Short Round Sub-Linear Zero-Knowledge Argument for Linear Algebraic Relations
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- SEO Jae Hong
- Security Architecture Laboratory, Network Security Research Institute, National Institute of Information and Communications Technology
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Zero-knowledge arguments allows one party to prove that a statement is true, without leaking any other information than the truth of the statement. In many applications such as verifiable shuffle (as a practical application) and circuit satisfiability (as a theoretical application), zero-knowledge arguments for mathematical statements related to linear algebra are essentially used. Groth proposed (at CRYPTO 2009) an elegant methodology for zero-knowledge arguments for linear algebraic relations over finite fields. He obtained zero-knowledge arguments of the sub-linear size for linear algebra using reductions from linear algebraic relations to equations of the form z = x *' y, where x, y ∈ Fnp are committed vectors, z ∈ Fp is a committed element, and *' : Fnp × Fnp → Fp is a bilinear map. These reductions impose additional rounds on zero-knowledge arguments of the sub-linear size. The round complexity of interactive zero-knowledge arguments is an important measure along with communication and computational complexities. We focus on minimizing the round complexity of sub-linear zero-knowledge arguments for linear algebra. To reduce round complexity, we propose a general transformation from a t-round zero-knowledge argument, satisfying mild conditions, to a (t - 2)-round zero-knowledge argument; this transformation is of independent interest.
収録刊行物
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- IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
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IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E95.A (4), 776-789, 2012
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詳細情報 詳細情報について
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- CRID
- 1390001206309863808
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- NII論文ID
- 10030937939
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- NII書誌ID
- AA10826239
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- BIBCODE
- 2012IEITF..95..776S
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- ISSN
- 17451337
- 09168508
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- 本文言語コード
- en
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- データソース種別
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- JaLC
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