Paper 2019/386

Field Extension in Secret-Shared Form and Its Applications to Efficient Secure Computation

Ryo Kikuchi, Nuttapong Attrapadung, Koki Hamada, Dai Ikarashi, Ai Ishida, Takahiro Matsuda, Yusuke Sakai, and Jacob C. N. Schuldt


Secure computation enables participating parties to jointly compute a function over their inputs while keeping them private. Secret sharing plays an important role for maintaining privacy during the computation. In most schemes, secret sharing over the same finite field is normally utilized throughout all the steps in the secure computation. A major drawback of this “uniform” approach is that one has to set the size of the field to be as large as the maximum of all the lower bounds derived from all the steps in the protocol. This easily leads to a requirement for using a large field which, in turn, makes the protocol inefficient. In this paper, we propose a “non-uniform” approach: dynamically changing the fields so that they are suitable for each step of computation. At the core of our approach is a surprisingly simple method to extend the underlying field of a secret sharing scheme, in a non-interactive manner, while maintaining the secret being shared. Using our approach, default computations can hence be done in a small field, which allows better efficiency, while one would extend to a larger field only at the necessary steps. As the main application of our technique, we show an improvement upon the recent actively secure protocol proposed by Chida et al. (Crypto’18). The improved protocol can handle a binary field, which enables XOR-free computation of a boolean circuit. Other applications include efficient (batch) equality check and consistency check protocols, which are useful for, e.g., password-based threshold authentication

Available format(s)
Cryptographic protocols
Publication info
Published elsewhere. Minor revision. ACISP 2019
secure computationsecret sharingactive security
Contact author(s)
kikuchi_ryo @ fw ipsj or jp
2019-04-16: received
Short URL
Creative Commons Attribution


      author = {Ryo Kikuchi and Nuttapong Attrapadung and Koki Hamada and Dai Ikarashi and Ai Ishida and Takahiro Matsuda and Yusuke Sakai and Jacob C.  N.  Schuldt},
      title = {Field Extension in Secret-Shared Form and Its Applications to Efficient Secure Computation},
      howpublished = {Cryptology ePrint Archive, Paper 2019/386},
      year = {2019},
      note = {\url{}},
      url = {}
Note: In order to protect the privacy of readers, does not use cookies or embedded third party content.