Network Working Group H. Tschofenig Request for Comments: 4081 D. Kroeselberg Category: Informational Siemens June 2005 Security Threats for Next Steps in Signaling (NSIS)
Status of This Memo
This memo provides information for the Internet community. It does
not specify an Internet standard of any kind. Distribution of this
memo is unlimited.
Copyright Notice
Copyright (C) The Internet Society (2005).
Abstract
This threats document provides a detailed analysis of the security
threats relevant to the Next Steps in Signaling (NSIS) protocol
suite. It calls attention to, and helps with the understanding of,
various security considerations in the NSIS Requirements, Framework, and Protocol proposals. This document does not describe
vulnerabilities of specific parts of the NSIS protocol suite.
Table of Contents
1. Introduction (2)
2. Communications Models (3)
3. Generic Threats (7)
3.1. Man-in-the-Middle Attacks (8)
3.2. Replay of Signaling Messages (11)
3.3. Injecting or Modifying Messages (11)
3.4. Insecure Parameter Exchange and Negotiation (12)
4. NSIS-Specific Threat Scenarios (12)
4.1. Threats during NSIS SA Usage (13)
4.2. Flooding (13)
4.3. Eavesdropping and Traffic Analysis (15)
4.4. Identity Spoofing (15)
4.5. Unprotected Authorization Information (17)
4.6. Missing Non-Repudiation (18)
4.7. Malicious NSIS Entity (19)
4.8. Denial of Service Attacks (20)
4.9. Disclosing the Network Topology (21)
4.10. Unprotected Session or Reservation Ownership (21)
4.11. Attacks against the NTLP (23)
Tschofenig & Kroeselberg Informational [Page 1]
5. Security Considerations (23)
6. Contributors (24)
7. Acknowledgements (24)
8. References (25)
8.1. Normative References (25)
8.2. Informative References (25)
1. Introduction
Whenever a new protocol is developed or existing protocols are
modified, threats to their security should be evaluated. To address security in the NSIS working group, a number of steps have been
taken:
NSIS Analysis Activities (see [RSVP-SEC] and [SIG-ANAL])
Security Threats for NSIS
NSIS Requirements (see [RFC3726])
NSIS Framework (see [RFC4080])
NSIS Protocol Suite (see GIMPS [GIMPS], NAT/Firewall NSLP
[NATFW-NSLP] and QoS NSLP [QOS-NSLP])
This document identifies the basic security threats that need to be
addressed during the design of the NSIS protocol suite. Even if the base protocol is secure, certain extensions may cause problems when
used in a particular environment.
This document cannot provide detailed threats for all possible NSIS
Signaling Layer Protocols (NSLPs). QoS [QOS-NSLP], NAT/Firewall
[NATFW-NSLP], and other NSLP documents need to provide a description of their trust models and a threat assessment for their specific
application domain. This document aims to provide some help for the subsequent design of the NSIS protocol suite. Investigations of
security threats in a specific architecture or context are outside
the scope of this document.
We use the NSIS terms defined in [RFC3726] and in [RFC4080]. Tschofenig & Kroeselberg Informational [Page 2]
2. Communications Models
The NSIS suite of protocols is envisioned to support various
signaling applications that need to install and/or manipulate state
at nodes along the data flow path through the network. As such, the NSIS protocol suite involves the communication between different
entities.
This section offers terminology for common communication models that are relevant to securing the NSIS protocol suite.
An abstract network topology with its administrative domains is shown in Figure 1, and in Figure 2 the relationship between NSIS entities
along the path is shown. For illustrative reasons, only end-to-end
NSIS signaling is depicted, yet it might be used in other variations as well. Signaling can start at any place and might terminate at any other place within the network. Depending on the trust relationship between NSIS entities and the traversed network parts, different
security problems arise.
The notion of trust and trust relationship used in this document is
informal and can best be captured by the definition provided in
Section 1.1 of [RFC3756]. For completeness we include the definition of a trust relationship, which denotes a mutual a priori relationship between the involved organizations or parties wherein the parties
believe that the other parties will behave correctly even in the
future.
An important observation for NSIS is that a certain degree of trust
has to be placed into intermediate NSIS nodes along the path between an NSIS Initiator and an NSIS Responder, specifically so that they
perform message processing and take the necessary actions. A
complete lack of trust between any of the participating entities will cause NSIS signaling to fail.
Note that it is not possible to describe a trust model completely
without considering the details and behavior of the NTLP, the NSLP
(e.g., QoS NSLP), and the deployment environment. For example,
securing the communication between an end host (which acts as the
NSIS Initiator) and the first NSIS node (which might be in the
attached network or even a number of networks away) is impacted by
the trust relationships between these entities. In a corporate
network environment, a stronger degree of trust typically exists than in an unmanaged network.
Figure 1 introduces convenient abbreviations for network parts with
similar properties: first-peer, last-peer, intra-domain, or
inter-domain.
Tschofenig & Kroeselberg Informational [Page 3]
+------------------+ +---------------+ +------------------+
| | | | | |
| Administrative | | Intermediate | | Administrative |
| Domain A | | Domains | | Domain B |
| | | | | |
| (Inter-domain Communication) |
| +-------->+---+<------------->+---+<--------+ |
| (Intra-domain | | | | (Intra-domain |
| Communication) | | | | Communication) |
| | | | | | | |
| v | | | | v |
+--------+---------+ +---------------+ +---------+--------+
^ ^
| |
First Peer Communication Last Peer Communication
| |
v v
+-----+-----+ +-----+-----+
| NSIS | | NSIS |
| Initiator | | Responder |
+-----------+ +-----------+
Figure 1: Communication patterns in NSIS
First-Peer/Last-Peer Communication:
The end-to-end communication scenario depicted in Figure 1
includes the communication between the end hosts and their nearest NSIS hops. "First-peer communications" refers to the peer-to-peer interaction between a signaling message originator, the NSIS
Initiator (NI), and the first NSIS-aware entity along the path.
This "first-peer communications" commonly comes with specific
security requirements that are especially important for addressing security issues between the end host (and a user) and the network it is attached to.
To illustrate this, in roaming environments, it is difficult to
assume the existence of a pre-established security association
directly available for NSIS peers involved in first-peer
communications, because these peers cannot be assumed to have any pre-existing relationship with each other. In contrast, in
enterprise networks usually there is a fairly strong
(pre-established) trust relationship between the peers.
Enterprise network administrators usually have some degree of
freedom to select the appropriate security protection and to
enforce it. The choice of selecting a security mechanism is
therefore often influenced by the infrastructure already
Tschofenig & Kroeselberg Informational [Page 4]
available, and per-session negotiation of security mechanisms is
often not required (although, in contrast, it is required in a
roaming environment).
Last-Peer communication is a variation of First-Peer communication in which the roles are reversed.
Intra-Domain Communication:
After verification of the NSIS signaling message at the border of an administrative domain, an NSIS signaling message traverses the network within the same administrative domain to which the first
peer belongs. It might not be necessary to repeat the
authorization procedure of the NSIS initiator again at every NSIS node within this domain. Key management within the administrative domain might also be simpler.
Security protection is still required to prevent threats by
non-NSIS nodes in this network.
Inter-Domain Communication:
Inter-Domain communication deals with the interaction between
administrative domains. For some NSLPs (for example, QoS NSLP),
this interaction is likely to take place between neighboring
domains, whereas in other NSLPs (such as the NAT/Firewall NSLP),
the core network is usually not involved.
If signaling messages are conveyed transparently in the core
network (i.e., if they are neither intercepted nor processed in
the core network), then the signaling message communications
effectively takes place between access networks. This might place a burden on authorization handling and on the key management
infrastructure required between these access networks, which might not know of each other in advance.
