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Table 1 Performance comparison

From: Secure multiparty computation of a comparison problem

Protocol

Third party

Result

Data type

Round

Computation

Yao (1982)

No

\(>, \le\)

Integer

2

Exponential

Cachin (1999)

Yes

\(>, =,<\)

Integer

3

Fischlin (2001)

No

\(>, \le\)

Integer

2

\(\lambda d \text {log} N +6d\lambda +3d\)

Ioannidis and Grama (2003)

No

\(\ge ,<\)

Integer

d

Blake and Kolesnikov (2004)

No

\(>,<\)

Integer

2

\(4d\text {log}N\)

Lin and Tzeng (2005)

No

\(>, \le\)

Integer

2

\(5d \text {log}p+4d-6\)

Grigoriev and Shpilrain (2014)

No

\(>, \le\)

Integer

2

\(6\text {log}p+3d\)

Maitra et al. (2015)

No

\(>, \le\)

Integer

2

\(2d\text {log}p\)

Protocols 2, 3

No

\(>, =,<\)

Integer

2

\(6L+4\)

Protocol 4

No

\(>, =,<\)

Rational number

1

Negligible

  1. d is the length of inputs, \(\lambda\) is set to 40–50 in the Fischlin’s method (Fischlin 2001), p is the modulus in the ElGamal encryption scheme (ElGamal 1984), N is the modulo, L is the length of the 0–1 encoding vector in out work