This M.Sc. thesis is based on the following papers • Bernstein Daniel J, Hamburg Mike , Krasnova Anna , Lange Tanja , Elligator: elliptic-curve points indistinguishable from uniform random strings, Proceedings of the 2013 ACM SIGSAC conference on Computer communications security, pp.967-980 ACM (2013). • Tibouchi Mehdi , Elligator Squared: Uniform Points on elliptic curves of Prime Order as uniform random strings, In International Conference on Financial Cryptography and Data Security, pp.139-156, Springer (2014).