To refine the above differentiation based on the network parts that
NSIS signaling may traverse, we subsequently consider relationships
between involved entities. Because a number of NSIS nodes might
actively participate in a specific protocol exchange, a larger number of possible relationships need to be analyzed than in other
protocols. Figure 2 illustrates possible relationships between the
entities involved in the NSIS protocol suite.
Tschofenig & Kroeselberg Informational [Page 5]
****************************************
* *
+----+-----+ +----------+ +----+-----+
+-----+ NSIS +-------+ NSIS +--------+ NSIS +-----+
| | Node 1 | | Node 2 | | Node 3 | |
| +----------+ +----+-----+ +----------+ |
| ? |
| ???????????????????????????? |
| ? |
+--+--+-----+ +---------+-+ | NSIS +//////////////////////////////////////////+ NSIS | | Initiator | | Responder | +-----------+ +-----------+ Legend:
-----: Peer-to-Peer Relationship
/////: End-to-End Relationship
*****: Middle-to-Middle Relationship
?????: End-to-Middle Relationship
Figure 2: Possible NSIS Relationships
End-to-Middle Communications:
The scenario in which one NSIS entity involved is an end-entity
(Initiator or Responder) and the other entity is any intermediate hop other than the immediately adjacent peer is typically called
the end-to-middle scenario (see Figure 2). A motivation for
including this scenario can, for example, be found in SIP
[RFC3261].
An example of end-to-middle interaction might be an explicit
authorization from the NSIS Initiator to some intermediate node.
Threats specific to this scenario may be introduced by some
intermediate NSIS hops that are not allowed to eavesdrop or modify certain objects.
Middle-to-Middle Communications:
Middle-to-middle communication refers to the exchange of
information between two non-neighboring NSIS nodes along the path. Intermediate NSIS hops may have to deal with specific security
threats that do not involve the NSIS Initiator or the NSIS
Responder directly.
Tschofenig & Kroeselberg Informational [Page 6]
End-to-End Communications:
NSIS aims to signal information from an Initiator to some NSIS
nodes along the path to a data receiver. In the case of
end-to-end NSIS signaling, the last node is the NSIS Responder, as it is the data receiver. The NSIS protocol suite is not an
end-to-end protocol used to exchange information purely between
end hosts.
Typically, it is not required to protect NSIS messages
cryptographically between the NSIS Initiator and the NSIS
Responder. Protecting the entire signaling message end-to-end
might not be feasible since intermediate NSIS nodes need to add,
inspect, modify, or delete objects from the signaling message.
3. Generic Threats
This section provides scenarios of threats that are applicable to
signaling protocols in general. Note that some of these scenarios
use the term "user" instead of "NSIS Initiator". This is mainly
because security protocols allow differentiation between entities
that are hosts and those that are users (based on the identifiers
used).
For the following subsections, we use the general distinction in two cases in which attacks may occur. These are according to the
separate steps, or phases, normally encountered when applying
protocol security (with, e.g., IPsec, TLS, Kerberos, or SSH).
Therefore, this section starts by briefly describing a motivation for this separation.
Security protection of protocols is often separated into two steps.
The first step primarily provides entity authentication and key
establishment (which result in a persistent state often called a
security association), whereas the second step provides message
protection (some combination of data origin authentication, data
integrity, confidentiality, and replay protection) using the
previously established security association. The first step tends to be more expensive than the second, which is the main reason for the
separation. If messages are transmitted infrequently, then these two steps may be collapsed into a single and usually rather costly one.
One such example is e-mail protection via S/MIME. The two steps may be tightly bound into a single protocol, as in TLS, or defined in
separate protocols, as with IKE and IPsec. We use this separation to cover the different threats in more detail.
Tschofenig & Kroeselberg Informational [Page 7]
3.1. Man-in-the-Middle Attacks
This section describes both security threats that exist if two peers do not already share a security association or do not use security
mechanisms at all, and threats that are applicable when a security
association is already established.
Attacks during NSIS SA Establishment:
While establishing a security association, an adversary fools the signaling message Initiator with respect to the entity to which it has to authenticate. The Initiator authenticates to the man-in-
the-middle adversary, who is then able to modify signaling
messages to mount DoS attacks or to steal services that get billed to the Initiator. In addition, the adversary may be able to
terminate the Initiator’s NSIS messages and to inject messages to a peer itself, thereby acting as the peer to the Initiator and as the Initiator to the peer. As a result, the Initiator wrongly
believes that it is talking to the "real" network, whereas it is
actually attached to an adversary. For this attack to be
successful, pre-conditions that are described in the following
three cases have to hold:
Missing Authentication:
In the first case, this threat can be carried out because of
missing authentication between neighboring peers: without
authentication, an NI, NR, or NF is unable to detect an
adversary. However, in some practical cases, authentication
might be difficult to accomplish, either because the next peer is unknown, because there are misbelieved trust relationships
in parts of the network, or because of the inability to
establish proper security protection (inter-domain signaling
messages, dynamic establishment of a security association,
etc.). If one of the communicating endpoints is unknown, then for some security mechanisms it is either impossible or
impractical to apply appropriate security protection.
Sometimes network administrators use intra-domain signaling
messages without proper security. This configuration allows an adversary on a compromised non-NSIS-aware node to interfere
with nodes running an NSIS signaling protocol. Note that this type of threat goes beyond those caused by malicious NSIS nodes (described in Section 4.7).
Tschofenig & Kroeselberg Informational [Page 8]
Unilateral Authentication:
In the case of unilateral authentication, the NSIS entity that does not authenticate its peer is unable to discover a man-in- the-middle adversary. Although mutual authentication of
signaling messages should take place between each peer
participating in the protocol operation, special attention is
given here to first-peer communications. Unilateral
authentication between an end host and the first peer (just
authenticating the end host) is still common today, but it
opens up many possibilities for man-in-the-middle attackers
impersonating either the end host or the (administrative domain represented by the) first peer.
Missing or unilateral authentication, as described above, is
part of a general problem of network access with inadequate
authentication, and it should not be considered something
unique to the NSIS signaling protocol. Obviously, there is a
strong need to address this correctly in a future NSIS protocol suite. The signaling protocols addressed by NSIS are different from other protocols in which only two entities are involved.
Note that first-peer authentication is especially important
because a security breach there could impact nodes beyond the
entities directly involved (or even beyond a local network).
Finally, note that the signaling protocol should be considered a peer-to-peer protocol, wherein the roles of Initiator and
Responder can be reversed at any time. Thus, unilateral
authentication is not particularly useful for such a protocol. However, some form of asymmetry might be needed in the
authentication process, whereby one entity uses an
authentication mechanism different from that of the other one. As an example, the combination of symmetric and asymmetric
cryptography should be mentioned.
Weak Authentication:
In the case of weak authentication, the threat can be carried
out because information transmitted during the NSIS SA
establishment process may leak passwords or allow offline
dictionary attacks. This threat is applicable to NSIS for the process of selecting certain security mechanisms.
Finally, we conclude with a description of a man-in-the-middle (MITM) attack during the discovery phase. This attack benefits from the
fact that NSIS nodes are likely to be unaware of the network Tschofenig & Kroeselberg Informational [Page 9]
topology. Furthermore, an authorization problem might arise if an
NSIS QoS NSLP node pretends to be an NSIS NAT/Firewall-specific node or vice versa.
An adversary might inject a bogus reply message, forcing the
discovery message initiator to start a messaging association
establishment with either an adversary or with another NSIS node that is not along the path. Figure 3 describes the attack in more detail for peer-to-peer addressed messages with a discovery mechanism. For end-to-end addressed messages, the attack is also applicable,
particularly if the adversary is located along the path and able to
intercept the discovery message that traverses the adversary. The
man-in-the-middle adversary might redirect to another legitimate NSIS node. A malicious NSIS node can be detected with the corresponding
security mechanisms, but a legitimate NSIS node that is not the next NSIS node along the path cannot be detected without topology
knowledge.
