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and okay so let me start by telling you what what structured preservation is about so if we think about public key cryptography then quite often we use mathematical structures or some form so for instance a prime order cyclic group right and if you multiply two elements it corresponds to adding together exponent the discrete logarithms of these elements and this is a very useful mathematical structure we can build health gamal encryption Peterson and commitment tional approves and so forth based on this mathematical structure and also these components fit together like an a puzzle right i mean you can use el-gamal encryption you can do snore proves about what you have encrypted and so forth repairing base cryptography we have a bit of more structure right because now we have to source groups and a target group and we have bilinear map appearing that maps to source groups elements into the target group okay so in some sense we have the usual group operations we can multiply group eleme
