Blinding to mask private key operations
1) Blinding has been used, for example, to design a version of El Gamal encryption that is resilient to certain side-channel attacks --- see [PK] and the references therein. 

2) The goal of the field of leakage-resilient cryptography is to model and study (from a theoretical perspective) what security can be guaranteed against side-channel attacks (including e.g., timing attacks). See this recent survey or this excellent blog post for more details on the type of models that are being considered.

[PK]: Pietrzak and Kiltz. Leakage Resilient ElGamal Encryption