Secure Computation with Fixed-Point Numbers

Secure computation is a promising approach to business problems in which several parties want to run a joint application and cannot reveal their inputs. Secure computation preserves the privacy of input data using cryptographic protocols, allowing the parties to obtain the benefits of data sharing and at the same time avoid the associated risks. These business applications need protocols that support all the primitive data types and allow secure protocol composition and efficient application development. Secure computation with rational numbers has been a challenging problem. We present in this paper a family of protocols for multiparty computation with rational numbers using fixed-point representation. This approach offers more efficient solutions for secure computation than other usual representations.

[1]  Kazuo Ohta,et al.  Multiparty Computation for Interval, Equality, and Comparison Without Bit-Decomposition Protocol , 2007, Public Key Cryptography.

[2]  Mikhail J. Atallah,et al.  Private collaborative forecasting and benchmarking , 2004, WPES '04.

[3]  Keith B. Frikken,et al.  Secure Collaborative Planning, Forecasting, and Replenishment (SCPFR) , 2005 .

[4]  Milos D. Ercegovac,et al.  Digital Arithmetic , 2003, Wiley Encyclopedia of Computer Science and Engineering.

[5]  I. Damglurd.  Unconditionally secure constant-rounds multi-party computation for equality, comparison, bits and exponentiation , 2006 .

[6]  Yuval Ishai,et al.  Share Conversion, Pseudorandom Secret-Sharing and Applications to Secure Computation , 2005, TCC.

[7]  Octavian Catrina,et al.  Multiparty Computation of Fixed-Point Multiplication and Reciprocal , 2009, 2009 20th International Workshop on Database and Expert Systems Application.

[8]  Shuzo Yajima,et al.  Efficient Initial Approximation for Multiplicative Division and Square Root by a Multiplication with Operand Modification , 1997, IEEE Trans. Computers.

[9]  Tatsuaki Okamoto,et al.  Public Key Cryptography - PKC 2007, 10th International Conference on Practice and Theory in Public-Key Cryptography, Beijing, China, April 16-20, 2007, Proceedings , 2007, Public Key Cryptography.

[10]  Jan Camenisch,et al.  Efficient Computation Modulo a Shared Secret with Application to the Generation of Shared Safe-Prime Products , 2002, CRYPTO.

[11]  Felix Brandt,et al.  How to obtain full privacy in auctions , 2006, International Journal of Information Security.

[12]  Moti Yung,et al.  Advances in Cryptology — CRYPTO 2002 , 2002, Lecture Notes in Computer Science.

[13]  Tomas Toft.  Solving Linear Programs Using Multiparty Computation , 2009, Financial Cryptography.

[14]  Moni Naor.  Advances in Cryptology - EUROCRYPT 2007, 26th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Barcelona, Spain, May 20-24, 2007, Proceedings , 2007, EUROCRYPT.

[15]  Ueli Maurer,et al.  General Secure Multi-party Computation from any Linear Secret-Sharing Scheme , 2000, EUROCRYPT.

[16]  Joseph Bonneau,et al.  What's in a Name? , 2020, Financial Cryptography.

[17]  Ivan Damgård,et al.  A Practical Implementation of Secure Auctions Based on Multiparty Integer Computation , 2006, Financial Cryptography.

[18]  Eike Kiltz,et al.  Secure Computation of the Mean and Related Statistics , 2005, IACR Cryptol. ePrint Arch..

[19]  Bart Preneel,et al.  Advances in cryptology - EUROCRYPT 2000 : International Conference on the Theory and Application of Cryptographic Techniques, Bruges, Belgium, May 14-18, 2000 : proceedings , 2000 .

[20]  Ivan Damgård,et al.  Non-interactive Proofs for Integer Multiplication , 2007, EUROCRYPT.

[21]  Ivan Damgård,et al.  Efficient Conversion of Secret-shared Values Between Different Fields , 2008, IACR Cryptol. ePrint Arch..

[22]  Jacques Stern,et al.  CryptoComputing with Rationals , 2002, Financial Cryptography.

[23]  Peter W. Markstein,et al.  Software Division and Square Root Using Goldschmidt's Algorithms , 2004 .