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Compiler Creates Succinct Classical Interactive Arguments with Post-Soundness Relying on Learning with Errors

Much of contemporary cryptography is based on the fundamental problem of safely validating intricate calculations, which motivates researchers to constantly look for techniques that may demonstrate the accuracy of these procedures with little communication. MIT’s Computer Science and Artificial Intelligence Laboratory’s Andrew Huang and Yael Tauman Kalai recently developed a novel compiler that turns any computational process into a concise interactive argument. This accomplishment overcomes the drawbacks of a number of earlier cryptographic techniques and guarantees that verification may be carried out effectively with solely classical computers.

This work makes it possible to provide concise and classically verifiable proofs for any protocol, which is a major step towards the development of resilient and useful cryptographic systems.

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Grounding Security in Post-Quantum Hardness

Importantly, this novel framework’s security relies on the Learning with Errors (LWE) problem’s well-researched post-sub-exponential hardness. Compared to certain earlier methods that depended on dubious assumptions about post-quantum security, this solid foundation represents a significant advancement.

A general transformation that can be used with a variety of protocols is the compiler. It converts any MIP protocol including ones with multiple provers or that are not concise into a completely concise classical QIA (Quantum Interactive Argument). Moreover, it applies to any QIP protocol that is sound only against semi-malicious provers, even those that begin with an initial state that may be malicious. The security of many different systems is said to be improved by the capacity to support potentially harmful beginning states.

A compiler for MIP protocols was also supplied by earlier work, such as the one presented by Kalai, Lombardi, Vaikuntanathan, and Yang (KLVY) at STOC 2022; however, the post-quantum soundness of that work is still being examined. Stronger security guarantees based on Learning with Errors LWE are provided by the updated compiler.

One significant difference is that, assuming the post-quantum hardness of Learning with Errors LWE, this compiler relates the soundness of the resulting classical QIA to the quantum value/soundness of the underlying MIP protocol instead of just the quantum computing operator value (a relationship that prior results focused on but found difficult to resolve generically)

The Two-Step Compilation Proces

There are two primary steps in the core transformation:

1. From QI QMATIME: From QIP The researchers first show that a language is a member of the complexity class QMATIME if it has a QIP with semi-malicious soundness and the prover operates in time. This class includes languages whose membership can be confirmed by a quantum computer operating in time poly. By flattening the QIP interaction into a sizable quantum circuit with the prover’s auxiliary state serving as its witness, this is accomplished.
2. From QMATIME to Succinct Classical QIA: They then develop a brief classical defence of any such language. In particular, the Morimae-Fitzsimons protocol is used to transform the witness state into one that can be verified by measuring qubits exclusively in the basis. This phase relies upon methods created for the classical verification of quantum operations.

A semi-succinct commitment method is incorporated into the construction to achieve succinctness and alleviate the enormous communication complexity that afflicted previous protocols that required communication proportional to the computation time. Unlike previous approaches that required distinct keys for each qubit, this methodology enables the verifier to submit a single concise commitment key. A protocol compression technique is then used to provide a completely concise argument.

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Efficiency and Complexity Guarantees

High efficiency is attained by the resultant classical QIA:

• Succinctness: As the security parameter increases, the communication complexity only increases polynomially. In terms of complexity, communication complexity increases with computing time in a very slow (polylogarithmic) manner.
• Verifier Runtime: The verifier runs effectively in the time period where the statement under verification is located.
• Prover Runtime: In relation to the initial protocol time, the prover’s runtime only increases polynomially.

This efficiency is contingent upon the auxiliary states of the honest prover being real-valued, which means that the coefficients in the state expansion are real values. Since Mahadev’s work, all known protocols for classically proving quantum computations share this limitation, which guarantees an efficient prover runtime.

The final system is secure, which means that no cheating prover operating in quantum time can persuade the verifier of a false assertion, assuming the post-quantum difficulty of Learning with Errors LWE. There may be rounds in the built argument system.

By bridging the gap between complicated quantum processing and verifiable classical systems, this study offers a generic, resilient transformation for quantum verification, paving the door for the mainstream use of secure quantum technology. There are still some intriguing unanswered problems, such as whether the protocol could be made publicly verifiable and whether the limitation to real-valued witnesses is required for prover efficiency.

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