Recent zk-SNARK constructions such as Marlin and PLONK relying on Polynomial commitment schemes are not inherently tied to R1CS constraints to specify the statement to be proven. This is roughly because the verifier equation is checked "in the clear" on a random opening of the prover polynomials, rather than "in the exponent" using a pairing. We provide a framework to capture more general and flexible constraints which we call turbo-PLONK programs. We give an example of how this framework allows for more concise representation of fixed-base elliptic curve scalar multiplication (only 1 turbo-PLONK gate for each two input bits), a primitive useful for constructing Pedersen hashes. We also include benchmarks of proving time for scalar multiplication on the Grumkin curve (a 255 bit curve embedded over bn254). Our results indicate a 2x improvement over Groth16.