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Calculus
==SECTION 4: FINITE STATE MODEL==
Topics in calculus
<P ALIGN=LEFT STYLE="margin-top: 0.19in; margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3><B><FONT SIZE=4>AS.04.01</FONT></B>The
Fundamental theorem | Function | Limits of functions | Continuity | Calculus with polynomials | Mean value theorem | Vector calculus | Tensor calculus
operation of the cryptographic module shall be specified using a </FONT></FONT></FONT>
</P>
Differentiation
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>finite
Product rule | Quotient rule | Chain rule | Implicit differentiation | Taylor's theorem | Related rates
state (or equivalent) represented by a state transition diagram </FONT></FONT></FONT>
</P>
Integration
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>and/or
Integration by substitution | Integration by parts | Integration by trigonometric substitution | Solids of revolution | Integration by disks | Integration by cylindrical shells | Improper integrals | Lists of integrals
a state transition table. (The state transition diagram and/or state </FONT></FONT></FONT>
</P>
For other uses of the term calculus see calculus (disambiguation)
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>transition
Calculus is a central branch of mathematics, developed from algebra and geometry, and built on two major complementary ideas.
table includes all operational and error states of the </FONT></FONT></FONT>
 
</P>
One concept is differential calculus. It studies rates of change, which are usually illustrated by the slope of a line. Differential calculus is based on the problem of finding the instantaneous rate of change of one quantity relative to another. Examples of typical differential calculus problems are finding the following quantities:
<P ALIGN=LEFT STYLE="margin-top: 0.08in; margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>cryptographic
 
module, the corresponding transitions from one state to </FONT></FONT></FONT>
The acceleration and speed of a free-falling body at a particular moment.
</P>
The loss in speed and trajectory of a fired projectile, such as an artillery shell or bullet.  
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>another,
Change in profitability over time of a growing business at a particular point in time.  
the input events that cause transitions from one state to </FONT></FONT></FONT>
The other key concept is integral calculus. It studies the accumulation of quantities, such as areas under a curve, linear distance traveled, or volume displaced. Examples of integral calculus problems include finding the following quantities:
</P>
 
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>another,
The amount of water pumped by a pump with a set power input but varying conditions of pumping losses and pressure.
and the output events resulting from transitions from one state </FONT></FONT></FONT>
The amount of money accumulated by a business under varying business conditions.  
</P>
The amount of parking lot plowed by a snowplow of given power with varying rates of snowfall.  
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>to
The two concepts, differentiation and integration, define inverse operations in a sense made precise by the fundamental theorem of calculus. In teaching calculus, either concept may be given priority. The usual educational approach is to introduce differential calculus first.
another.)</FONT></FONT></FONT></P>
 
<P ALIGN=LEFT STYLE="margin-top: 0.19in; margin-bottom: 0in"><FONT COLOR="#000080"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3><I><B>Assessment:</B></I></FONT></FONT></FONT></P>
Contents [hide]
<P ALIGN=LEFT STYLE="margin-top: 0.11in; margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3><B><FONT SIZE=4>AS.04.02</FONT></B>The
1 History
cryptographic module shall include the following operational and </FONT></FONT></FONT>
2 Differential calculus
</P>
3 Integral calculus
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>error
4 Foundations
states:</FONT></FONT></FONT></P>
5 Fundamental theorem of calculus
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>Power
6 Applications
on/off states. States for primary, secondary, or backup power.</FONT></FONT></FONT></P>
7 See also
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>These
8 Further reading
states may distinguish between power sources being applied to </FONT></FONT></FONT>
9 External links
</P>
<P ALIGN=LEFT STYLE="margin-top: 0.08in; margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>the
 
cryptographic module.</FONT></FONT></FONT></P>
 
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>Crypto
[edit]
officer states. States in which the crypto officer services are </FONT></FONT></FONT>
History
</P>
Main article: History of calculus
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>performed
 
(e.g., cryptographic initialization and key management).</FONT></FONT></FONT></P>
Though the origins of integral calculus are generally regarded as going no farther back than to the ancient Greeks, there is evidence that the ancient Egyptians may have harbored such knowledge as well. (See Moscow Mathematical Papyrus.) Eudoxus is generally credited with the method of exhaustion, which made it possible to compute the area and volume of regions and solids. Archimedes developed this method further, while also inventing heuristic methods which resemble modern day concepts. An Indian Mathematician, Bhaskara (1114-1185), gave an example of what is now called the "differential coefficient" and the basic idea of what is now known as "Rolle's theorem". The 14th century Indian mathematician Madhava along with other mathematicians of the Kerala school made major inroads into Calculus that were not repeated anywhere in the world until the 17th century by Newton and Leibniz. Leibniz and Newton are usually designated the inventors of calculus, mainly for their separate discoveries of the fundamental theorem of calculus and work on notation.
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>Key/CSP
 
