In this paper we show how to construct a data structure for a string S of size N compressed into a context-free grammar of size n that supports efficient Karp-Rabin fingerprint queries to any substring of S. That is, given indices i and j, the answer to a query is the fingerprint of the substring S[i, j]. We present the first O(n) space data structures that answer fingerprint queries without decompressing any characters. For Straight Line Programs (SLP) we get O(log N) query time, and for Linear SLPs (an SLP derivative that captures LZ78 compression and its variations) we get O(log log N) query time. We extend the result to solve the longest common extension problem in query time O(log N log l) and O(log l log log l + log log N) for SLPs and Linear SLPs, respectively. Here, l denotes the length of the LCE. (C) 2017 Elsevier Inc. All rights reserved.