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Verifiable Proof of Health using Public Key Cryptography

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Abstract

In the current pandemic, testing continues to be the most important tool for monitoring and curbing the disease spread and early identification of the disease to perform health-related interventions like quarantine, contact tracing and etc. Therefore, the ability to verify the testing status is pertinent as public places prepare to safely open. Recent advances in cryptographic tools have made it possible to build a secure and resilient digital-id system. In this work, we propose to build an end to end COVID-19 results verification protocol that takes privacy, computation, and other practical concerns into account for designing an inter-operable layer of testing results verification system that could potentially enable less stringent and more selective lockdowns. We also discuss various concern encompassing the security, privacy, ethics and equity aspect of the proposed system.
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Verifiable Proof of Health using Public Key Cryptography
Abhishek Singh1 and Ramesh Raskar1
Abstract
In the current pandemic, testing continues to be the most important tool for monitoring and curbing the disease
spread and early identification of the disease to perform health-related interventions like quarantine, contact
tracing and etc. Therefore, the ability to verify the testing status is pertinent as public places prepare to safely open.
Recent advances in cryptographic tools have made it possible to build a secure and resilient digital-id system. In this
work, we propose to build an end to end COVID-19 results verification protocol that takes privacy, computation,
and other practical concerns into account for designing an inter-operable layer of testing results verification system
that could potentially enable less stringent and more selective lockdowns. We also discuss various concern
encompassing the security, privacy, ethics and equity aspect of the proposed system.
1 Introduction
The economy is one of the sector that has suffered enormous negative impact during this pandemic. One of the
major reason for such a disruption is the lockdown policy enforced by governments causing all the public places to
shut down. While such a policy is important for curbing the disease spread, its side effects manifest in different forms
including financial loss, mental health, economic collapse and etc. In this work, we describe a cryptographic scheme
through which citizens, healthcare authorities, and public place owners can work collaboratively by restricting access
to infectious individuals for public places. Such a scheme would allow less stringent and more selective lockdowns
and a potential reduction in the disease spread by cutting down infection chain at the places of public gathering.
Previous works [1, 2] in the analysis of disease spread have shown the possibility of such public places turning into a
super spreading zone. Therefore, such a health passport would benefit the current overarching goal of managing the
economy and disease spread simultaneously. That being said, it is important to highlight that the design and
deployment of such a technique should be done after discussion with various experts including policy makers,
epidemiologists, privacy experts, and ethicists. Hence, the scope of this paper is only about the design of the
cryptographic scheme and not a final end to end solution.
There has been a reasonable number of prior work in this area that aim to build a similar health passport for verified
access. A majority of them borrow technology from the blockchain technology and verifiable credentials. However,
as we show in our section 3, our proposed protocol does not require any heavyweight computing infrastructure and
it requires a minimal communication with the internet for the protocol to operate successfully. One of the drawback
of such a design is its limited capability to only verify a testing or immunization result and not support any arbitrary
credential verification or transaction, which we consider is sufficient under the scope of the current pandemic.
The proposed protocol in this work offers threefold advantage:
It uses simple widely known yet secure cryptographic primitives.
It is designed to be integrated with the existing testing ecosystem in an inter-operable fashion.
The protocol addresses the challenges that are relevant to the practical deployment such as offline verification
and health status forgery.
