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We study an index calculus algorithm to solve the discrete logarithm problem (DLP) in degree 0 class groups of non-hyperelliptic curves of genus 3 over finite fields. We present a heuristic analysis of the algorithm which indicates that the DLP in degree 0 class groups of non-hyperelliptic curves of genus 3 can be solved in an expected time ofÕ(q). This heuristic result relies on one heuristic assumption which is studied experimentally. We also present experimental data which show that adoi:10.1007/s00145-007-9014-6 fatcat:clczgl7xr5b5vgekyvma25fxga