 Welcome, this talk will be about batch arguments for MP and its joint work with Brentwaters. In a batch argument for MP, a prover has a collection of MMP statements, and their goal is to convince the verifier that all M statements are valid. A simple approach to do so is to have the prover send over a collection of MMP witnesses, one for each statement. The verifier then checks that each statement witness pair is valid and accepts if all of them are. In this case, the size of the proof scales linearly with the number of instances. A natural question is whether we can do better. Namely, can we authenticate MMP statements with a proof whose size is sublinear in M? This is the setting of batch arguments. The goal here is to amortize the cost of MP verification. Namely, we seek a construction where a proof on MMP statements scales polynomially with a security parameter, but importantly, polylogrismically with the number of instances being proved. We do allow the proof size to grow with the size of checking a single instance, and hence this is not a succinct argument or a snark. The goal is really to amortize the proof size and verification cost over a batch of instances. In this work, we focus on constructing new, noninteractive batch arguments for MP. First, batch arguments are a special case of succinct arguments or snarks, and indeed, any snark for MP automatically gives a batch argument for MP. However, existing snark constructions either rely on idealized models, non-fossifiable knowledge assumptions, or on powerful cryptographic tools like indistinguishability obfuscation. If we consider the relaxation to batch arguments, a pair of recent works by Shodori, Jane and Jin have shown how to realize them from either the subexponential DDH assumption together with QR, or from the plain learning with errors assumption. Both of these constructions leverage correlation-intractable hash functions to provably instantiate the Fiat-Chemier heuristic. Finally, if we consider pairing-based assumptions, Kalai, Paneth, and Yang showed how to construct a batch argument using a non-standard Q-type assumptions on groups with bilinear maps. In this work, we give the first construction of batch arguments for MP from standard assumptions on bilinear groups. We can instantiate our approach with either the subgroup decision assumption on composite-order bilinear groups, or from the standard K-linear assumption over prime-order groups. A key feature of our construction is that it gives a direct construction of batch arguments that departs heavily from previous techniques in the study of succinct arguments. Namely, we do not rely on heavyweight cryptographic tools like correlation intractable hash functions, or on information theoretic building blocks like probabilistically checkable proofs, both of which have featured prominently in near-the-all-previous constructions of similar primitives. Instead, we give a direct construction in the manner of the classic non-succinct, non-interactive zero-knowledge proof of Groves-Ostrovsky and Sahai. As corollaries to our main construction, we also obtain a RAM delegation scheme, also known as a snark4p, with a sublinear-side CRS from standard bilinear map assumptions, as well as an aggregate signature scheme that supports bounded aggregation in the plain model. Our approach follows a commit-improve strategy, much like the Neziks of Groves-Ostrovsky and Sahai. The prover here has a batch of M statements, and we consider the Mp-complete language of Boolean circuit satisfiability. For each wire in the Boolean circuit, the prover starts by constructing a vector commitment to the M wire assignment, one assignment for each instance. Critically, we require that the commitment is succinct. In our case, the size of the commitment is a single group element and independent of the number of instances. Next, the prover constructs a sequence of proofs for validating wire labels, that each gate is properly computed, and that all of the gates, all of the circuit, output gates, output 1. Each of these validity checks is a quadratic operation and can be checked in the exponent. The tricky part is arguing soundness. In a Groves-Ostrovsky-Sahai-Nezik, soundness relied on extracting the committed values from the commitment, but that will no longer be possible since the commitments are now succinct. For details here, please come to our talk on Tuesday. To summarize, the focus of this work is on constructing batch arguments for Mp, using standard assumptions over bilinear maps. A distinctive feature of our work is that the construction is simple, direct, and completely avoids any heavy cryptographic or information theoretic machinery characteristic of many previous approaches. As corollaries to our main construction, we also obtain a RAM delegation scheme, as well as an aggregate signature scheme in the standard model, from standard bilinear map assumptions. I hope to see you at the talk on Tuesday, and the paper is also available now on Eprint. Thank you very much.