+-----------+ Messaging Association
Message | Adversary | Establishment
Association +--->+ +<----------------+
Establish- | +----+------+ |(4)
ment | IPx | |
(3)| |Discovery Reply v
| | (IPx) +---+-------+
v | (2) | NSIS |
+------+-----+ | /----------->+ Node B +--------
| NSIS +<--+ / Discovery +-----------+
| Node A +---------/ Request IPr
+------------+ (1)
IPi
Figure 3: MITM Attack during the Discovery Exchange
This attack assumes that the adversary is able to eavesdrop on the
initial discovery message sent by the sender of the discovery
message. Furthermore, we assume that the discovery reply message by the adversary returns to the discovery message initiator faster than the real response. This represents some race condition
characteristics if the next NSIS node is very close (in IP-hop terms) to the initiator. Note that the problem is self-healing since the
discovery process is periodically repeated. If an adversary is
unable to mount this attack with every discovery message, then the
correct next NSIS node along the path will be discovered again. A
ping-pong behavior might be the consequence.
Tschofenig & Kroeselberg Informational [Page 10]
As shown in message step (2) in Figure 3, the adversary returns a
discovery reply message with its own IP address as the next NSIS-
aware node along the path. Without any additional information, the
discovery message initiator has to trust this information. Then a
messaging association is established with an entity at a given IP
address IPx (i.e., with the adversary) in step (3). The adversary
then establishes a messaging association with a further NSIS node and forwards the signaling message. Note that the adversary might just
modify the Discovery Reply message to force NSIS Node A to establish a messaging association with another NSIS node that is not along the path. This can then be exploited by the adversary. The interworking with NSIS-unaware NATs in particular might cause additional
unexpected problems.
As a variant of this attack, an adversary not able to eavesdrop on
transmitted discovery requests could flood a node with bogus
discovery reply messages. If the discovery message sender
accidentally accepts one of those bogus messages, then a MITM attack as described in Figure 3 is possible.
3.2. Replay of Signaling Messages
This threat scenario covers the case in which an adversary
eavesdrops, collects signaling messages, and replays them at a later time (or at a different place, or uses parts of them at a different
place or in a different way; e.g., cut-and-paste attacks). Without
proper replay protection, an adversary might mount man-in-the-middle, denial of service, and theft of service attacks.
A more difficult attack (that may cause problems even if there is
replay protection) requires that the adversary crash an NSIS-aware
node, causing it to lose state information (sequence numbers,
security associations, etc.), and then replay old signaling messages. This attack takes advantage of re-synchronization deficiencies.
3.3. Injecting or Modifying Messages
This type of threat involves integrity violations, whereby an
adversary modifies signaling messages (e.g., by acting as a
man-in-the-middle) in order to cause unexpected network behavior.
Possible actions an adversary might consider for its attack are
reordering, delaying, dropping, injecting, truncating, and otherwise modifying messages.
An adversary may inject a signaling message requesting a large amount of resources (possibly using a different user’s identity). Other
resource requests may then be rejected. In combination with identity Tschofenig & Kroeselberg Informational [Page 11]
spoofing, it is possible to carry out fraud. This attack is only
feasible in the absence of authentication and signaling message
protection.
Some threats directly related to these are described in Sections 4.4, 4.7, and 4.8.
3.4. Insecure Parameter Exchange and Negotiation
First, protocols may be useful in a variety of scenarios with
different security requirements. Second, different users (e.g., a
university, a hospital, a commercial enterprise, or a government
ministry) have inherently different security requirements. Third,
different parts of a network (e.g., within a building, across a
public carrier’s network, or over a private microwave link) may need different levels of protection. It is often difficult to meet these (sometimes conflicting) requirements with a single security mechanism or fixed set of security parameters, so often a selection of
mechanisms and parameters is offered. Therefore, a protocol is
required to agree on certain security mechanisms and parameters. An insecure parameter exchange or security negotiation protocol can help an adversary to mount a downgrading attack to force selection of
mechanisms weaker than those mutually desired. Thus, without binding the negotiation process to the legitimate parties and protecting it, an NSIS protocol suite might only be as secure as the weakest
mechanism provided (e.g., weak authentication), and the benefits of
defining configuration parameters and a negotiation protocol are
lost.
4. NSIS-Specific Threat Scenarios
This section describes eleven threat scenarios in terms of attacks on and security deficiencies in the NSIS signaling protocol. A number
of security deficiencies might enable an attack. Fraud is an example of an attack that might be enabled by missing replay protection,
missing protection of authorization tokens, identity spoofing,
missing authentication, and other deficiencies that help an adversary steal resources. Different threat scenarios based on deficiencies
that could enable an attack are addressed in this section.
The threat scenarios are not independent. Some of them (e.g., denial of service) are well-established security terms and, as such, need to be addressed, but they are often enabled by one or more deficiencies described under other scenarios.
Tschofenig & Kroeselberg Informational [Page 12]
4.1. Threats during NSIS SA Usage
Once a security association is established (and used) to protect
signaling messages, many basic attacks are prevented. However, a
malicious NSIS node is still able to perform various attacks as
described in Section 4.7. Replay attacks may be possible when an
NSIS node crashes, restarts, and performs state re-establishment.
Proper re-synchronization of the security mechanism must therefore be provided to address this problem.
4.2. Flooding
This section describes attacks that allow an adversary to flood an
NSIS node with bogus signaling messages to cause a denial of service attack.
We will discuss this threat at different layers in the NSIS protocol suite:
Processing of Router Alert Options:
The processing of Router Alert Option (RAO) requires that a router do some additional processing by intercepting packets with IP
options, which might lead to additional delay for legitimate
requests, or even rejection of some of them. A router being
flooded with a large number of bogus messages requires resources
before finding out that these messages have to be dropped.
If the protocol is based on using interception for message
delivery, this threat cannot be completely eliminated, but the
protocol design should attempt to limit the processing that has to be done on the RAO-bearing packet so that it is as similar as
possible to that for an arbitrary packet addressed directly to one of the router interfaces.
Attacks against the Transport Layer Protocol:
Certain attacks can be mounted against transport protocols by
flooding a node with bogus requests, or even to finish the
handshake phase to establish a transport layer association. These types of threats are also addressed in Section 4.11.
Tschofenig & Kroeselberg Informational [Page 13]
Force NTLP to Do More Processing:
Some protocol fields might allow an adversary to force an NTLP
node to perform more processing. Additionally it might be
possible to interfere with the flow control or the congestion
control procedure. These types of threats are also addressed in
Section 4.11.
Furthermore, it might be possible to force the NTLP node to
perform some computations or signaling message exchanges by
injecting "trigger" events (which are unprotected).
Force NSLP to Do More Processing:
An adversary might benefit from flooding an NSLP node with
messages that must be stored (e.g., due to fragmentation handling) before verifying the correctness of signaling messages.
Furthermore, causing memory allocation and computational efforts
might allow an adversary to harm NSIS entities. If a signaling
message contains, for example, a digital signature, then some
additional processing is required for the cryptographic
verification. An adversary can easily create a random bit
sequence instead of a digital signature to force an NSIS node into heavy computation.
Idempotent signaling messages are particularly vulnerable to this type of attack. The term "idempotent" refers to messages that
contain the same amount of information as the original message.
