Presents　the　definition　of　a　coprime　sequence　and　the　concept　of　the　lever　function,　elaborates　the　three　algorithms　of　the　REESSE1-E　public-key　signature　scheme　for　key　generation,　digital　signature　and　identity　verification,　proves　the　correctness　of　the　verification　algorithm,　and　illustrates　how　the　hardnesses　are　constructed　by　means　of　variable　combination.　The　paper　analyzes　the　security　of　the　REESSE1-E　against　inferring　a　private　key　from　a　public　key,　extracting　a　private　key　from　a　signature,　and　faking　a　signature　only　through　a　public　key,　through　known　signatures　with　a　public　key,　or　through　chosen　messages,　which　manifests　that　the　lowest　security　of　REESSE1-E　based　on　variable　combination　is　equivalent　to　the　discrete　logarithm　problem.