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BGN Authentication and Its Extension to Convey Message Commitments

机译:BGN身份验证及其扩展,以传达消息承诺

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摘要

We instantiate the cryptosystem proposed by Boneh, Goh, and Nissim in TCC'05 into an entity authentication scheme, in which an entity is authenticated by an interactive zero-knowledge proof on its private key. Completeness and soundness of our scheme is supported by the indistinguishability of BGN ciphertexts of sums and products, which essentially relies on the semantic security of the BGN cryptosystem. We further extend our scheme so that the authentication conveys Pedersen commitments on a message, while the BGN authentication serves the 'proving you know how to open' functionality for the commitment. Our message commitment scheme is both statistically hiding and computationally binding provided the subgroup decision problem is hard.
机译:我们将Boneh,Goh和Nissim在TCC'05中提出的加密系统实例化为一个实体身份验证方案,在该方案中,一个实体通过其私钥上的交互式零知识证明进行身份验证。我们的方案的完整性和可靠性得到了BGN密码和和乘积的不可区分性的支持,这在本质上依赖于BGN密码系统的语义安全性。我们进一步扩展了方案,以使身份验证在消息中传达Pedersen承诺,而BGN身份验证则为承诺提供“证明您知道如何打开”功能。我们的消息承诺方案在统计上是隐藏的,在计算上是绑定的,前提是小组决策问题很难解决。

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