An example would be a refresh message that is equivalent to a
create message. This property allows a refresh message to create state along a new path, where no previous state is available. For this to work, specific classes of cryptographic mechanisms
supporting this behavior are needed. An example is a scheme based on digital signatures, which, however, should be used with care
due to possible denial of service attacks.
Problems with the usage of public-key-based cryptosystems in
protocols are described in [AN97] and in [ALN00].
In addition to the threat scenario described above, an incoming
signaling message might trigger communication with third-party
nodes such as policy servers, LDAP servers, or AAA servers. If an adversary is able to transmit a large number of signaling messages (for example, with QoS reservation requests) with invalid
credentials, then the verifying node may not be able to process
other reservation messages from legitimate users.
Tschofenig & Kroeselberg Informational [Page 14]
4.3. Eavesdropping and Traffic Analysis
This section covers threats whereby an adversary is able to eavesdrop on signaling messages. The signaling packets collected may allow
traffic analysis or be used later to mount replay attacks, as
described in Section 3.2. The eavesdropper might learn QoS
parameters, communication patterns, policy rules for firewall
traversal, policy information, application identifiers, user
identities, NAT bindings, authorization objects, network
configuration and performance information, and more.
An adversary’s capability to eavesdrop on signaling messages might
violate a user’s preference for privacy, particularly if unprotected authentication or authorization information (including policies and
profile information) is exchanged.
Because the NSIS protocol signals messages through a number of nodes, it is possible to differentiate between nodes actively participating in the NSIS protocol and those that do not. For certain objects or
messages, it might be desirable to permit actively participating
intermediate NSIS nodes to eavesdrop. On the other hand, it might be desirable that only the intended end points (NSIS Initiator and NSIS Responder) be able to read certain other objects.
4.4. Identity Spoofing
Identity spoofing relevant for NSIS occurs in three forms: First,
identity spoofing can happen during the establishment of a security
association based on a weak authentication mechanism. Second, an
adversary can modify the flow identifier carried within a signaling
message. Third, it can spoof data traffic.
In the first case, Eve, acting as an adversary, may claim to be the
registered user Alice by spoofing Alice’s identity. Eve thereby
causes the network to charge Alice for the network resources
consumed. This type of attack is possible if authentication is based on a simple username identifier (i.e., in absence of cryptographic
authentication), or if authentication is provided for hosts, and
multiple users have access to a single host. This attack could also be classified as theft of service.
In the second case, an adversary may be able to exploit the
established flow identifiers (required for QoS and NAT/FW NSLP).
These identifiers are, among others, IP addresses, transport protocol type (UDP, TCP), port numbers, and flow labels (see [RFC1809] and
[RFC3697]). Modification of these flow identifiers allows
adversaries to exploit or to render ineffective quality of service Tschofenig & Kroeselberg Informational [Page 15]
reservations or policy rules at middleboxes. An adversary could
mount an attack by modifying the flow identifier of a signaling
message.
In the third case, an adversary may spoof data traffic. NSIS
signaling messages contain some sort of flow identifier that is
associated with a specified behavior (e.g., a particular flow
experiences QoS treatment or allows packets to traverse a firewall). An adversary might, therefore, use IP spoofing and inject data
packets to benefit from previously installed flow identifiers.
We will provide an example of the latter threat. After NSIS nodes
along the path between the NSIS initiator and the NSIS receiver
processes a properly protected reservation request, transmitted by
the legitimate user Alice, a QoS reservation is installed at the
corresponding NSIS nodes (for example, the edge router). The flow
identifier is used for flow identification and allows data traffic
originated from a given source to be assigned to this QoS
reservation. The adversary Eve now spoofs Alice’s IP address. In
addition, Alice’s host may be crashed by the adversary with a denial of service attack or may lose connectivity (for example, because of
mobility). If Eve is able to perform address spoofing, then she is
able to receive and transmit data (for example, RTP data traffic)
that receives preferential QoS treatment based on the previous
reservation. Depending on the installed flow identifier granularity, Eve might have more possibilities to exploit the QoS reservation or a pin-holed firewall. Assuming the soft state paradigm, whereby
periodic refresh messages are required, Alice’s absence will not be
detected until a refresh message is required, forcing Eve to respond with a protected signaling message. Again, this attack is applicable not only to QoS traffic, but also to a Firewall control protocol,
with a different consequence.
The ability for an adversary to inject data traffic that matches a
certain flow identifier established by a legitimate user and to get
some benefit from injecting that traffic often also requires the
ability to receive the data traffic or to have one’s correspondent
receive it. For example, an adversary in an unmanaged network
observes a NAT/Firewall signaling message towards a corporate
network. After the signaling message exchange was successful, the
user Alice is allowed to traverse the company firewall based on the
establish packet filter in order to contact her internal mail server. Now, the adversary Eve, who was monitoring the signaling exchange, is able to build a data packet towards this mail server that will pass
the company firewall. The packet will hit the mail server and cause some actions, and the mail server will reply with some response
messages. Depending on the exact location of the adversary and the Tschofenig & Kroeselberg Informational [Page 16]
degree of routing asymmetry, the adversary might even see the
response messages. Note that for this attack to work, Alice does not need to participate in the exchange of signaling messages.
We could imagine using attributes of a flow identifier that is not
related to source and destination addresses. For example, we could
think of a flow identifier for which only the 21-bit Flow ID is used (without source and destination IP address). Identity spoofing and
injecting traffic is much easier since a packet only needs to be
marked and an adversary can use a nearly arbitrary endpoint
identifier to achieve the desired result. Obviously, though, the
endpoint identifiers are not irrelevant, because the messages have to hit some nodes in the network where NSIS signaling messages installed state (in the above example, they would have to hit the same
firewall).
Data traffic marking based on DiffServ is such an example. Whenever an ingress router uses only marked incoming data traffic for
admission control procedures, various attacks are possible. These
problems have been known in the DiffServ community for a long time
and have been documented in various DiffServ-related documents. The IPsec protection of DiffServ Code Points is described in Section 6.2 of [RFC2745]. Related security issues (for example denial of service attacks) are described in Section 6.1 of the same document.
4.5. Unprotected Authorization Information
Authorization is an important criterion for providing resources such as QoS reservations, NAT bindings, and pinholes through firewalls.
Authorization information might be delivered to the NSIS-
participating entities in a number of ways.
Typically, the authenticated identity is used to assist during the
authorization procedure (as described in [RFC3182], for example).
Depending on the chosen authentication protocol, certain threats may exist. Section 3 discusses a number of issues related to this
approach when the authentication and key exchange protocol is used to establish session keys for signaling message protection.
Another approach is to use some sort of authorization token. The
functionality and structure of such an authorization token for RSVP
is described in [RFC3520] and [RFC3521].
Achieving secure interaction between different protocols based on
authorization tokens, however, requires some care. By using such an authorization token, it is possible to link state information between different protocols. Returning an unprotected authorization token to the end host might allow an adversary (for example, an eavesdropper) Tschofenig & Kroeselberg Informational [Page 17]
to steal resources. An adversary might also use the token to monitor communication patterns. Finally, an untrustworthy end host might
also modify the token content.
The Session/Reservation Ownership problem can also be regarded as an authorization problem. Details are described in Section 4.10. In
enterprise networks, authorization is often coupled with membership
in a particular class of users or groups. This type of information
either can be delivered as part of the authentication and key
agreement procedure or has to be retrieved via separate protocols
from other entities. If an adversary manages to modify information
relevant to determining authorization or the outcome of the
authorization process itself, then theft of service might be
possible.
4.6. Missing Non-Repudiation
Signaling for QoS often involves three parties: the user, a network
that offers QoS reservations (referred to as "service provider") and a third party that guarantees that the party making the reservation
actually receives a financial compensation (referred to as "trusted
third party").
