Introduced in cryptography for code-breaking purpose, the Weil and Tate pairings are at the heart of an ever increasing number of protocols since the work of the researcher who first discovered their constructive properties. The interested reader should refer to the survey by the researchers for further details. According to, when dealing with general curves providing common levels of security, the Tate pairing seems to be more efficient than the Weil pairing. Let E be a super singular elliptic curve over Fpm, where p is a prime and m a positive integer, and let E (Fpm) denote the group of its points.