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Lecture notes in computer science

Accelerating Multiparty Computation by Efficient Random Number Bitwise-Sharing Protocols

Naoto Kiribuchi, Ryo Kato, Takashi Nishide, Tsukasa Endo, Hiroshi Yoshiura

Published Jan 1, 2012• 1 citation
Publisher
DOI
10.1007/978-3-642-27890-7_16

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Efficient Multiparty Protocols Using Circuit Randomization

Donald Beaver

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MULTIPARTY COMPARISON - An Improved Multiparty Protocol for Comparison of Secret-shared Values

Tord Ingolf Reistad

Multiparty computation is a computation between multiple players which want to compute a common function based on private input. It was first proposed over 20 years ago and has since matured into a well established science. The goal of this thesis has been to develop efficient protocols for different operations used in multiparty computation and to propose uses for multiparty computation in real world systems. This thesis therefore gives the reader an overview of multiparty computation from the simplest primitives to the current state of software frameworks for multiparty computation, and provides ideas for future applications. Included in this thesis is a proposed model of multiparty computation based on a model of communication complexity. This model provides a good foundation for the included papers and for measuring the efficiency of multiparty computation protocols. In addition to this model, a more practical approach is also included, which examines different secret sharing schemes and how they are used as building blocks for basic multiparty computation operations. This thesis identifies five basic multiparty computation operations: sharing, recombining, addition, multiplication and negation, and shows how these five operations can be used to create more complex operations. In particular two operations “less-than” and “bitwise decomposition” are examined in detail in the included papers. “less-than” performs the “<” operator on two secret shared values with a secret shared result and “bitwise decomposition” takes a secret shared value and transforms it into a vector of secret shared bitwise values. The overall goal of this thesis has been to create efficient methods for multiparty computation so that it might be used for practical applications in the future.

International Conference on Security and Cryptography•Jan 1, 2009•19 citations

Reducing Communication Complexity of Random Number Bitwise-Sharing for Efficient Multi-party Computation

Naoto Kiribuchi, Ryo Kato, Takashi Nishide +2 more

It is becoming more and more important to make use of personal or classified information while keeping it confidential. A promising tool for meeting this challenge is secure multi-party computation (MPC). However, one of the biggest problems with MPC is that it requires a vast amount of communication. We analyzed existing MPC protocols and found that the random number bitwise-sharing protocol used by many of them is notably inefficient. By devising a representation of the truth values and using special form prime numbers, we propose efficient random number bitwise-sharing protocols, dubbed “Extended-Range I and II,” which reduce the communication complexity to approximately 1/6th that of the best of the existing such protocol. We reduced the communication complexity to approximately 1/26th by reducing the abort probability, thereby making previously necessary backup computation unnecessary. Using our improved protocol, “Lightweight Extended-Range II,” we reduced the communication complexities of equality testing, comparison, interval testing, and bit-decomposition, all of which use the random number bitwise-sharing protocol, by approximately 91, 79, 67, and 23% (for 32-bit data), respectively. We also reduce the communication complexity of private exponentiation by about 70% (for 32-bit data and five parties).

Journal of Information Processing•Jan 1, 2012•0 citations

Generalizing Efficient Multiparty Computation

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Lecture notes in computer science•Jan 1, 2015•5 citations

Theory and Practice of Multiparty Computation

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Constant-Round Multiparty Computation for Interval Test, Equality Test, and Comparison