In this context,"repudiation" refers to a problem where either the
user or the service provider later deny the existence or some
parameters (e.g., volume or price) of a QoS reservation towards the
trusted third party. Problems stemming from a lack of non-
repudiation appear in two forms:
Service provider’s point-of-view:
A user may deny having issued a reservation request for which it
was charged. The service provider may then want to be able to
prove that a particular user issued the reservation request in
question.
User’s point-of-view:
A service provider may claim to have received a number of
reservation requests from a particular user. The user in question may want to show that such reservation requests have never been
issued and may want to see correct service usage records for a
given set of QoS parameters.
In today’s networks, non-repudiation is not provided. Therefore, it might be difficult to introduce with NSIS signaling. The user has to trust the network operator to meter the traffic correctly, to collect and merge accounting data, and to ensure that no unforeseen problems Tschofenig & Kroeselberg Informational [Page 18]
occur. If a signaling protocol with the non-repudiation property is desired for establishing QoS reservations, then it certainly impacts the protocol design.
Non-repudiation functionality places additional requirements on the
security mechanisms. Thus, a solution would normally increase the
overhead of a security solution. Threats related to missing non-
repudiation are only considered relevant in certain specific
scenarios and for specific NSLPs.
4.7. Malicious NSIS Entity
Network elements within a domain (intra-domain) experience a
different trust relationship with regard to the security protection
of signaling messages from that of edge NSIS entities. It is assumed that edge NSIS entities are responsible for performing cryptographic processing (authentication, integrity and replay protection,
authorization, and accounting) for signaling messages arriving from
the outside. This prevents unprotected signaling messages from
appearing within the internal network. If, however, an adversary
manages to take over an edge router, then the security of the entire network is compromised. An adversary is then able to launch a number of attacks, including denial of service; integrity violations; replay and reordering of objects and messages; bundling of messages;
deletion of data packets; and various others. A rogue firewall can
harm other firewalls by modifying policy rules. The chain-of-trust
principle applied in peer-to-peer security protection cannot protect against a malicious NSIS node. An adversary with access to an NSIS
router is also able to get access to security associations and to
transmit secured signaling messages. Note that even non-peer-to-peer security protection might not be able to prevent this problem fully. Because an NSIS node might issue signaling messages on behalf of
someone else (by acting as a proxy), additional problems need to be
considered.
An NSIS-aware edge router is a critical component that requires
strong security protection. A strong security policy applied at the edge does not imply that other routers within an intra-domain network do not need to verify signaling messages cryptographically. If the
chain-of-trust principle is deployed, then the security protection of the entire path (in this case, within the network of a single
administrative domain) is only as strong as the weakest link. In the case under consideration, the edge router is the most critical
component of this network, and it may also act as a security gateway or firewall for incoming and outgoing traffic. For outgoing traffic, this device has to implement the security policy of the local domain and to apply the appropriate security protection.
Tschofenig & Kroeselberg Informational [Page 19]
For an adversary to mount this attack, either an existing NSIS-aware node along the path has to be attacked successfully, or an adversary must succeed in convincing another NSIS node to make it the next NSIS peer (man-in-the-middle attack).
4.8. Denial of Service Attacks
