Information Security and Economics in Computer
Networks: An Interdisciplinary Survey anda Proposal of Integrated Optimization of Investment
Kanta MatsuuraInstitute of Industrial Science, University of Tokyo (Japan)

Abstract

When we take part in economic activities (e.g. e-commerce) over an open
computer network, we need information-security technologies. On the other
hand, applied cryptography also needs economic approaches a lot of security
breaches occur due to economically insucient incentive and the resultant mismanagement. Many users may feel uneasy about nancial uncertainty of security
threats. Information-security management is closely related with nancial decision making.
In response to the bi-directional relevance, cryptographers have recently noticed the importance of studying interdisciplinary area between information security and economics. This paper rstly shows a survey on the emerging area, as
well as statistics in the two apparently most relevant international conferences.
After that, as an example that is highly related to computational economics,
an integrated optimization of investment in information security and nancial
insurance is proposed. The author claims that the area involves good researchsubjects in computational economics.

Key words: information security, e-commerce, optimum investment, insurance.

1 Introduction
When we take part in economic activities (e.g. e-commerce) over an open computer network, we need information-security technologies. A good example is Secure Electronic
Transaction (SET) for on-line use of credit cards in the SET Specication Books1]{3],
we can see how signicant the role of information-security technologies is.
Prof. K. Matsuura, Institute of Industrial Science, University of Tokyo,
Komaba 4-6-1, Meguro-ku, Tokyo 153-8505, JAPAN. Tel.: +81-3-5452-6284, Fax.: +81-3-5452-6285,
E-mail: kanta@iis.u-tokyo.ac.jp
 Correspondence to:1

On the other hand, applied cryptography also needs economic approaches a lotof security breaches occur due to economically insu cient incentive and the resultant
mismanagement4], 5]. Many users may feel uneasy about nancial uncertainty of
security threats. Information-security management is closely related with nancial
decision making6].
In response to the bi-directional relevance, cryptographers have recently noticed
the importance of studying interdisciplinary area between information security andeconomics. For instance, the author started a series of studies on nancial risk management in crypto-based networks in early 20017]{12]. And then, in May 2002, theFirst Workshop on Economics and Information Security was held at University of California, Barkeley 13], 14]. They decided to have the second workshop in a more formal
way.
This paper rstly shows a survey on the emerging area, as well as statistics in the
two apparently most relevant international conferences, in Section 2. After that, as an
example that is highly related to computational economics, an integrated optimizationof investment in information security and nancial insurance is proposed in Section 3.
Finally Section 4 concludes the paper.

2 Information Security and Economics

2.1 Taxonomy

I categorize the interdisciplinary area into the following seven sub-areas. The rst
three might seem to have no direct relation with economics but I do not omit themhere because they are necessary when we see the trends in related conferences.

2.1.1 Primitives
We can nd cryptographic primitives whose major applications are economic activities (e.g. e-commerce) over an open computer network. A typical example is blind
signature15], 16]. In lots of digital-cash systems, anonymity is achieved by using blind
signature a bank can generate its digital signature on a digital coin without seeing therecipient information.
Although this category seems a bit far from economics, a famous international
conference, Financial Cryptography, accommodates a lot of papers on cryptographic
primitives17].

2.1.2 Protocols
More close to economics are cryptographic protocols for secure digital cash and electronic transactions 16], 18], 19], on-line auction20]{23], and digital tickets24]. Someof them strongly rely on existing nancial/transaction infrastructure such as credit-card
networks, while others do not.
We have to say that another type of cryptographic protocol is required for achieving
economically desirable social systems. For example, an empirical study in network2

economics25] shows that cost sharing through usage-sensitive pricing is eective formanaging Internet growth. This charging policy needs a support by cryptographicallysecure audit-log protocols 26]{31]. Without the cryptographic protocols, no one canverify the integrity of log entries in order to solve possible dispute settlement.

2.1.3 Enhancing Circulation

In order to enhance the market of digital objects, we need mechanisms which protect
digital rights with respect to digital contents and softwares32]{36] as a total system,
Digital Rights Management (DRM) enables an electronic marketplace where previously
unimaginable/impossible business models can be designed and implemented.
Social-scientic analysis and optimization of digital-right management systems areimportant as well37], 38]. Discussion in this respect brings a lot of open problems
mainly due to immature study on the mechanism and eects of monopoly related to digital
copyright protectionand the ongoing fragmentation of intellectual property rights.

2.1.4 Modeling
In information-security management, a di cult task is to nd good measures of security, vulnerability, and related properties (i) the value of the protected information,(ii) the threat to that information, and (iii) the assurance level are extremely importantto quantify39]. Therefore, how to price information-security service is an importantand di cult task.
When we tackle those problems, it is worth trying to study modeling based on
economic approaches. For example, nancial cost required for successful attacks could
be used as a good measure of system security40]. The author's recent framework to
price \(information-)security securities" is based on stochastic models similar to thosein nancial theory7]{12]. The intrinsic dierence from conventional nance is in thedenition of objects in crypto-based networks that is, uncertain digital objects aremodelled as follows.