entry states. States for entering cryptographic keys and </FONT></FONT></FONT>
There has been considerable debate about whether Newton or Leibniz was first to come up with the important concepts of calculus. The truth of the matter will likely never be known. Leibniz' greatest contribution to calculus was his notation; he often spent days trying to come up with the appropriate symbol to represent a mathematical idea. This controversy between Leibniz and Newton was unfortunate in that it divided English-speaking mathematicians from those in Europe for many years, setting back British analysis (i.e. calculus-based mathematics) for a very long time. Newton's terminology and notation was clearly less flexible than that of Leibniz, yet it was retained in British usage until the early 19th century, when the work of the Analytical Society successfully saw the introduction of Leibniz's notation in Great Britain. It is now thought that Newton had discovered several ideas related to calculus earlier than Leibniz had; however, Leibniz was the first to publish. Today, both Leibniz and Newton are considered to have discovered calculus independently.
</P>
 
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>CSPs
Lesser credit for the development of calculus is given to Barrow, Descartes, de Fermat, Huygens, and Wallis. A Japanese mathematician, Kowa Seki, lived at the same time as Leibniz and Newton and also elaborated some of the fundamental principles of integral calculus, though this was not known in the West at the time, and he had no contact with Western scholars. [1]
into the cryptographic module.</FONT></FONT></FONT></P>
 
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>User
[edit]
states. States in which authorized users obtain security services, </FONT></FONT></FONT>
Differential calculus
</P>
Main article: Derivative
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>perform
 
cryptographic operations, or perform other Approved or </FONT></FONT></FONT>
The derivative measures the sensitivity of one variable to small changes in another variable. Consider the formula:
</P>
 
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>non-Approved
for an object moving at constant speed.  
functions.</FONT></FONT></FONT></P>
One's speed in a car describes the change in location relative to the change in time. However, the speed itself may be changing and the formula above cannot account for that. Calculus deals with this more complex but natural and familiar situation.
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>Self-test
 
states. States in which the cryptographic module is </FONT></FONT></FONT>
Differential calculus determines the instantaneous speed, at any given specific instant in time, not just average speed during an interval of time. The formula Speed = Distance/Time applied to a single instant is the meaningless quotient "zero divided by zero". This is avoided, however, because the quotient Distance/Time is not used for a single instant (as in a still photograph), but for intervals of time that are very short.
</P>
 
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>performing
The derivative answers the question: as the elapsed time approaches zero, what does the average speed computed by Distance/Time approach? In mathematical language, this is an example of "taking a limit."
self-tests.</FONT></FONT></FONT></P>
 
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>Error
More formally, differential calculus defines the instantaneous rate of change (the derivative) of a mathematical function's value, with respect to changes of the variable. The derivative is defined as a limit of a difference quotient.
states. States when the cryptographic module has encountered </FONT></FONT></FONT>
 
</P>
The derivative of a function gives information about small pieces of its graph. It is directly relevant to finding the maxima and minima of a function — because at those points the graph is flat (i.e. the slope of the graph is zero). Another application of differential calculus is Newton's method, an algorithm to find zeroes of a function by approximating the function by its tangent lines. Differential calculus has been applied to many questions that are not first formulated in the language of calculus.
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>an
 
error (e.g., failed a self-test or attempted to encrypt when missing </FONT></FONT></FONT>
The derivative lies at the heart of the physical sciences. Newton's law of motion, Force = Mass × Acceleration, has meaning in calculus because acceleration is a derivative. Maxwell's theory of electromagnetism and Einstein's theory of gravity (general relativity) are also expressed in the language of differential calculus, as is the basic theory of electrical circuits and much of engineering.
</P>
 
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>operational
[edit]
keys or CSPs). Error states may include &quot;hard&quot; errors that </FONT></FONT></FONT>
Integral calculus
</P>
Main article: Integral
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>indicate
 
an equipment malfunction and that may require maintenance, </FONT></FONT></FONT>
The definite integral evaluates the cumulative effect of many small changes in a quantity. The simplest instance is the formula
</P>
 
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>service
or repair of the cryptographic module, or recoverable &quot;soft&quot;
for calculating the distance a car moves during a period of time when it is traveling at constant speed. The distance moved is the cumulative effect of the small distances moved in each of the many seconds the car is on the road. The calculus is able to deal with the natural situation in which the car moves with changing speed.
</FONT></FONT></FONT>
 
</P>
Integral calculus determines the exact distance traveled during an interval of time by creating a series of better and better approximations, called Riemann sums, that approach the exact distance.
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>errors
 
that may require initialization or resetting of the module.</FONT></FONT></FONT></P>
More formally, we say that the definite integral of a function on an interval is a limit of Riemann sum approximations.
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><BR>
 
