Multi-precision multiplication over public key cryptography should be considered for performance enhancement due to its computational complexity. Particularly, embedded device is not suitable to execute high complex computation, public key cryptography, because of its limited computational power and capacity. To overcome this flaw, research on multi-precision multiplication with fast computation and small capacity is actively being conducted. In the paper, we explore the cutting-edge technology of multi-precision multiplication for efficient implementation of public key cryptography over sensor network. This survey report will be used for further research on implementation of public key cryptography over sensor network.