Denition 2.1 (Setok) A security token or setok is a digital material which nominally contains the following four attributes:
 contents which may include MAC (Message Authentication Code), digital sig-

natures, or other security-related control sequences if necessary, a non-negative explicit price (denoted by S) which is paid when the setok ispurchased by a customer,3 a set of non-negative explicit values (denoted by V1 , V2 ,   , Vm where m isreferred to as the dimension of the explicit values) which represent some qualitiesof the contents in a way that larger values of each element imply better qualities
regarding the feature represented by the element when the setok is purchased, and a timestamp which indicates when the setok is purchased,
and is associated with
 a non-negative implicit price (denoted by S ) and a set of non-negative implicit values (denoted by V1 , V2 ,   , Vn where n isreferred to as the dimension of the implicit values)in the following way.
 The explicit price is specied as the occurrence of a price-interpretation process Y (t)=y (t S (t)) i.e. the specic numerical value y (t0  S (t0)) is written as
the explicit price of the setok which is purchased at time t = t0 . Each occurrence of the price-interpretation process is called the up-to-date price at timet. The price-interpretation process is a non-negative process and also called the
up-to-date price process. y(t s) is called a price-interpretation function
and monotone increasing with respect to s. Customers are unable to change theexplicit price.
 The explicit values are specied as the occurrences of value-interpretation processes H1(t)=h1(t, V1(t), V2(t),   , Vn(t)), H2 (t)=h2(t, V1(t), V2(t),   , Vn(t)),
  , Hm (t)=hm (t, V1 (t), V2 (t),   , Vn (t)) i.e. the specic numerical value hi (t0 ,V1(t0 ), V2(t0),   , Vn(t0 )) is written as the i-th explicit value of the setok which
is purchased at time t = t0 (i = 1, 2,   , m). Each occurrence hi (t, V1(t), V2 (t),  , Vn (t)) is called the i-th up-to-date value at time t. The value-interpretation
processes are non-negative processes, and also called the up-to-date value processes. h1 (t, v1 , v2,   , vn), h2 (t, v1 , v2,   , vn),   , hm(t, v1, v2 ,   , vn ) arecalled value-interpretation functions. Customers are unable to change theexplicit values.
Customers in open networks are distrusted. Depending on the payment scheme,
customers may be even anonymous when they buy setoks. So each payment must be
settled on site in exchange of the corresponding pieces of the setok. This should bedone in a secure way we have to ensure that no customer can exploit a setok without
payment, and that no server can exploit a payment without sending the setok. Due tothe security requirements, actual protocols would use digital signature. Each digital
signature is generated on a particular piece of object. Thus setoks are transmitted tocustomers in discrete pieces e.g. \three pieces" are possible but \two and a half
pieces" are impossible. A piece of setok will be referred to as a share of the setok.
The price-interpretation function can model the eect of taxes, transaction costs,
regulatory issues, and so on. The value-interpretation functions can model the eect of
security policies, regulatory issues, editorial policies of nancial reports, transmission
delay, and so on.

42.1.5 Motivation/Incentive
In the First Workshop on Economics and Information Security, participants discussed a
lot on how to provide economic incentives to deploy information-security mechanisms41].
The discussion included
 cost reduction by standardization in information-security industry42],
 cost-benet ratio of privacy-enhancing technologies43], and an optimization of more general cost-benet ratio by introducing quantied e ort
and successful outcome44].
Apparently opposite but in practice similar approach is the use of discouragementenhancing the cost of attack can discourage malicious entities from attacking 45]{ 50].
Liability transfer with respect to information security is related with this approach,too51].

2.1.6 Information-Security Market

There are at least two approaches for studying information-security market.
The rst one is optimization of investment to information security. The existing
reports discuss nothing but investment amount at a single time interval 52]{54]. They
are obviously in their infancy I recommend researchers to take time-series approaches
similar to real-option studies55], 56].
The second approach is a more basic research to discuss market mechanisms in
information-security industry. The di culty of this approach is said to be from relatively strange regulation issues 57].

2.1.7 Economic/Social Infrastructure
Information-security in computer networks requires technological infrastructures suchas
 Public-Key Infrastructure (PKI) 58], 59],
 routing infrastructure60], and Domain Name System (DNS)61].
Protection of those infrastructures themselves is also important62], 63]. In addition,
if users want to feel easier, they need appropriate economic/social infrastructures suchas
 information-security insurance 64]{66],
 security securities67], or nancial derivatives on information-security objects 7]{12], and social mechanisms for promoting information dissemination and collection regarding information security6].
5

2.2 Trend in Related Conferences

According to the taxonomy presented in 2.1, let us see the recent trend in two international conferences: the Fifth International Conference of Financial Cryptography in2001 (FC01) as a representative of conventional studies, and the First Workshop on
Economics and Information Security in 2002 (WEIS02) as a representative of emerging(more interdisciplinary) studies. The number of research papers in those conferenceswere quite similar (27 in the former while 25 in the latter). Table 1 shows the distribution of the papers the change from FC01 to WEIS02 suggests the emerging importanceof relationship between economics and information security.
Table 1: Taxonomy of research papers presented at Financial Cryptography 2001
(FC01) and Workshop on Economics and Information Security 2002 (WEIS02).
Class
Primitives
Protocols
Enhancing Circulation
Modeling
Motivation/Incentive
Information-Security Market
Economic/Social Infrastructure