</P>
Applications of integral calculus arise whenever the problem is to compute a number that is in principle (approximately) equal to the sum of the solutions of many, many smaller problems.
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>Note:
 
This assertion is tested as part of AS04.05.</FONT></FONT></FONT></P>
The classic geometric application is to area computations. In principle, the area of a region can be approximated by chopping it up into many very tiny squares and adding the areas of those squares. (If the region has a curved boundary, then omitting the squares overlapping the edge does not cause too great an error.) Surface areas and volumes can also be expressed as definite integrals.
<P ALIGN=LEFT STYLE="margin-top: 0.29in; margin-bottom: 0in"><FONT COLOR="#000080"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3><I><B>Assessment:</B></I></FONT></FONT></FONT></P>
 
<P ALIGN=LEFT STYLE="margin-top: 0.11in; margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3><B><FONT SIZE=4>AS.04.03</FONT></B>Recovery
Many of the functions that are integrated are rates, such as a speed. An integral of a rate of change of a quantity on an interval of time tells how much that quantity changes during that time period. It makes sense that if one knows their speed at every instant in time for an hour (i.e. they have an equation that relates their speed and time), then they should be able to figure out how far they go during that hour. The definite integral of their speed presents a method for doing so.
from error states shall be possible except for those caused by </FONT></FONT></FONT>
 
</P>
Many of the functions that are integrated represent densities. If, for example, the pollution density along a river (tons per mile) is known in relation to the position, then the integral of that density can determine how much pollution there is in the whole length of the river.
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>hard
 
errors that require maintenance, service, or repair of the </FONT></FONT></FONT>
Probability, the basis for statistics, provides one of the most important applications of integral calculus.
</P>
 
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>cryptographic
[edit]
module.</FONT></FONT></FONT></P>
Foundations
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><BR>
The rigorous foundation of calculus is based on the notions of a function and of a limit; the latter has a theory ultimately depending on that of the real numbers as a continuum. Its tools include techniques associated with elementary algebra, and mathematical induction.
</P>
 
<P ALIGN=LEFT STYLE="margin-top: 0.2in; margin-bottom: 0in"><FONT COLOR="#000080"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3><I><B>Assessment:</B></I></FONT></FONT></FONT></P>
The modern study of the foundations of calculus is known as real analysis. This includes full definitions and proofs of the theorems of calculus. It also provides generalisations such as measure theory and distribution theory.
<P ALIGN=LEFT STYLE="margin-top: 0.11in; margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3><B><FONT SIZE=4>AS.04.04</FONT></B>If
 
the cryptographic module contains a maintenance role, then a </FONT></FONT></FONT>
[edit]
</P>
Fundamental theorem of calculus
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>maintenance
The fundamental theorem of calculus states that differentiation and integration are, in a certain sense, inverse operations. More precisely, antiderivatives can be calculated with definite integrals, and vice versa.
state shall be included.</FONT></FONT></FONT></P>
 
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>Note:
This connection allows us to recover the total change in a function over some interval from its instantaneous rate of change, by integrating the latter.
This assertion is tested as part of AS04.05.</FONT></FONT></FONT></P>
 
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><BR>
This realization, made by both Newton and Leibniz, was key to the massive proliferation of analytic results after their work became known.
</P>
 
<P ALIGN=LEFT STYLE="margin-top: 0.03in; margin-bottom: 0in"><FONT COLOR="#000080"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3><I><B>Assessment:</B></I></FONT></FONT></FONT></P>
The fundamental theorem provides an algebraic method of computing many definite integrals --without performing limit processes--by finding formulas for antiderivatives. It is also a prototype solution of a differential equation. Differential equations relate an unknown function to its derivatives, and are ubiquitous in the sciences.
<P ALIGN=LEFT STYLE="margin-top: 0.11in; margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3><B><FONT SIZE=4>AS.04.05</FONT></B>Documentation
 
shall include a representation of the finite state (or </FONT></FONT></FONT>
1st Fundamental Theorem of Calculus: If a function f is continuous on the interval [a, b] and F is an antiderivative of f on the interval [a, b], then
</P>
 
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>equivalent)
using a state transition diagram and/or state transition table </FONT></FONT></FONT>
2nd Fundamental Theorem of Calculus: If f is continuous on an open interval I containing a, then, for every x in the interval,
</P>
 
