Log parsing is a critical step that transforms unstructured log data into structured formats, facilitating subsequent log-based analysis. Traditional syntax-based log parsers are efficient and effective, but they often experience decreased accuracy when processing logs that deviate from the predefined rules. Recently, large language models (LLM) based log parsers have shown superior parsing accuracy. However, existing LLM-based parsers face three main challenges: 1)time-consuming and labor-intensive manual labeling for fine-tuning or in-context learning, 2)increased parsing costs due to the vast volume of log data and limited context size of LLMs, and 3)privacy risks from using commercial models like ChatGPT with sensitive log information. To overcome these limitations, this paper introduces LibreLog, an unsupervised log parsing approach that leverages open-source LLMs (i.e., Llama3-8B) to enhance privacy and reduce operational costs while achieving state-of-the-art parsing accuracy. LibreLog first groups logs with similar static text but varying dynamic variables using a fixed-depth grouping tree. It then parses logs within these groups using three components: i)similarity scoring-based retrieval augmented generation: selects diverse logs within each group based on Jaccard similarity, helping the LLM distinguish between static text and dynamic variables; ii)self-reflection: iteratively query LLMs to refine log templates to improve parsing accuracy; and iii) log template memory: stores parsed templates to reduce LLM queries for improved parsing efficiency. Our evaluation on LogHub-2.0 shows that LibreLog achieves 25% higher parsing accuracy and processes logs 2.7 times faster compared to state-of-the-art LLM-based parsers. In short, LibreLog addresses privacy and cost concerns of using commercial LLMs while achieving state-of-the-arts parsing efficiency and accuracy.