A number of denial of service (DoS) attacks can cause NSIS nodes to
malfunction. Other attacks that could lead to DoS, such as man-in-
the-middle attacks, replay attacks, and injection or modification of signaling messages, etc., are mentioned throughout this document.
Path Finding:
Some signaling protocols establish state (e.g., routing state) and perform some actions (e.g., querying resources) at a number of
NSIS nodes without requiring authorization (or even proper
authentication) based on a single message (e.g., PATH message in
RSVP).
An adversary can utilize this fact to transmit a large number of
signaling messages to allocate state at nodes along the path and
to cause resource consumption.
An NSIS responder might not be able to determine the NSIS
initiator and might even tend to respond to such a signaling
message with a corresponding reservation message.
Discovery Phase:
Conveying signaling information to a large number of entities
along a data path requires some sort of discovery. This discovery process is vulnerable to a number of attacks because it is
difficult to secure. An adversary can use the discovery
mechanisms to convince one entity to signal information to another entity that is not along the data path, or to cause the discovery process to fail. In the first case, the signaling protocol could appear to continue correctly, except that policy rules are
installed at the incorrect firewalls or QoS resource reservations take place at the wrong entities. For an end host, this means
that the protocol failed for unknown reasons.
Tschofenig & Kroeselberg Informational [Page 20]
vlookup函数的使用方法及实例vlookup函数的使用方法及实例 excel中vlookup函数的应用，重要在于实践。 下面我们先了就下函数的构成;接着举个例子说下;最后总结下急提下遇到的相关问题： (本作者采用的是excel2003版，不过这函数在任何版本都适应) 2首先我们介绍下使用的函数vlookup 的几个参数，vlookup是判断引用数据的函数，它总共有四个参数，依次是： 1、判断的条件 2、跟踪数据的区域 3、返回第几列的数据 4、是否精确匹配 该函数的语法规则如下： =VLOOKUP(lookup_value,table_array,col_index_num,range_looku p) 该函数的语法规则可以查看到，如下图： (excel07版) 如下图，已知表sheet1中的数据如下，如何在数据表二sheet2 中如下引用：当学号随机出现的时候，如何在B列显示其对应的物理成绩? 根据问题的需求，这个公式应该是：
vmdk文件损坏打不开怎么修复vmware vmdk文件损坏打不开修复方法一 EasyRecovery数据恢复软件支持恢复VMDK文件并存储在本地文件系统中。由于数据和有关虚拟服务器的配置信息都存储在VMDK文件中，而每个虚拟系统下通常又有多个VMDK镜像，此时选择正确的VMDK镜像对成功的完成文件恢复扫描而言就显得至关重要了。载入VMDK镜像并选择对应的卷，以开始扫描VMDK文件。 根据EasyRecovery软件给出的提示操作，完成VMDK文件恢复。 当然要想保证VMDK文件恢复的顺利进行，还需注意以下几点： 1、当发现数据丢失之后，不要进行任何操作，因操作系统运行时产生的虚拟内存和临时文件会破坏数据或覆盖数据; 2、不要轻易尝试Windows的系统还原功能，这并不会找回丢失的文件，只会为后期的恢复添置不必要的障碍; 3、不要反复使用杀毒软件，这些操作是无法找回丢失文件的。 vmware vmdk文件损坏打不开修复方法二
For... Next 循环语句For…next 循环简称为For 循环。它是一种指定循环次数（事先知道循环次数）的循环程序结构。在这种结构中，使用了一个称为循环变量的特殊变量作为计数器，指定它的初始数值，然后每重复执行一次循环，循环变量就会自动增加或减少一个指定的数值(称为步长值)，直到循环变量的改变达到最终的指定值，循环才停止执行。1．For …Next 语句的语法格式 For <循环变量>=<初值> To <终值> [Step 步长] [语句块] [Exit For ]Next [循环变量] 功能：用来控制重复执行一组语句。指定循环变量以步长为增量，从初值到终值依次取值，并且对于循环变量的每一个值，把语句块执行一次。 说明：（1）关键字For 和Next 成对出现，For 是循环语句的开始，Next 是循环语句的终端，必须出现在For 语句的后面。在关键字For 和Next 之间的语句块叫循环体，它们将被重复执行指定的次数，执行的次数由初值、终值、步长值决定。（2）初值、终值和步长值都是数值表达式，步长值可以是正数，也可以为负数。如果步长值为1，可以省略不写，即系统默认步长值为1。 （3）<循环变量>为必要参数，是用作循环计数器的数值变量，这个变量不能是数组元素。在循环体内，一般不提倡再给循环变量另外赋值。循环变量从初值开始，逐次按照步长值增加或减少而改变，直到超过终值，这时循环停止执行。这里所说的“超过”有两种含义：即大于或者小于。 （4）<初值>和<终值>也都是必要参数。当初值小于终值时，<步长值>必须是正数；反过来，如果初值大于终值，则步长值必须为负数。（5）如果循环体中安排了Exit For 语句，当程序执行到该语句时直接跳出循环结构，不再执行循环体中Exit For 的后续语句（如果有），而是转到Next 后面的其他指令 继续执行。 （6）Next 语句中的[<循环变量>]可以省略。 2. For... Next 语句的执行过程：进入For...Next 循环后，程序按照以下步骤执行：（1）若初值、终值和步长值为表达式，求出它们的值，并保存起来：资料试卷布置情况与有关高中资料试卷电气系统接线等情况，然后根据规范与规程规定，制定设备调试高中资料试卷方案。
VLOOKUP函数调用方法如下：（本次以提取RRU挂高数据为例） 一、本次涉及的相关文档。 1．《某地区TD宏站现场勘测数据汇总表》如表1-1，共1000多站，本次共列出104个站点的信息： 查看原文档请双击图标：某地区TD宏站现场 查勘数据汇总表，表1-1抓图如下： 2．某工程报价单，共30个宏站，如表1-2（本报价单其他信息均删除，只保留了站点名） 查看原文档请双击图标：某工程报价单.xlsx ，表1-2抓图如下： 二、本次我们以从表1-1中提取表1-2中30个站点的RRU挂高为例，具体步骤如下： 1．先在表1-2中增加“RRU挂高”这一列，然后先提取“某城关水泵厂南”的RRU挂高。操作方法为双击下图所示灰色表格，然后鼠标左键单击列表上面的fx插入函 数。 2．点fx后弹出如下图标，在下拉列表中选择“VLOOKUP”，点确定。
3．点确定后，弹出VLOOKUP函数调用表，包含4个部分（lookup_value、Table_array、C ol_index_num、Range_lookup）。 lookup_value:需要在数据表首列进行搜索的值，本次值为表1-1中的位置B2，用 鼠标单击表1-1中的“某城关水泵厂南”，即可自动输入。。 Table_array：需要在其中搜索数据的信息表，即在表1-2中选择一个搜索区域， 注意所选区域第一列必须是与Lookup_value中查找数值相匹配的 列（本次表1-1中的B列），最后一列必须大于等于RRU挂高那一列 （大于等于C列）,至于下拉行数肯定要大于等于106行。如下图： 选择相关区域后，VLOOKUP表中的Table_array会自动输入表1-1中所选区域，如 下图：
