Searchable encrypted log provides a facility to disclose only records which match some specified conditions. However, searching on an encrypted log takes a long time because checking for the condition usually requires a vast number of public key operations. In the field of plain text search, inverted index is a typical data structure to improve the performance of search speed which turns a bunch of comparison into a simple table lookup. This paper introduces an encrypted version of inverted index which can be used for a searchable encrypted log. Encrypted inverted index enables to determine all records that contain a keyword while contents of other records are kept secret. Statistic information such as frequency of each word is also not revealed. A prototype system is implemented to show the efficiency.