FC01
33.3%
33.3%
18.5%
7.4%
3.7%
0.0%
3.7%

WEIS02
0.0%
0.0%
4.0%
24.0%
32.0%
32.0%
8.0%

3 Investment in Information Security
Among the interdisciplinary studies reviewed above, optimization problems would interest researchers in computational economics a lot. One of the most clear optimization
issues is a theory on information-security investment by Gordon and Loeb52]. The
theory is based on a simple model with a single decision variable. Although the theory
provides an important step toward more advanced security management, it fails toincorporate an important variable into the model: that is, information-security insurance. Hence, in this section, after a brief review of the model (Gordon-Loeb model),an extension for simultaneous optimization of insurance will be proposed.

3.1 Gordon-Loeb Model

Gordon and Loeb52] presented an economic model that determines the optimal amountof a rm's investment for protecting a set of information in a single-period model. An
information set is characterized by the following three parameters:
 : the monetary loss conditioned on a breach occurring.
t : the probability of a threat occurring.
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v : the vulnerability, dened as the probability that a threat once realized (i.e., an
attack) would be successful.
Although the three parameters can change over time in the real world, Gordon-Loebmodel assumes them as pre-estimated constants.
Let S (z v) denote the probability that an information set with vulnerability v
will be breached, conditional on the realization of a threat and given that the rm
has made an information-security investment of z to protect that information set. The
function S (z v) is referred to as the security-breach probability function. As is common
with nearly all economic models, S (z v) is assumed to be su ciently smooth and well
behaved, continuously twice dierentiable in particular.
In addition to a general theory, Gordon and Loeb studied several classes of securitybreach probability functions. One of them is given by
S (z v) = vz+1(1)where the parameter (> 0) is a measure of the productivity of information security. For this class, we can derive a closed-form solution to an optimization problem
which maximizes the expected net benets from an investment in information security(ENBIS) dened as
ENBIS = fv ; S (z v)g t ; z:(2)That is, the optimum investment is given byln v)g :(3)z = z (v) = ln f;1=(vt
ln v

3.2 A Proposal of Integrated Optimization

In Gordon-Loeb model, there are at least two substantial restrictions.
1. The loss  is treated as a constant. This suggests that the investment studied
in the model is restricted to hardware/software technologies and management
services of information security.
2. The investment z is continuous, and hence the investment subjects are treated
not as discrete pieces but as a whole.
If we strictly conform to the restrictions above, we would nd it di cult to have decision
making with respect to information-security insurance. So in the following, I propose
an extension for integrating the investment optimization with the insurance decision
making.
With respect to the restriction 1, we want to incorporate compensation by insurance. Suppose that investment in insurance reduces the loss. This implies that theloss is not a constant but a variable which can change according to the investment in
information-security insurance.
With respect to the restriction 2, we want to incorporate a discrete nature of insurance we have to choose an insurance contract from a countable and nite set of
possible choices.
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The two observations above lead us to the following integration.
Suppose that there are m possible choices of insurance contracts. Let the i-th
choice costs zi ( 0) (i = 1 2     m). And let (0 ) i ( ) (i = 1 2     m) be theloss reduction achieved by the insurance1 . Then we solve the following optimization
problem:max fv ; S (z v)] t ( ; i) ; z ; zi g :(4)
i2f12mgz0
Our goal is to nd the optimum solution (i z ) for this problem.
For the class of security-breach probability functions dened by Eq. (1), we canderive the following theorem.

Theorem 3.1 (Solution for the Integrated Optimization Problem)

Assume that the introduction of insurance does not change the productivity of information security. Let the optimum investment including insurance be (i  z  ). Then, i isdetermined by the exhaustive search with respect to i for nding the maximum of( ; i) ln v)g ; z :vt ( ; i) + 1 ; ln f;1= (vtiln v
And then z  is given byz = ln f;1= (vt (ln v; i ) ln v)g :(Proof in Brief) For a given choice of insurance i,( ; i) ln v)gz = zi (v) = ln f;1= (vt ln v(5)

maximizes the ENBIS. Insert Eq. (5) into the integrated optimization problem (4). 2

4 Concluding Remarks
The rst part of this paper surveyed the interdisciplinary area between information
security and economics. We categorized the area into seven sub-areas: (1) primitives,(2) protocols, (3) enhancing circulation, (4) modeling, (5) motivation/incentive, (6)information-security market, and (7) economic/social infrastructure. The statistics
in the two apparently most relevant international conferences suggest the emerging
importance of relationship between economics and information security.
After the survey and analysis, an integrated optimization of investment in information security and nancial insurance was proposed. Since most users would thinkof insurance as their nal defences, security management integrated with insurance isquite important. When we proceed to more complicated models (e.g. multiple-period
models) for such management, there would arise a lot of research topics in the areaof computational economics. The author hopes that this paper brings a good starting
point.
1 zi=  = 0 indicates that the i-th choice is \no insurance."i8References
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