excel博大精深，其使用中有许多细节的地方需要注意。 vlookup函数的使用，其语法我就不解释了，百度很多，其实我自己也没看懂语法的解释，下面就按照我自己的理解来说说怎么用的。首先，这个函数是将一个表中的数据导入另一个表中，其中这两个表有一列数据是相同项，但是排列顺序不同。举例说明； 表1 表2 将表1中的face量一列导入表2中，但两表中的名称一列的排列顺序是不同的。此时需要使用vlookup函数。 下面介绍vlookup的使用方法。
将鼠标放到表2中的D2单元格上，点击fx,会出现一个对话框，里面有vlookup函数。若在常用函数里面没有，下拉找“查找与引用”，里面有此函数。点确定。表示此函数是在表2中的D2单元格中应用。 此时出现对话框： 在第个格里输入B2，直接用鼠标在表2中点击B2单元格即可。表示需要在查找的对象是表2中的B2单元格中的内容。
然后是第二个格，点表1，用鼠标选择整个表的所有数据。表示要在表1中的B1—C14区域查找表2中的B2单元格中的内容。
第三个格里输入在表2中要导入的列数在表1中的列数的数字。在此例中为C列，其列数数字为2.表示将表1中（B1—C14）区域中查找到的单元格里的内容相对应的列（第2列）中的单元格中的内容（face量列中的数据）导入表2中相应的单元格（D2）。 最后一个格中输入“0”。表示查找不到就出现#N/A。点确定，即出现相应数据，然后下拉复制格式。
当下拉出现这种情况的时候： 其实是其查找区域在下拉过程中随着行的改变而改变了。需要对查找区域做一下固定。其方法为，在选择区域后，在区域前面加“$”号（$B$1：$C$14）。
信息技术 - FOR/NEXT循环语句教学设计_高中信息技术2009-10-24 18:33:09来源: 作者:佚名【大中小】浏览:43607次评论:1条 ■以下为本文简介：－－－－－－－－－－－－一、课前分析教学内容：FOR/NEXT循环语句。 1、教材分析 1）教学内容和地位：程序设计是教学中的重点也是难点，循环结构是其中的一种设计结构，其作用是...... 以下为本文简介：－－－－－－－－－－－－ 一、课前分析 教学内容：FOR/NEXT循环语句。 1、教材分析 1）教学内容和地位：程序设计是教学中的重点也是难点，循环结构是其中的一种设计结构，其作用是使一段程序反复执行。FOR/NEXT语句是循环运算的专家，在程序设计中频繁出现。本节课的学习，会使学生对算法有一个更深刻的理解，为实现独立编程起到了关键性作用。 2）教学重点与难点：本节课重点是掌握FOR/NEXT循环语句的格式，并能运用其来编制简单的小程序。难点是解决问题的方法和思路，要绘制好流程图，确定循环变量和循环体。因为用流程图描述算法，能够把解决问题的步骤清晰、直观地表示出来。 2、教学目标分析： １）认知目标：通过FOR/NEXT语句的学习，写出简单的循环程序。
２）能力目标：培养学生分析问题，解决问题的能力。 ３）情感目标：激发学生学习热情，培养学生学习的积极性。 二、教学过程 1、创设问题情境 师：同学们，请先看这个图形(画5个竖行排列的“*”)，想想看用以前学过的程序设计语言怎样来编写它的程序呢？(本节程序均设置为单击命令按钮cmdstart运行即代码加在private sub cmdstart_click()) 生（稍做思考，然后回答）：使用PRINT语句 PRINT “*” PRINT “*” PRINT “*” PRINT “*” PRINT “*” 师：同学们做得很好，那么，我想画10行，100行，1000行“*”呢？难道就这样顺序写下去吗？这样编写是不是太繁琐了。如果能让计算机去完成这部分重复的内容，而我们只要告诉计算机重复操作的次数就可以了，这个愿望能否实现呢？能!通过我们今天学习的FOR/NEXT循环语句，就可以很容易的实现这个愿望。 [疑问是建构教学的起点。新课伊始，就提出一个真实的问题，力求创设一种教学情境，它可以激起学生的未知欲，有利于建立新的认识结构。] 2、给出程序，并通过流程图加以理解 师出示上题程序代码并通过流程图和卡通图片分析
VLOOKUP函数的使用方法(入门级) VLOOKUP函数是Excel中几个最重函数之一，为了方便大家学习，兰色幻想特针对VLOOKUP 函数的使用和扩展应用，进行一次全面综合的说明。本文为入门部分 一、入门级 VLOOKUP是一个查找函数，给定一个查找的目标，它就能从指定的查找区域中查找返回想要查找到的值。它的基本语法为： VLOOKUP（查找目标，查找范围，返回值的列数，精确OR模糊查找) 下面以一个实例来介绍一下这四个参数的使用 例1：如下图所示，要求根据表二中的姓名，查找姓名所对应的年龄。 公式：B13 =VLOOKUP(A13,$B$2:$D$8,3,0) 参数说明： 1 查找目标：就是你指定的查找的内容或单元格引用。本例中表二A列的姓名就是查找目标。我们要根据表二的“姓名”在表一中A列进行查找。 公式：B13 =VLOOKUP(A13,$B$2:$D$8,3,0) 2 查找范围（VLOOKUP(A13,$B$2:$D$8,3,0) ）：指定了查找目标，如果没有说从哪里查找，EXCEL肯定会很为难。所以下一步我们就要指定从哪个范围中进行查找。VLOOKUP的这第二个参数可以从一个单元格区域中查找，也可以从一个常量数组或内存数组中查找。本例中要从表一中进行查找，那么范围我们要怎么指定呢？这里也是极易出错的地方。大家一定要注意，给定的第二个参数查找范围要符合以下条件才不会出错： A 查找目标一定要在该区域的第一列。本例中查找表二的姓名，那么姓名所对应的表一的姓名列，那么表一的姓名列（列）一定要是查找区域的第一列。象本例中，给定的区域要从第二列开始，即$B$2:$D$8，而不能是$A$2:$D$8。因为查找的“姓名”不在$A$2:$D$8区域的第一列。 B 该区域中一定要包含要返回值所在的列，本例中要返回的值是年龄。年龄列（表一的D列）一定要包括在这个范围内，即：$B$2:$D$8，如果写成$B$2:$C$8就是错的。 3 返回值的列数（B13 =VLOOKUP(A13,$B$2:$D$8,3,0)）。这是VLOOKUP第3个参数。它是一个整数值。它怎么得来的呢。它是“返回值”在第二个参数给定的区域中的列数。本例中我们
教学设计 题目：For-Next循环培训院校：新疆教育学院数信分院专业班级：1132初中信息技术班学号： 1132102118 姓名：胡安太
13.For-Next循环 标题：For-Next循环 课时：第一课时 年级：初三 教学重点，难点：使用FOR-Next语句实现循环结构的方法，循环变量。一．教学目标 1.知识目标 (1)循环体，循环控制变量（变量）,了解循环的概念、理解循环结构的基本思 想 (2)把握for…next语句的基本结构(循环嵌套，内循环，外循环) (3)理解for…next语句的执行过程；(实现循环结构的方法) 2.素质目标 （1）学生学习循环过程中能够培养学生的思考能力 （2）学习过程中可以充分发挥学生的逻辑能力。 3.情感目标 （1）养成学生独立思考的良好习惯 （2）提高学生面对现实，敢于面对失败的意识，加强他人的忍耐性。 (3)通过一个个任务的实战演练，感知使用循环结构解决问题的便捷和优越，培养学生运用循环思想解决实际问题的能力，进一步激发学生学习编程的爱好。 (4) 通过在实际的问题中分析提炼循环结构，从程序设计领域进一步提升学生
的信息素养 二．教学过程 1.（1）复习程序的顺序结构 前面我们讲过程序的顺序结构，计算机最基本的结构。 师：谁能回答，什么是顺序结果？ 学生：回答上述的问题。如果能回的老师表扬，没有人回答，有老师来复述。 （2）复习程序的分支结构 师：有时候处理问题时，比如判断一个年份是否闰年，需要根据某个条件进行判断。 1.什么是分支结构？ 2.我们所学的那个语句是分支结构的？ 3.谁能写下来它的格式？ 学生：让几个学生回答这个问题。如果答对了表扬，答错了，那就老师引导学生回顾那些内容。下面是回顾内容：
VLOOKUP函数是Excel中的一个纵向查找函数，它与LOOKUP函数和HLOOKUP函数属于一类函数，在工作中都有广泛应用。VLOOKUP是按列查找，最终返回该列所需查询列序所对应的值；与之对应的HLOOKUP是按行查找的。 VLOOKUP函数的语法结构 整个计算机就相当于一门语言，首先我们就是要获取该函数的语法结构。以下是官网的语法结构 VLOOKUP（lookup_value, table_array, col_index_num, [range_looku p]）。 书上表述就是VLOOKUP（查找值，查找范围，查找列数，精确匹配或者近似匹配） 在我们的工作中，几乎都使用精确匹配，该项的参数一定要选择为false。否则返回值会出乎你的意料。 VLOOKUP函数使用示范 vlookup就是竖直查找，即列查找。通俗的讲，根据查找值参数，在查找范围的第一列搜索查找值，找到该值后，则返回值为：以第一列为准，往后推数查找列数值的这一列所对应的值。这也是为什么该函数叫做vlookup（v为vertic al-竖直之意，lookup即时英文的查找之意）。 现有如下手机的每日销售毛数据（图左），A分销商需要提供四个型号的销售数据（图右）
这个时候，你大概可能回去一个一个人工查找，因为我所提供的数据数量很少，但是其实工作中这种数据很庞大的，人工查找无疑即浪费时间，而且不能让A分销商相信你所提供数据的准确性。接下来，我们就需要本次的主角登场了。使用vlookup函数。 第一步：选中要输入数据的单元格，=VLOOKUP（H3,$A$3:$F$19,5,FALSE）如图
