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Oblivious polynomial evaluation

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Abstract

The problem of two-party oblivious polynomial evaluation (OPE) is studied, where one party (Alice) has a polynomialP(z) and the other party (Bob) with an inputx wants to learnP(x) in such an oblivious way that Bob obtainsP(x) without learning any additional information aboutP except what is implied byP(x) and Alice does not know Bob's inputx. The former OPE protocols are based on an intractability assumption except for OT protocols. In fact, evaluatingP(x) is equivalent to computing the product of the coefficient vectors (a 0,...,a n ) and (1, …,x n). Using this idea, an efficient scale product protocol of two vectors is proposed first and then two OPE protocols are presented which do not need any other cryptographic assumption except for OT protocol. Compared with the existing OPE protocol, another characteristic of the proposed protocols is the degree of the polynomial is private. Another OPE protocol works in case of existence of untrusted third party.

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Authors and Affiliations

  1. State Key Lab of Information Security, Graduate School of Chinese Academy of Sciences, 100039, Beijing, P.R. China

    Hong-Da Li, Dong-Yao Ji, Deng-Guo Feng & Bao Li

Authors
  1. Hong-Da Li
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  2. Dong-Yao Ji
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  3. Deng-Guo Feng
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  4. Bao Li
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Correspondence to Hong-Da Li.

Additional information

Supported by the National High Technology Research and Development 863 Program of China (Grant No. 2001AA144040).

Hong-Da Li, male, born in 1960, received the Ph.D. degree from Northwestern Polytechnical University in 2001. His current research interests are cryptology and cryptographic protocol. E-mail: lihongda@is.ac.cn;hdli@gscas.ac.cn

Dong-Yao Ji, male, born in 1962, received the Ph.D. degree from Xidian University in 2001. His current research interests are cryptology and cryptographic protocol.

Deng-Guo Feng, male, born in 1963. He is a professor and Ph.D. supervisor. His research interests focus on information security.

Bao Li, male, born in 1965, received his Ph.D. degree in cryptography in 1995 from Xidian University. His research interests include cryptographic protocols and public key cryptosystems.

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Li, HD., Ji, DY., Feng, DG. et al. Oblivious polynomial evaluation. J. Compt. Sci. & Technol. 19, 550–554 (2004). https://doi.org/10.1007/BF02944757

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  • DOI: https://doi.org/10.1007/BF02944757

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