2 Related Work
There has been a significant work in the domain of verifiable ecosystem of credentials using digital tools. The most
notable work is the verifiable credential standard described by W3C [3]. Many existing frameworks utilize the similar
setup of verifiable credential [4]. COVID-19 credentials initiative [5] is a consortium of multiple big companies and
groups working in the domain of verifiable credential working towards building technology around addressing some
2
of the use-cases for COVID-19. There are many other frameworks proposed recently [611]. However, this line of
work also comes with criticism [12]. While our work is inspired by all of these initiatives, the key difference is the
underlying protocol used in our work that does not require any distributed ledger or a verifiable credential type of
setup but simply relies on public key cryptography. Furthermore, we aim to address some of the practical problems
associated with these verifiers in a realistic setting such as offline verification, integration with testing site and the
PHA server for a given jurisdiction. We are able to obtain such advantages without using any sophisticated
cryptographic primitives because of the assumption of tightly couple ecosystem which these verifiable credentials
based work do not assume. This paper draws some of the ideas from the work done in cryptography for message
authentication and signatures [1315]. There are several protocols that allow designing authentication to message
and signature schemes such as HMACs [16]. However, these works do not suffice for preventing forgery while also
performing offline verification. Here, by forgery, we refer to the situation where multiple users carry same verified
information and show the same verifiable proof even though it does not belong to them. Either forgery is resolved
by exchanging message with the issuer or by offline authentication algorithms where message. We solve both of the
problem in our protocol by allowing the server to embed user identifier (user’s public key) in the signed copy of result.
This prevents the forgery of the message as long as the private key of the user is not leaked.
3 Methodology
3.1 Problem Definition
At a high level, a health based verification system involves three parties issuer, holder, and verifier. For the use-case
of COVID-19, the issuer is a public healthcare authority (PHA) that usually sets up a testing site and issues the test
results to individuals. The individuals here act as holder of the result and want the access to public places based on
their health status. Finally, the verifier verifies the health status of the holder by inspecting the health status of the
individuals. The goal of the verifier is to only authorize access to those individual who satisfy the following
requirements -
Carry a health status that belongs to holder
The health status should be authorized by issuer
The health status contains appropriate result(ex - negative test in the last 7 days).
3.2 Terminologies
We use to denote the XOR operation. Whenever a tuple of data is exchanged, all of the elements of the tuple are
in the format (x,y,z) where x,y and z are separate messages to be exchanged. Under the given setup we refer the
holder as A and issuer as PHA.
3.3 Requirements
Functional
F1: The verifier should be able to verify the health status without requiring an internet connection.
F2: The holder should be able to present the health status without requiring an internet connection.
F3: The verification process should be quick and computationally efficient.
F4: No two users should be able to share the health status with each other and gain the access through verifier
fraudulently.
Privacy
3
P1: The verifier should only be able to query the health status of an individual that presents health status with
consent.
P2: The verifier should not be able to learn any other information about the holder except their health status.
P3: Any individual should not be able to query the health status of any arbitrary user except only the user who
queries its own entry.
P4: Existence of an individual on the public health database should not be identifiable.
3.4 Threat Model
There are two categories of threat at a high level in this proposed protocol. The first category refers to forgery where
a user attempts to bypass the verification. This could happen by either altering the content in result status R
(modifying positive test as a negative test or changing the last tested timestamp to a permissible one). This can also
happen if user can obtain someone else’s R. The second category is associated with privacy. Under this threat model
the verifier acts as a semi-honest adversary attempting to reveal more information about the holder. This could either
happen through revealing more information during verification stage or post verification stage where the verifier
attempts to query the data on server through information learned during verification. Under our threat model, no
two parties are colluding with each other at any point of time. However, any arbitrary number of verifiers or holders
can collude among each other to leak additional information holder or to bypass verifier respectively. Furthermore,
in this proposed protocol, the issuer is a trusted entity which is an obvious assumption to make because the issuer
knows the result and identity of every holder from the beginning of the testing phase and for the scope of this paper,
issuer is Public Healthcare Authority. In line with that, the protocol assumes that issuer’s public key PHApk is known
to everyone.
3.5 Preliminaries
While the proposed protocol is agnostic to the underlying encryption algorithm as long as it supports public and
private key cryptography. For the sake of description, we base our system on el-gamal [17] which is a well known
public key crypto system. We define the protocol as follows:
KeyGen(G,q,g) → sk,pk: Construct group G of order q with generator g. The private key is an integer e randomly
sampled from the group G. The public key is ge and the group G.
Encrypt(m,sk) → (c1,c2): a third party can encrypt a message m by first sampling random d from the group G
and computing c1 gd and c2 m · (ge)d.
