In this paper, we focus on isogenies over abelian varieties for isogeny-based cryptography and efficient computation of the hash function using multiradical (3, 3)-isogenies. In particular, we performed a detailed analysis of the explicit formulae to compute multiradical (3, 3)-isogenies and optimized many parts for the efficient hash function. We optimized the formulae manually and achieved a \(16.8\%\) reduction in complexity arithmetic operations compared to the implementation of the previous work. In particular, we achieved an efficiency improvement of about \(86.5\%\) for the most complicated part of the hash functionHash function excluding the Gröbner basis computation. In addition, we provided a comparison of hash functions using isogenies on elliptic curves and Jacobians of genus 2 curves. We discuss further improvements and optimization of the multiradical (3, 3)-isogenies that make the hash function based on them faster than in the case of elliptic curves.