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Formal modeling of random oracle programmability and verification of signature unforgeability using task-PIOAs

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Abstract

The task-structured probabilistic I/O automata (task-PIOA) framework provides a method to formulate and to prove the computationally bounded security of non-sequential processing systems in a formal way. Formalizing non-sequential processes for strong adversaries is not easy. Actually, existing security analyses using the task-PIOA framework are for cryptographic protocols (e.g., the EGL oblivious transfer) only against simple adversaries (e.g., honest but curious adversary). For example, there is no case study for digital signature against strong active adversaries (i.e., EUF-CMA) in the task-PIOA framework. In this paper, we propose the first formalization of digital signature against EUF-CMA in the task-PIOA framework. To formalize the non-sequential process of EUF-CMA, we introduce a new technique for the iteration of an identical action in a single session. Using the task-PIOA framework allows us to verify security of signature schemes in the non-sequential scheduling manner. We show the validity and usefulness of our formulation by giving a formal security analysis of the FDH signature scheme. In order to prove the security, we also introduce a method to utilize the power of random oracles. As far as we know, this work is the first case study to clarify usefulness of random oracles in this framework.

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Notes

  1. Though Funct is defined with a parameter Tdp, we can essentially parameterize it with arbitrary and universal verification key space. In this paper, for the security proof in Sect. 4, we show the code by replacing universal verification key space to Tdp concretely.

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Authors and Affiliations

  1. Ibaraki University, 4-12-1 Nakanarusawa-cho Hitachi-shi, Ibaraki, 316-8511, Japan

    Kazuki Yoneyama

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  1. Kazuki Yoneyama
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Correspondence to Kazuki Yoneyama.

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This paper does not receive any funding because the work is done as a business at my company.

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Additional information

This paper is the full version of the extended abstract appeared in [22].

This paper follows ethical rules of the journal as follows: Originality: This paper extends our earlier conference paper [22]. The earlier paper gives an idea of formalizing random oracle programmability and a security proof of the FDH signature using task-PIOAs. However, it does not contain any concrete formalization or the proof. This submission provides a significantly new work: concrete codes for all task-PIOAs and the security proof of the FDH signature using task-PIOAs.

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Yoneyama, K. Formal modeling of random oracle programmability and verification of signature unforgeability using task-PIOAs. Int. J. Inf. Secur. 17, 43–66 (2018). https://doi.org/10.1007/s10207-016-0352-y

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