Efficient Proof Composition for Verifiable Computation Julien Keuffer 1,2 , Refik Molva 2 , and Herv´ e Chabanne 1,3 1 Idemia, Issy-les-Moulineaux, France 2 Eurecom, Biot, France 3 Telecom ParisTech, Paris, France {julien.keuffer,herve.chabanne}@idemia.com refik.molva@eurecom.fr Abstract. Outsourcing machine learning algorithms helps users to deal with large amounts of data without the need to develop the expertise re- quired by these algorithms. Outsourcing however raises severe security is- sues due to potentially untrusted service providers. Verifiable computing (VC) tackles some of these issues by assuring computational integrity for an outsourced computation. In this paper, we design a VC protocol tai- lored to verify a sequence of operations for which no existing VC scheme is suitable to achieve realistic performance objective for the entire se- quence. We thus suggest a technique to compose several specialized and efficient VC schemes with a general purpose VC protocol, like Parno et al.’s Pinocchio, by integrating the verification of the proofs generated by these specialized schemes as a function that is part of the sequence of op- erations verified using the general purpose scheme. The resulting scheme achieves the objectives of the general purpose scheme with increased effi- ciency for the prover. The scheme relies on the underlying cryptographic assumptions of the composed protocols for correctness and soundness. Keywords: Verifiable computation, Proof composition, Neural networks 1 Introduction While achieving excellent results in diverse areas, machine learning algorithms require expertise and a large training material to be fine-tuned. Therefore, cloud providers such as Amazon or Microsoft have started offering Machine Learning as a Service (MLaaS) to perform complex machine learning tasks on behalf of users. Despite these advantages, outsourcing raises a new requirement: in the face of potentially malicious service providers the users need additional guaran- tees to gain confidence in the results of outsourced computations. As an answer to this problem, verifiable computing (VC) provides proofs of computational in- tegrity without any assumptions on hardware or on potential failures. Existing VC systems can theoretically prove and verify all NP computations [8]. Nev- ertheless, despite the variety of existing solutions, existing VC schemes have to make trade-offs between expressiveness and functionality [20] and therefore can- not efficiently handle the verifiability of a sequence of operations with a high