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>that
shall specify:</FONT></FONT></FONT></P>
[edit]
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>*
Applications
all operational and error states of the cryptographic module,</FONT></FONT></FONT></P>
The development and use of calculus has had wide reaching effects on nearly all areas of modern living. It underlies nearly all of the sciences, especially physics. Virtually all modern developments such as building techniques, aviation, and other technologies make fundamental use of calculus. Many algebraic formulas now used for ballistics, heating and cooling, and other practical sciences were worked out through the use of calculus. In a handbook, an algebraic formula based on calculus methods may be applied without knowing its origins.
<P ALIGN=LEFT STYLE="margin-top: 0.08in; margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>*
 
the corresponding transitions from one state to another,</FONT></FONT></FONT></P>
The success of calculus has been extended over time to differential equations, vector calculus, calculus of variations, complex analysis, and differential topology.
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>*
the input events, including data inputs and control inputs, that
cause </FONT></FONT></FONT>
</P>
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>transitions
from one state to another, and</FONT></FONT></FONT></P>
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>*
the output events, including internal module conditions, data </FONT></FONT></FONT>
</P>
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>outputs,
and status outputs resulting from transitions from one state to </FONT></FONT></FONT>
</P>
<P ALIGN=LEFT STYLE="margin-top: 0.19in; margin-bottom: 0in"><FONT COLOR="#000080"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3><I><B>Assessment:</B></I></FONT></FONT></FONT></P>
==VE.04.05.01==
<P ALIGN=LEFT STYLE="margin-top: 0.11in; margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3><B><FONT SIZE=4>VE.04.05.01</FONT></B>The
vendor shall provide a description of the finite state model. This </FONT></FONT></FONT>
</P>
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>description
shall contain the identification and description of all states of</FONT></FONT></FONT></P>
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>the
module, and a description of all corresponding state transitions. </FONT></FONT></FONT>
</P>
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>The
descriptions of the state transitions shall include internal module </FONT></FONT></FONT>
</P>
<P ALIGN=LEFT STYLE="margin-top: 0.08in; margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>conditions,
data inputs and control inputs that cause transitions from </FONT></FONT></FONT>
</P>
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>one
state to another, data outputs and status outputs resulting from </FONT></FONT></FONT>
</P>
<P ALIGN=LEFT STYLE="margin-bottom: 0in"><FONT COLOR="#000000"><FONT FACE="Times New Roman, Times New Roman, serif"><FONT SIZE=3>transitions
from one state to another.</FONT></FONT></FONT></P>
[[Category:NSS]]

Latest revision as of 10:56, 28 January 2007

SECTION 4: FINITE STATE MODEL

AS.04.01The operation of the cryptographic module shall be specified using a

finite state (or equivalent) represented by a state transition diagram

and/or a state transition table. (The state transition diagram and/or state

transition table includes all operational and error states of the

cryptographic module, the corresponding transitions from one state to

another, the input events that cause transitions from one state to

another, and the output events resulting from transitions from one state

to another.)

Assessment:

AS.04.02The cryptographic module shall include the following operational and

error states:

Power on/off states. States for primary, secondary, or backup power.

These states may distinguish between power sources being applied to

the cryptographic module.

Crypto officer states. States in which the crypto officer services are

performed (e.g., cryptographic initialization and key management).

Key/CSP entry states. States for entering cryptographic keys and

CSPs into the cryptographic module.

User states. States in which authorized users obtain security services,

perform cryptographic operations, or perform other Approved or

non-Approved functions.

Self-test states. States in which the cryptographic module is

performing self-tests.

Error states. States when the cryptographic module has encountered

an error (e.g., failed a self-test or attempted to encrypt when missing

operational keys or CSPs). Error states may include "hard" errors that

indicate an equipment malfunction and that may require maintenance,

service or repair of the cryptographic module, or recoverable "soft"

errors that may require initialization or resetting of the module.


Note: This assertion is tested as part of AS04.05.

Assessment:

AS.04.03Recovery from error states shall be possible except for those caused by

hard errors that require maintenance, service, or repair of the

cryptographic module.


Assessment:

AS.04.04If the cryptographic module contains a maintenance role, then a

maintenance state shall be included.

Note: This assertion is tested as part of AS04.05.


Assessment:

AS.04.05Documentation shall include a representation of the finite state (or

equivalent) using a state transition diagram and/or state transition table

that shall specify:

* all operational and error states of the cryptographic module,

* the corresponding transitions from one state to another,

* the input events, including data inputs and control inputs, that cause

transitions from one state to another, and

* the output events, including internal module conditions, data

outputs, and status outputs resulting from transitions from one state to

Assessment:

VE.04.05.01

VE.04.05.01The vendor shall provide a description of the finite state model. This

description shall contain the identification and description of all states of

the module, and a description of all corresponding state transitions.

The descriptions of the state transitions shall include internal module

conditions, data inputs and control inputs that cause transitions from

one state to another, data outputs and status outputs resulting from

transitions from one state to another.