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Thus, the system might not be 100% secure In addition, the system might also be vulnerable to attacks not thought of during the design phase Other factors that govern the design include the risks and returns to the attacker as well as the degree of risk that is acceptable to the defender Even though cryptography is one of the main means that security engineers use for protecting information systems, it is not the only tool that can be used for such a task Other technical measures such as biometrics or steganography can also be used In addition, legal measures such as liability regulations or insurance might also be necessary to protect systems Organizational measures such as proper security policies and correct information classi cation also play an important part in ensuring the security of the system Peoplerelated measures such as screening, motivation, and education also cannot be ignored In this book, though, our focus will mainly be on using cryptographic tools to achieve the desired security objectives for protecting information systems Hence it is vital to understand the various cryptographic concepts, and this is the objective of this chapter We start off by looking at the basic concepts of cryptography in Section 22 We look at the various objectives that are attainable using various cryptographic mechanisms We also discuss the fundamental cryptographic mechanisms Readers familiar with the basic concepts of cryptography can skip this section Note that our objective is to give a brief overview of the various cryptographic concepts Readers who need more details should refer to other material [7] These concepts are used in several other places in the book

2 j(r 1+H) (x)

If X is self-similar in the usual sense, then this decomposition is a renormalized distribution of mass, as de ned in section 513

In identifying project stakeholders (Figure 71), we need to go beyond the project organization s internal environment to determine which external stakeholder groups can impact our operations and the degree to which they are able to influence the project s implementation Internal stakeholders are a vital component in any stakeholder analysis and their impact is usually felt in relatively positive ways; that is, while serving as limiting and controlling influences, most internal stakeholders do want to see the project developed successfully On the other hand, external stakeholder groups may operate in a manner that is hostile to project development Consider

5252 Gaussian hyperbolic process THEOREM 57 With the same notations as those of Theorem 56, we obtain the decomposition: X(x) =

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where the sequence 1 ,, d consists of normalized Gaussian random 2D variables Hyperbolic processes enable us to model multiscale random structures, with preferred directions 526 Renormalization of sums of correlated random variable Let BH denote fractional Brownian motion of parameter H Let us consider the increments of size h > 0: Xk = h H (BH ((k + 1)h) BH (kh)) The following properties are well-known: X0 is a normalized Gaussian random variable; the sequence (Xk ) is stationary; a law of large numbers can be written as: 1 n + n + 1 lim

Cryptographic mechanisms are designed in order to achieve certain objectives These objectives are typically referred to as the attributes associated with the cryptographic mechanism We start this section by explaining some of the attributes in Section 221 We then explain the various mechanisms that cryptography provides in order to achieve these objectives (attributes) in Section 222 221 Attributes

(as)

(59)

Dif culties only start when trying to estimate the convergence speed in (59) Before exhibiting the results of these questions, let us give an outline of the Rosenblatt process and law The Rosenblatt law is de ned by its characteristic data function, which can be found in [TAQ 75, p 299] We can de ne a stochastic process (ZD (t))t>0 called the Rosenblatt process whose law in every moment is a Rosenblatt law of parameter D We can nd the functional characteristic of (ZD (t1 ), , ZD (tk )), with k 1, in [TAQ 75] 527 Convergence towards fractional Brownian motion 5271 Quadratic variations Many statistical estimation procedures are based on quadratic variations It is hence useful to recall quadratic variations of fractional Brownian motion THEOREM 58 Let: Xk,N = N H BH k+1 N BH k N

be the renormalized increments of a fractional Brownian motion of order H The following results are proven in [GUY 89, TAQ 75]: when 0 < H < 3 : 4

The security techniques that we explain later have been designed with one or more attributes in mind There are several attributes but the following form the basic set This is because the other objectives can be derived from these basic ones:

[N t]

Page 147 the case in which a city is seeking to upgrade its subway system, adding new lines and improving facilities There is a strong potential for those who are interested in preserving antiquities to actively resist the completion of such a project if they perceive that the tunnel digging could be destroying valuable artifacts Cleland refers to these types of external stakeholders as intervenor groups and demonstrates that they have the potential to pose a major threat to the successful completion of projects6 Among the set of project stakeholders that project managers must consider are included: Internal

2 (Xk,N 1)

converges in law, when N + , towards H BH (t), where BH is fractional Brownian motion of order H; for 3 < H < 1: 4

[N t]

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