Decrypt((c1,c2),pk) m: is performed by the receiving party only if they know the private key e as m
(c2) · ((c1)e)1(mod(n)). The inverse can be easily computed by using the value of q.
4
Figure 1: Protocol description: The above user journey diagram illustrates the protocol and message exchanges.
Note that the protocol assumes that the testing site and the PHA server coordinate together to obtain every
tested user’s information and process it accordingly.
While the above definition suits well for the protocol, there are known issues with the plain El-gamal system [17] for
which it could be substituted with secure and more efficient public key based protocols.
3.6 Protocol
Setup phase
The issuer PHA performs KeyGen operation to obtain PHApk and PHAsk. PHApk can be released publicly or given
to business owners in a secure manner based on the access control policy on who can do verification.
The holder A performs KeyGen operation to gather Apk and Ask. Ask is securely stored in a trusted enclave which
even A can not access through system layer security but can only be used by authorized app to perform
encryption.
Test phase
A goes to a testing station and generates a one time identifier ot_id and provides a QR-code containing
information (ot_id,Apk)
Testing site generates a unique sess_id for A and provide it to them through QR-code or any other message
exchange service. The testing site locally stores the tuple (ot_id,Apk,sess_id).
This sess_id is used to carry the testing specimen around and used as the primary identifier for the testing
result as well as specimen.
PHA Server
sess_id
C = Encrypt(ot_id^PHA_sk,
(R, A_pk))
Verifier
Q =
(
C
t), A_pk, ot_id)
Download Phase
The User downloads the data by
querying PHA server with sess_id.
The PHA server downloads C from
the server which contains the health
status in encrypted format
Verification Phase
The User shows QR code which has
C multiplied by current timestamp and
also provide its own public key and
ot_id. The verifier decrypts Q, verifies
timestamp and then decrypts C and
then verify A_pk
A
A
Testing Site
ot_id, A_pk
sess_id
Testing Phase
The User sets up a public and private
key in the beginning and then uses
one time id (ot_id) for every visit to
the testing site. The testing site scans
the tuple and provides sess_id
A
5
Upload phase
Once the testing result data R is ready for the user A the testing site sends (sess_id,ot_id,Apk,R) to the PHA.
Based on the result, the PHA can take additional action like contact tracing and etc. or upload the result to the
PHA server described as follows.
The PHA uploads the following encrypted result C = Encrypt(PHAsk ot_id,(R,Apk)) and hosts it as a tuple
(sess_id,C).
Download phase
A downloads C by sending sess_id to the server.
A performs the following computation to decrypt the result R,Apk = Decrypt(PHApk ot_id,C)
A verifies Apk received from the server and interprets the result.
Verification phase
A computes time based signature S by performing S = encrypt(C · t,Ask) where t is the current timestamp,
rounded off to account for clock drift.
A computes QR code as follows Q = (S,ot_id,Apk) and shows it to the verifier V
V obtains (S,ot_id,Apk) = Q
V obtains C · t = Decrypt(id PHApk,S)
V generates t locally and computes its multiplicative inverse t1 to obtain C
V verifies the identity of A by verifying the signature S = Decrypt(Apk,C × t)
4 Analysis
4.1 Security
The overall security of the protocol not only depends on the security offered by the cryptographic mechanisms but
also on the assumption that a user A can not share its secret key sk with other users otherwise other users can use
the same key to use A’s health status. This is a reasonable assumption given that key management can be performed
these days on smartphone using secure enclaves [18]. In the Section 3.3 we discuss various functional and privacy
requirements of the protocol. P1 and P3 are enforced by making sure that C is not known to any curious user unless
they hold Apk as well as ot_id for the given record. P2 requirement is met by ensuring that the health status R is not
tied to any other additional health of the user. For practical purposes, the issuer might want to communicate more
health information to the user which could be performed by appending an additional layer of encryption to sensitive
set of health information that does not need to be shared with the verifier. P4 requirement is attained through the
secrecy and ephemeral nature of the ot_id and sess_id.
