Elliptic curve groups have been a popular choice in the implementation of traditional and post-quantum cryptographic schemes, including Diffie-Hellman type key-exchange protocols and digital signature algorithms. While some of these applications require to perform multidimensional scalar point multiplication (d-Mul), some of the others enjoy extra speed-ups from utilizing d-Mul with some precomputation or efficiently computable endomorphisms. When the underlying scalars in d-Mul are secret, it is crucial to follow a regular pattern of operations in the implementation because otherwise scalars may be recovered through side channel attacks. Therefore, it has been of great interest to design efficient and secure scalar multiplication algorithms. In this talk, I will give a survey of d-Mul algorithms with some recent theoretical and implementation results.

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