How to garble arithmetic circuits

Benny Applebaum, Yuval Ishai, Eyal Kushilevitz

Research output: Contribution to journalArticlepeer-review


Yao's garbled circuit construction transforms a boolean circuit C : {0, 1}n →{0, 1}m into a "garbled circuit" Ĉ along with n pairs of k-bit keys, one for each input bit, such that Ĉ together with the n keys corresponding to an input x reveal C(x) and no additional information about x. The garbled circuit construction is a central tool for constant-round secure computation and has several other applications. Motivated by these applications, we suggest an efficient arithmetic variant of Yao's original construction. Our construction transforms an arithmetic circuit C : Zn → Zm over integers from a bounded (but possibly exponential) range into a garbled circuit Ĉ along with n affine functions Li : Z → Zk such that °C together with the n integer vectors Li(xi) reveal C(x) and no additional information about x. The security of our construction relies on the intractability of the learning with errors problem.

Original languageEnglish
Pages (from-to)905-929
Number of pages25
JournalSIAM Journal on Computing
Issue number2
StatePublished - 2014


  • Arithmetic circuits
  • Cryptography
  • Garbled circuits
  • Secure multiparty computation

All Science Journal Classification (ASJC) codes

  • General Computer Science
  • General Mathematics


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