Zero-knowledge　scalable　transparent　arguments　of　knowledge　(zk-STARKs)　are　a　promising　approach　to　solving　the　blockchain　scalability　problem　while　maintaining　security,　decentralization　and　privacy.　However,　compared　with　zero-knowledge　proofs　with　trusted　setups　deployed　in　existing　scalability　solutions,　zk-STARKs　are　usually　less　efficient.　In　this　paper,　we　introduce　Ligerolight,　an　optimized　zk-STARK　for　the　arithmetic　circuit　satisfiability　problem　following　the　framework　of　Ligero　(ACM　CCS　2017)　and　Aurora　(Eurocrypt　2019)　based　on　interactive　oracle　proof,　which　could　be　used　for　blockchain　scalability.　Evaluations　show　that　Ligerolight　has　performance　advantages　compared　with　existing　zk-STARKs.　The　prover　time　is　30%　faster　than　Aurora　to　generate　proof　for　computing　an　authentication　path　of　a　Merkle　tree　with　32　leaves.　The　proof　size　is　about　131　KB,　one-tenth　of　Ligero　and　50%　smaller　than　Aurora.　The　verifier　time　is　2　times　as　fast　as　Aurora.　Underlying　Ligerolight　is　a　new　batch　zero-knowledge　inner　product　argument,　allowing　to　prove　multiple　inner　product　relations　once.　Using　this　argument,　we　build　a　batch　multivariate　polynomial　commitment　with　poly-logarithmic　communication　complexity　and　verification.　This　polynomial　commitment　is　particularly　efficient　when　opening　multiple　points　in　multiple　polynomials　at　one　time,　and　may　be　of　independent　interest　in　constructing　scalability　solutions.　©　2023　IEEE.