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A multi-level μTesla protocol was proposed to enable each sensor to authenticate messages broadcasted from the base station in a sensor network that has N sensors. This authentication is accomplished through symmetric keys, chained by a one-way hash function, where the first key is pre-installed in each sensor. A sensor using such a protocol to authenticate messages broadcasted from nearby sensors needs to pre-install the first keys of all nearby sensors. Unfortunately, sensors may be spread randomly over a surface and a sensor does not know which sensors will be nearby. Thus, each sensor is forced to pre-install the first keys of (N-1) sensors, where N (between thousands and millions) is large enough to explode sensor memory space. This paper proposes a new bootstrapping scheme where each sensor needs to pre-install only one key.