This paper introduces the Unicity Execution Layer, a modular component of the Unicity framework enabling secure off-chain transactions while maintaining trustless double-spending prevention. We present a formal security model where token ownership is represented by public keys and transfers require digital signatures. We prove three fundamental security properties: (1) no double-spending--each token state can be spent at most once, (2) no blocking--only the legitimate owner can prevent a token from being spent, and (3) service-side privacy--the Unicity Service cannot link transactions with the same token. The user-side privacy is addressed by introducing generalized multi-public-key signature schemes that allow one secret to generate multiple unlinkable public keys, and interactive and non-interactive concrete instantiations, enabling private transactions with stable public identity with minimal key management overhead.

翻译：本文介绍了统一性执行层，该层是统一性框架的一个模块化组件，能够在保持无信任双重支付预防的同时，实现安全的链下交易。我们提出了一种形式化安全模型，其中代币所有权由公钥表示，转移需要数字签名。我们证明了三个基本安全属性：（1）无双重支付——每个代币状态最多只能被花费一次；（2）无阻塞——只有合法所有者才能阻止代币被花费；（3）服务端隐私——统一性服务无法将同一代币的多个交易关联起来。用户端隐私通过引入广义多公钥签名方案来解决，该方案允许一个秘密生成多个不可关联的公钥，并提供了交互式与非交互式的具体实例实现，从而在最小化密钥管理开销的同时，实现具有稳定公开身份的隐私交易。