TY - JOUR
T1 - Secure Group Testing
AU - Cohen, Alejandro
AU - Cohen, Asaf
AU - Gurewitz, Omer
N1 - Funding Information:
Manuscript received April 3, 2020; revised August 9, 2020 and September 17, 2020; accepted September 20, 2020. Date of publication October 9, 2020; date of current version August 17, 2021. This work was supported in part by the NSF under Grant CNS-1824529 and in part by the Cyber-Security Research Center, Ben-Gurion University. This article was presented in part at the 2016 IEEE International Symposium on Information Theory, ISIT 2016. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Tobias Oechtering. (Corresponding author: Alejandro Cohen.) Alejandro Cohen is with the Research Laboratory of Electronics, MIT, Cambridge, MA 02139 USA (e-mail: cohenale@mit.edu).
Publisher Copyright:
© 2005-2012 IEEE.
PY - 2021/1/1
Y1 - 2021/1/1
N2 - The principal goal of Group Testing (GT) is to identify a small subset of 'defective' items from a large population, by grouping items into as few test pools as possible. The test outcome of a pool is positive if it contains at least one defective item, and is negative otherwise. GT algorithms are utilized in numerous applications, and in many of them maintaining the privacy of the tested items, namely, keeping secret whether they are defective or not, is critical. In this paper, we consider a scenario where there is an eavesdropper (Eve) who is able to observe a subset of the GT outcomes (pools). We propose a new non-adaptive Secure Group Testing (SGT) scheme based on information-theoretic principles. The new proposed test design keeps the eavesdropper ignorant regarding the items' status. Specifically, when the fraction of tests observed by Eve is 0 ≤ δ < 1 , we prove that with the naive Maximum Likelihood (ML) decoding algorithm the number of tests required for both correct reconstruction at the legitimate user (with high probability) and negligible information leakage to Eve is 11-δ times the number of tests required with no secrecy constraint for the fixed K regime. By a matching converse, we completely characterize the Secure GT capacity. Moreover, we consider the Definitely Non-Defective (DND) computationally efficient decoding algorithm, proposed in the literature for non-secure GT. We prove that with the new secure test design, for δ < 1/2 , the number of tests required, without any constraint on K , is at most 11/2-δ times the number of tests required with no secrecy constraint.
AB - The principal goal of Group Testing (GT) is to identify a small subset of 'defective' items from a large population, by grouping items into as few test pools as possible. The test outcome of a pool is positive if it contains at least one defective item, and is negative otherwise. GT algorithms are utilized in numerous applications, and in many of them maintaining the privacy of the tested items, namely, keeping secret whether they are defective or not, is critical. In this paper, we consider a scenario where there is an eavesdropper (Eve) who is able to observe a subset of the GT outcomes (pools). We propose a new non-adaptive Secure Group Testing (SGT) scheme based on information-theoretic principles. The new proposed test design keeps the eavesdropper ignorant regarding the items' status. Specifically, when the fraction of tests observed by Eve is 0 ≤ δ < 1 , we prove that with the naive Maximum Likelihood (ML) decoding algorithm the number of tests required for both correct reconstruction at the legitimate user (with high probability) and negligible information leakage to Eve is 11-δ times the number of tests required with no secrecy constraint for the fixed K regime. By a matching converse, we completely characterize the Secure GT capacity. Moreover, we consider the Definitely Non-Defective (DND) computationally efficient decoding algorithm, proposed in the literature for non-secure GT. We prove that with the new secure test design, for δ < 1/2 , the number of tests required, without any constraint on K , is at most 11/2-δ times the number of tests required with no secrecy constraint.
KW - Group testing (GT)
KW - information-theoretic security
UR - http://www.scopus.com/inward/record.url?scp=85092520341&partnerID=8YFLogxK
U2 - 10.1109/TIFS.2020.3029877
DO - 10.1109/TIFS.2020.3029877
M3 - Article
AN - SCOPUS:85092520341
SN - 1556-6013
VL - 16
SP - 4003
EP - 4018
JO - IEEE Transactions on Information Forensics and Security
JF - IEEE Transactions on Information Forensics and Security
M1 - 9218939
ER -