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Privacy-Preserving Greater-Than Integer Comparison without
Binary Decomposition
Sigurd Eskeland
Norwegian Computing Center, Postboks 114 Blindern, 0314 Oslo, Norway
Keywords:
Privacy-Preserving Integer Comparison, Privacy Protocols, Homomorphic Cryptography.
Abstract:
Common for the overwhelming majority of privacy-preserving greater-than integer comparison schemes is
that cryptographic computations are conducted in a bitwise manner. To ensure secrecy, each bit must be
encoded in such a way that nothing is revealed to the opposite party. The most noted disadvantage is that the
computational and communication cost of bitwise encoding is at best linear to the number of bits. Also, many
proposed schemes have complex designs that may be difficult to implement. Carlton et al. (2018) proposed an
interesting scheme that avoids bitwise decomposition and works on whole integers. A variant was proposed by
Bourse et al. (2019). Despite that the stated adversarial model of these schemes is honest-but-curious users,
we show that they are vulnerable to malicious users. Inspired by the two mentioned papers, we propose a
novel comparison scheme, which is resistant to malicious users.
1 INTRODUCTION
The idea of the Millionaire’s Problem (Yao, 1982) is
to facilitate two millionaires, who do not trust each
other and who do not want to reveal their worth to
each other, to find out who is the richest. Although
such tasks could trivially be solved by a trusted third
party who decides which party has the greatest value,
the goal is to replace the trusted party with a privacy-
preserving protocol. In other words, it is the ability to
conduct privacy-preserving greater-than integer com-
parisons (PPGTC) without a trusted third party.
PPGTC may be used as a subprotocol for
conducting privacy-preserving computations on en-
crypted data sets. Practical applications are auctions
with private biddings, voting systems, privacy-
preserving database retrieval and data-mining,
privacy-preserving statistical analysis, genetic
matching, face recognition, privacy-preserving set
intersection computation, etc.
Privacy-preserving integer comparison is an ac-
tive research field that is based on techniques such as
homomorphic encryption, garbled circuits, oblivious
transfer, and secret sharing. Authors generally tend
to claim some improvement over some other scheme
in particular with regard to efficiency, but the actual
efficiency may not be readily comparable (for exam-
ple, due to methods are very different) nor available
in many papers. Common for the overwhelming ma-
jority of privacy-preserving greater-than integer com-
parison schemes is that cryptographic computations
are conducted in a bitwise manner. To ensure se-
crecy, each bit of the private inputs must be encoded
in such a way that nothing is revealed to the oppo-
site party. Bitwise cryptographic processing results in
high computational and communication costs that is
proportional to data input sizes. Also, many proposed
schemes have complex designs that may be difficult
to implement.
Carlton et al. (2018) a PPGTC scheme that works
on whole integers and that does not require bitwise
coding or encryption. Inspired by (Damg
˚
ard et al.,
2008a; Damg
˚
ard et al., 2008b), it makes use of a spe-
cial RSA modulus. Blinding is conducted to protect
the input values. At the end of the protocol, a plain-
text equality test (PET) subprotocol determines the
outcome of the comparison, which imposes an addi-
tional performance cost. Bourse et al. (2019) pro-
posed a slightly modified two-pass PPGTC protocol
that avoids the PET subprotocol, and whose function
is simply replaced by a control value that is sent to
party A in the last pass. By means of this value,
party A determines the outcome of the comparison.
A disadvantage of the Bourse scheme compared
to the Carlton scheme is a significantly smaller up-
per bound of private inputs and a composite modu-
lus, whose size exceeds those recommended for RSA,
even at small input bounds.
340
Eskeland, S.
Privacy-Preserving Greater-Than Integer Comparison without Binary Decomposition.
DOI: 10.5220/0009822403400348
In Proceedings of the 17th International Joint Conference on e-Business and Telecommunications (ICETE 2020) - SECRYPT, pages 340-348
ISBN: 978-989-758-446-6
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