We present a new approach to garbling arithmetic circuits using techniques from homomorphic secret sharing, obtaining constructions with high rate that support free addition gates. In particular, we build upon non-interactive protocols for computing distributed discrete logarithms in groups with an easy discrete-log subgroup, further demonstrating the versatility of tools from homomorphic secret sharing. Relying on distributed discrete log for the Damgård-Jurik cryptosystem (Roy and Singh, Crypto ‘21), whose security follows from the decisional composite residuosity assumption (DCR), we get the following main results: As a side result, we show that our scheme based on IND-CPA security achieves rate 3/5 for levelled circuits.