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Multi-precision multiplication and squaring are the performance-critical operations for the implementation of public-key cryptography, such as exponentiation in RSA, and scalar multiplication in elliptic curve cryptography (ECC). In this paper, we provide a survey on the multi-precision multiplication and squaring techniques, and make special focus on the comparison of their performance and memory footprint on sensor nodes using 8-bit processors. Different from the previous work, our advantages are in at least three aspects. Firstly, this survey includes the existing techniques for multi-precision multiplication and squaring on sensor nodes over prime fields. Secondly, we analyze and evaluate each method in a systematic and objective way. Thirdly, this survey also provides suggestions for selecting appropriate multiplication and squaring techniques for concrete implementation of public-key cryptography. At the end of this survey, we propose the research challenges on e?cient implementation of the multiplication and the squaring operations based on our observation.