We show that one-way functions suffice for constructing very efficient argument systems for proving the correctness of bounded-space computations. Taking $\kappa$ to be a cryptographic security parameter and $n$ to be the input length, our argument system applies to general computations running in time $T$ and space $S$. The protocol has ${\mathit{polylog}}(T)$ rounds, the communication complexity is $S\cdot {\mathit{poly}}({\mathit{log}}(T),\kappa)$ and the verifier runtime is $(S + n) \cdot {\mathit{poly}}({\mathit{log}}(T),\kappa)$. In particular, the complexity of the verifier is only poly-logarithmic in the computation length. The honest prover runs in time ${\mathit{poly}}(T,\kappa)$, so the protocol is doubly-efficient. If the one-way function is secure against $\lambda(\kappa)$-size adversaries, then the argument system is sound against cheating provers of size $\lambda(\kappa)/{\mathit{poly}}(T)$.

Prior to this work, doubly-efficient argument systems with poly-logarithmic dependence on $T$ required assuming (at least) the existence of collision-resistant hash functions [Kilian, STOC 1992]. For unconditionally sound doubly-efficient protocols, the RRR protocol for bounded-space computations [Reingold, Rothblum and Rothblum, STOC 2016] has communication and verification complexities that grow with $T^{\sigma}$ for an arbitrarily small constant $\sigma > 0$.