Takashi Nishide, Kazuo Ohta

We propose constant-round protocols for interval tests, equality tests, and comparisons where shared secret inputs are not given bitwise. In [9]. Damgard et al. presented a novel protocol called the bit-decomposition, which can convert a polynomial sharing of an element in prime field p into sharings of bits. Though, by using the bit-decomposition protocol, those protocols can be constructed with constant round complexities theoretically, it involves expensive computation, leading to relatively high round and communication complexities. In this paper, we construct more efficient protocols for those protocols without relying on the bit-decomposition protocol. In the interval test protocol, checking whether a shared secret exists in the known interval is reduced to checking whether a bitwise-shared random secret exists in the appropriate interval. In the comparison protocol, comparing two shared secrets is reduced to comparing the two secrets via p/2 indirectly where p is an odd prime for an underlying linear secret sharing scheme. In the equality test protocol, checking whether two shared secrets are equal is reduced to checking whether the difference of the two secrets is zero and furthermore checking whether the difference is a zero is reduced to checking quadratice residuosity of a random secret in a probabilistic way.

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences•May 1, 2007•10 citations
Multiparty computation is a computation between multiple players which want to compute a common function based on private input. It was first proposed over 20 years ago and has since matured into a well established science. The goal of this thesis has been to develop efficient protocols for different operations used in multiparty computation and to propose uses for multiparty computation in real world systems. This thesis therefore gives the reader an overview of multiparty computation from the simplest primitives to the current state of software frameworks for multiparty computation, and provides ideas for future applications. Included in this thesis is a proposed model of multiparty computation based on a model of communication complexity. This model provides a good foundation for the included papers and for measuring the efficiency of multiparty computation protocols. In addition to this model, a more practical approach is also included, which examines different secret sharing schemes and how they are used as building blocks for basic multiparty computation operations. This thesis identifies five basic multiparty computation operations: sharing, recombining, addition, multiplication and negation, and shows how these five operations can be used to create more complex operations. In particular two operations “less-than” and “bitwise decomposition” are examined in detail in the included papers. “less-than” performs the “<” operator on two secret shared values with a secret shared result and “bitwise decomposition” takes a secret shared value and transforms it into a vector of secret shared bitwise values. The overall goal of this thesis has been to create efficient methods for multiparty computation so that it might be used for practical applications in the future.
It is becoming more and more important to make use of personal or classified information while keeping it confidential. A promising tool for meeting this challenge is secure multi-party computation (MPC). However, one of the biggest problems with MPC is that it requires a vast amount of communication. We analyzed existing MPC protocols and found that the random number bitwise-sharing protocol used by many of them is notably inefficient. By devising a representation of the truth values and using special form prime numbers, we propose efficient random number bitwise-sharing protocols, dubbed “Extended-Range I and II,” which reduce the communication complexity to approximately 1/6th that of the best of the existing such protocol. We reduced the communication complexity to approximately 1/26th by reducing the abort probability, thereby making previously necessary backup computation unnecessary. Using our improved protocol, “Lightweight Extended-Range II,” we reduced the communication complexities of equality testing, comparison, interval testing, and bit-decomposition, all of which use the random number bitwise-sharing protocol, by approximately 91, 79, 67, and 23% (for 32-bit data), respectively. We also reduce the communication complexity of private exponentiation by about 70% (for 32-bit data and five parties).
We propose constant-round protocols for interval tests, equality tests, and comparisons where shared secret inputs are not given bitwise. In [9]. Damgard et al. presented a novel protocol called the bit-decomposition, which can convert a polynomial sharing of an element in prime field p into sharings of bits. Though, by using the bit-decomposition protocol, those protocols can be constructed with constant round complexities theoretically, it involves expensive computation, leading to relatively high round and communication complexities. In this paper, we construct more efficient protocols for those protocols without relying on the bit-decomposition protocol. In the interval test protocol, checking whether a shared secret exists in the known interval is reduced to checking whether a bitwise-shared random secret exists in the appropriate interval. In the comparison protocol, comparing two shared secrets is reduced to comparing the two secrets via p/2 indirectly where p is an odd prime for an underlying linear secret sharing scheme. In the equality test protocol, checking whether two shared secrets are equal is reduced to checking whether the difference of the two secrets is zero and furthermore checking whether the difference is a zero is reduced to checking quadratice residuosity of a random secret in a probabilistic way.