The　idea　behind　Lempel-Ziv　(LZ)　data　compression　algorithm　and　Yacobi　fast　exponentiation　algorithm　is　investigated.　Also　based　on　the　fulfillment　of　the　fast　cascade　exponentiation　algorithm,　a　novel　method　is　proposed　to　obtain　rational　tradeoff　between　memory　size　and　fast　computing　speed　by　modifying　the　process　of　creating　compression　tree　in　Yacobi　algorithm.　The　analysis　shows　that　this　new　algorithm　is　suitable　for　fast　computation　in　embedded　encryption　systems.