper presents upTPM, a framework that achieves unbounded preprocessing with constant signer storage. Each TPM stores a single 32-byte secret seed from which an unlimited sequence of nonce commitments is deterministically derived. Commitments are published to an untrusted coordinator before use; nonce scalars never leave the TPM. We formalize three properties not provided by existing schemes: (1)~unbounded deterministic preprocessing with constant storage; (2)~asynchronous commitment refill, allowing any signer to unilaterally extend its commitment pool; and (3)~TPM-attested commitments, a hardware-backed authenticity and state-binding mechanism that strengthens resistance to host-software compromise. We prove EU-CMA security in the random oracle model under the discrete logarithm assumption and Pseudo Random Function (PRF) security, with a one-time-use invariant enforced by TPM hardware state. We extend the construction to $(t,n)$-threshold signatures and provide a detailed analysis of coordinator trust, crash recovery, and performance evaluations.

翻译：基于Schnorr的多重签名方案支持对随机数承诺进行离线预处理，从而将在线签名缩减为单轮交互。然而，预处理本质上是有界的：每个预处理的随机数对都会占用签名者的存储空间，一旦耗尽，就需要一轮交互式承诺来补充。这一限制对TPM 2.0设备尤为严重，因其可用NVRAM通常仅为6-16KB，且网络连接具有间歇性。本文提出upTPM框架，通过恒定签名者存储实现了无界预处理。每个TPM仅存储一个32字节的机密种子，由此可确定性衍生出无限序列的随机数承诺。承诺在使用前发布给不可信协调器，而随机数标量始终驻留在TPM内部。我们形式化了现有方案未提供的三个特性：(1) 恒定存储下的无界确定性预处理；(2) 异步承诺补充，允许任意签名者单方面扩展其承诺池；(3) TPM认证承诺——一种硬件支持的真实性与状态绑定机制，增强对主机软件妥协的抵抗能力。在随机预言机模型下，我们基于离散对数假设和伪随机函数(PRF)安全性证明了EU-CMA安全性，并通过TPM硬件状态强制执行一次性使用不变量。我们将该构造扩展至(t,n)门限签名，并对协调器信任、崩溃恢复及性能评估进行了详细分析。