The edit distance is a metric widely used in genomics to measure the similarity of two DNA chains. Motivated by privacy concerns, we propose a 2PC protocol to compute the edit distance while preserving the privacy of the inputs. Since the edit distance algorithm can be expressed as a mixed-circuit computation, our approach uses protocols based on secret-sharing schemes like Tinier and SPDZ2k and also daBits to perform domain conversion and edaBits to perform arithmetic comparisons. We modify the Wagner-Fischer edit distance algorithm, aiming at reducing the number of rounds of the protocol, and achieve a flexible protocol with a trade-off between rounds and multiplications. We implement our proposal in the MP-SPDZ framework, and our experiments show that it reduces the execution time respectively by 81% and 54% for passive and active security with respect to a baseline implementation in a LAN. The experiments also show that our protocol reduces traffic by two orders of magnitude compared to a BMR-MASCOT implementation.