Simulation setting parameters.

In the Internet of Things (IoT), there are often devices that are computationally too constrained to establish a security key using traditional key distribution mechanisms such as those based on the Diffie-Hellman key exchange. To address this, current solution commonly rely on key predistribution schemes (KPSs). Among KPSs, the Blom scheme provably provides the highest resilience against node capture attacks. This, however, comes at high computational overhead, because the Blom scheme requires many multiplications over a large finite field. To overcome this computational overhead, we present TurboBlom, a novel amendment of the Blom scheme. TurboBlom circumvents the need for field multiplications by utilizing specialized generator matrices, such as random zero-one matrices. We demonstrate that, through this approach, TurboBlom can significantly reduce the computational overhead of the Blom scheme by orders of magnitude. In our next key finding, we demonstrate that TurboBlom offers a level of resilience against node capture that is virtually on par with the Blom scheme. Notably, we prove that the gap between the resilience of the two schemes is exponentially small. These features of TurboBlom (i.e., low computational overhead and high resilience) make it suitable for computationally constrained devices. Such devices exist in abundance in IoT, for example, as part of Low Power and Lossy Networks (LLNs). To demonstrate a sample application of TurboBlom, we show how to use it to enable sender authentication in the Routing Protocol for LLNs (RPL), a standard routing protocol for IoT.在物联网（Internet of Things，IoT）场景中，常存在计算能力受限的设备，无法通过传统密钥分发机制（如基于迪菲-赫尔曼密钥交换的机制）建立安全密钥。为解决这一问题，当前主流方案通常依赖密钥预分发方案（key predistribution schemes，KPSs）。在各类KPS中，布隆姆方案（Blom scheme）被证明具备最高的节点捕获攻击抵御能力，但该方案需在大有限域上执行大量乘法运算，因此伴随极高的计算开销。为克服这一计算开销瓶颈，本文提出TurboBlom——一种针对布隆姆方案的新型改进方案。TurboBlom通过引入专用生成矩阵（如随机0-1矩阵），规避了有限域乘法运算的需求。经分析验证，该方案可将布隆姆方案的计算开销降低数个数量级。本研究的另一项关键发现为：TurboBlom的节点捕获抵御能力几乎与布隆姆方案持平，且经证明二者的抵御能力差距呈指数级微小。TurboBlom兼具低计算开销与高抵御能力的特性，使其适配计算能力受限的设备——这类设备在物联网场景中大量存在，例如低功耗有损网络（Low Power and Lossy Networks，LLNs）中的节点。为展示TurboBlom的典型应用场景，本文演示了如何将其应用于低功耗有损网络路由协议（Routing Protocol for LLNs，RPL，物联网标准路由协议）中，以实现发送方认证功能。