4.2 Computation Efficiency
The computation in this protocol does not involve any heavyweight computation and only relies on a single public
key encryption decryption by the holder for every verification round. Since the verification is supposed to happen
only when a user visits a public place or business, two subsequent computation will have a sufficient time window
6
between them making it practically possible. For n users the issuer has to perform n encryption that requires two
exponentiation operation for el-gamal [17] and decryption requires one exponentiation.
Exponentiation operation for m bits of data requires complexity of O(mlog23) under Karatsuba algorithm. Furthermore,
some of this exponentiation operations could be pre-computed because of the el-gamal algorithm and all n
encryptions are independent of each other making the protocol parallelize at a linear scale.
4.3 Communication Efficiency
For m bits of information, the key expansion of el-gamal [17] algorithm used in the proposed protocol would
introduce the message complexity of 2 · m. As shown in the Figure 1, message exchange mostly involves exchange
of identifiers and ciphertext, hence, communication is always linear with the size of message m and small enough to
be communicated with a single QR-code. In the message exchange performed in the verification phase, the total
bits required for messaging can be given as 2 · m + |Apk| + |ot_id| where |Apk| refers to the size of the public key
which is typically 2048 bits and |ot_id| refers to the one time identifier which is usually 256 bits. Overall, this
information can fit within a QR-code and hence can be communicated from holder to verifier in a single round. In
addition to this, our protocol requires minimum interaction with an online server by mandating functional
requirements F1 and F2.
5 Discussion
5.1 Unintended Consequences
The idea of restricted access based on either a negative test result or . The letter [19, 20] from EFF and
ACLU California highlights several criticism for the California’s bill [21] for the use of verifiable credential technology
[3] to develop immunity passport.
Privacy leakage Most of the privacy concerns have been discussed in the section 4 and one of the central point for
leaking privacy and bypassing the verification security is the secrecy of the secret key of the holder. This is possible
to obtain if the phone is jailbroken or rooted which might be the case for some of the phones especially the ones
with old unupdated operating systems. Furthermore, this could encourage the work in attacking the system layer of
security, however, it has been becoming increasingly difficult with the latest operating systems and the app can
enforce a minimum version of operating system to enforce higher security. The other possibility with this protocol is
that the result R of a user is shared permanently with the verifier which might not be a good idea if the result R
contains other sensitive information about the user as well. Hence, in our proposed protocol, we keep it limited to
only the test result of a user that does not hold much of significance once the pandemic is over.
Equity The proposed protocol relies on the smartphones that inevitably would lead to equity concerns. This would
be even more substantiated in the developing countries. Hence we want the stakeholders to be cognizant of this
aspect of the proposed protocol. The ongoing direction of this work is to adjust the verification scheme such that it
is supported by a paper based QR-code which can be given to the users who do not have access to the smartphones.
Behavioral changes One of the major unintended consequence of a health status based access could be to
attain immunity through risky pathways. Such a behavioral change could lead to more infection spread and fatalities
due to more number of people exposing themselves in order to get access to public places for their own self-
interest or financial reasons. This is one of the unintended consequence of the restricted access control that can not
be addressed entirely by the proposed technology.
7
5.2 Effectiveness of restricted access
Notwithstanding the above mentioned points, this work does not advocate for restricting access to individuals who
are not able to present their testing results due to different reasons. Rather, such a system could be used for data
collection and retrospective analysis for future interventions. One such example is public places increasing their risk
level if the total percentage of people entering the venue and showing the digital passport decline. A majority of the
community discussion around the restricted access has been on a binary level of whether to use it completely or not
at all. We hope that such systems can be introduced gradually and mindfully to the existing ecosystem such that it
allows decision making in data-driven manner and allow the technology to mature.
6 Conclusion
In this work, we present a protocol for testing verification for curbing the COVID-19 disease spread by restricting the
access to only recently tested individuals. The focus of this work is not on the actual deployment but rather protocol
design that circumvents some of the practical issues which existing systems have. We also discuss various unintended
consequences of such a platform and in what ways it can be addressed. This work does not advocate for immunity
passports but rather verification of testing results that would encourage testing and reduce the chance of infectious
individuals entering a public place.
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