For—Next循环语句（第一课时） 一、学习者分析 在此之前，学生已经学习了程序的基本要素、顺序结构、分支结构，对程序结构有了一定的了解和掌握，知道顺序结构和分支结构的区别，同时在学习上也出现了分化。为了不让学生的分化加剧，增加学生的畏难情绪，安排了两个课时进行循序渐进的教学、增加学生的学习兴趣，减弱畏难情绪。 二、教材内容分析 （一）、本节的主要内容及在本章中的地位 本节是广州市信息技术教科书初中第二册第二章第六节循环结构中的For—Next 循环语句。是程序设计初步的重点、难点。由于循环结构相对顺序结构和分支结构比较抽象和不易理解，因此在教学中宜自然地引入For—Next循环语句的功能、格式。 （二）、教学重点、难点 重点：For—Next循环语句的格式和作用。 难点：For—Next循环语句的执行过程和应用。 （三）、课时安排：2课时（本节为第一课时）。 三、教学目标 （一）知识与技能 1、掌握For-Next循环语句的格式。 2、了解For-Next循环语句的作用，理解画同心圆程序的执行过程。 3、理解改变循环变量的值控制循环次数的意义。 4、根据实际情况，能够应用For-Next循环语句修改及编写程序。 （二）过程与方法 1、通过观看例子，模仿、修改、编写程序，掌握For-Next循环语句的格式和特点。 2、通过观察、分析画同心圆的程序，逐步掌握For-Next循环语句的执行过程和应用。 3、通过体验探究、思考、讨论等形式，了解For-Next循环语句程序设计在解决问题过程中的方法和作用，学会利用For-Next循环语句处理已知重复次数的循环问题。 （三）情感态度与价值观 1、学生通过教师的情景设置以及对程序的体验修改，克服学习过程中的畏难情绪，在不断的探究和思考中培养探索精神，能够真正体验成功的喜悦。 2、学生通过分层次的任务设计，提升学习兴趣、求知欲、对程序设计的兴趣，养成认真、严谨的学习态度和良好的心理素养。 四、教学理念和方法 本节课教师主要采用的方法包括：体验法、指导法以及任务驱动。体验法是以教师为主导，学生主动探究、亲身体验、思考总结提高，在学习过程中体验学习的乐趣和方法。指导法可以在学生操作过程中观察学生的实际掌握情况，发现存在的问题并及时加以指正。任务驱动可以激发和保持学生的学习兴趣，尽可能多地提供学生动手实践的机会。通过教师的情景设置，不断提高学习任务的梯度，使学生逐步掌握知识，培养学生的实践和创新能力。 五、教学资源 深蓝易思多媒体教学系统、学生使用的主题网站（包含课堂评价系统）、教师使用的主题网站（包含powerpoint课件和课堂评价的统计系统）、教科书、计算机、投影等。
VLOOKUP函数的使用方法（入门级）一、入门级 VLOOKUP是一个查找函数，给定一个查找的目标，它就能从指定的查找区域中查找返回想要查找到的值。它的基本语法为： VLOOKUP（查找目标，查找范围，返回值的列数，精确OR模糊查找) 下面以一个实例来介绍一下这四个参数的使用 例1：如下图所示，要求根据表二中的姓名，查找姓名所对应的年龄。 公式：B13 =VLOOKUP(A13,$B$2:$D$8,3,0) 参数说明： 1 查找目标：就是你指定的查找的内容或单元格引用。本例中表二A列的姓名就是查找目标。我们要根据表二的“姓名”在表一中A列进行查找。
公式：B13 =VLOOKUP(A13,$B$2:$D$8,3,0) 2 查找范围（VLOOKUP(A13,$B$2:$D$8,3,0) ）：指定了查找目标，如果没有说从哪里查找，EXCEL肯定会很为难。所以下一步我们就要指定从哪 个范围中进行查找。VLOOKUP的这第二个参数可以从一个单元格区域中查找， 也可以从一个常量数组或内存数组中查找。本例中要从表一中进行查找，那么范 围我们要怎么指定呢？这里也是极易出错的地方。大家一定要注意，给定的第二 个参数查找范围要符合以下条件才不会出错： A 查找目标一定要在该区域的第一列。本例中查找表二的姓名，那么姓名 所对应的表一的姓名列，那么表一的姓名列（列）一定要是查找区域的第一列。 象本例中，给定的区域要从第二列开始，即$B$2:$D$8，而不能是$A$2:$D$8。 因为查找的“姓名”不在$A$2:$D$8区域的第一列。 B 该区域中一定要包含要返回值所在的列，本例中要返回的值是年龄。年 龄列（表一的D列）一定要包括在这个范围内，即：$B$2:$D$8，如果写成$B $2:$C$8就是错的。 3 返回值的列数（B13 =VLOOKUP(A13,$B$2:$D$8,3,0)）。这是VLO OKUP第3个参数。它是一个整数值。它怎么得来的呢。它是“返回值”在第 二个参数给定的区域中的列数。本例中我们要返回的是“年龄”，它是第二个参 数查找范围$B$2:$D$8的第3列。这里一定要注意，列数不是在工作表中的列 数（不是第4列），而是在查找范围区域的第几列。如果本例中要是查找姓名所
《For…next循环结构》教学设计（修改稿） 海口市第一中学王锡君 2007年全国高中信息技术课展评二等奖作品 一、教材分析： 《for…next循环》选至高中选修教材《算法与程序设计》（教科社版）2.3.3节《循环结构》。教材中《循环结构》主要包含《for…next循环》和《do while…loop循环》等两部分内容，各用一课时，共计两课时。本设计为第1课时。 循环结构是最为常用的语法结构之一，也是三大基本结构中难度最大的一个；不仅是本章的重点与难点，也是全书的重点之一。学好程序的基本结构，是学生理解和学习后续章节的基础。 二、学情分析： 在学习本课之前，学生本应已熟悉VB程序的编程环境与运行方法，了解顺序及选择结构的程序执行流程，具备一定的算法基础和归纳总结能力。 但根据安排，授课对象为天津实验中学高一学生，绝大多数学生并接触过程序设计和VB环境，动手能力较差。并且《算法与程序设计》≠某一编程工具（语言）的教学。故本课有意弱化学生在纯VB环境中的代码编写，而重在理解循环结构的基本思想，学会怎样分析循环问题、设计算法，并提炼for语句的基本结构，旨在培养学生根据需要采用循环结构解决实际问题的能力，故任务设置以完善半成品居多。 三、教学目标： 1. 知识与技能：
1) 了解循环的概念、理解循环结构的基本思想； 2) 掌握for…next语句的基本结构； 3) 理解for…next语句的执行过程； 4) 尝试采用循环结构编写简单的程序，解决实际问题。 2. 过程与方法： 经历分析、实践、讲解、探究、归纳，通过循序渐进、层层深入，逐步深化对循环思想和执行过程的理解。3. 情感、态度与价值观： 1) 通过一个个任务的实战演练，感知使用循环结构解决问题的便捷和优越，培养学生运用循环思想解决实际问题的能力，进一步激发学生学习编程的兴趣。 2) 通过在实际的问题中分析提炼循环结构，从程序设计领域进一步提升学生的信息素养。 四、教学重点、难点: 1) 教学重点：①掌握for…next语句的基本结构；②理解for…next语句的执行过程 2) 教学难点：根据需要采用循环结构解决实际问题，并提炼出for语句的基本结构。 五、教学方法：讲授演示法、对比分析法、任务驱动法、分层教学法等。 六、教学过程： （一）创设情景、激情导入
VLOOKUP函数 使用举例 如图 vlookup函数示例 所示，我们要在A2:F12区域中提取100003、100004、100005、100007、100010五人的全年总计销量，并对应的输入到I4:I8中。一个一个的手动查找在数据量大的时候十分繁琐，因此这里使用VLOOKUP函数演示： 首先在I4单元格输入“=Vlookup(”，此时Excel就会提示4个参数。
Vlookup结果演示 第一个参数，很显然，我们要让100003对应的是I4，这里就输入“H4,” ； 第二个参数，这里输入我们要查找的区域(绝对引用)，即“$A$2:$F$12,”； 第三个参数，“全年总计”是区域的第六列，所以这里输入“6”，输入“5”就会输入第四季度的项目了； 第四个参数，因为我们要精确的查找工号，所以留空即可。 最后补全最后的右括号“)”，得到公式“=VLOOKUP(H4,$A$2:$F$12,6)”，使用填充柄填充其他单元格即可完成查找操作。 VLOOKUP函数使用注意事项 说到VLOOKUP函数，相信大家都会使用，而且都使用得很熟练了。不过，有几个细节问题，大家在使用时还是留心一下的好。 一．VLOOKUP的语法 VLOOKUP函数的完整语法是这样的： VLOOKUP(lookup_value,table_array,col_index_num,range_lookup) 1．括号里有四个参数，是必需的。最后一个参数range_lookup是个逻辑值，我们常常输入一个0字，或者False;其实也可以输入一个1字，或者true。两者有什么区别呢？前者表示的是完整寻找，找不到就传回错误值#N/A；后者先是找一模一样的，找不到再去找很接近的值，还找不到也只好传回错误值#N/A。这对我们其实也没有什么实际意义，只是满足好奇而已，有兴趣的朋友可以去体验体验。 2．Lookup_value是一个很重要的参数，它可以是数值、文字字符串、或参照地址。我们常常用的是参照地址。用这个参数时，有三点要特别提醒：A）参照地址的单元格格式类别与去搜寻的单元格格式的类别要一致，否则的话有时明明看到有资料，就是抓不过来。特别是参照地址的值是数字时，最为明显，若搜寻的单元格格式类别为文字，虽然看起来都是123，但是就是抓不出东西来的。
课题编制计算机程序解决问题 --For/Next循环语句 课时一课时 课型新授授课人韦开静授课时间2012.3.12 授课班级高一（7）学科信息技术 教材分析 循环结构是程序设计的三种基本结构之一，是程序设计的基础；它的主要应用方向是让计算机重复做大量相同或相似的事情。教材只是通过SIN函数引出了For/Next循环语句，并没有给出它的语法格式，及其语句的具体执行过程。我认为这样会导致一些学生进行简单模仿，而不是真正的掌握和理解。学生只有熟练掌握了For/Next循环语句的格式，理解循环执行过程，才能在实际应用中游刃有余。所以，本节课我们将学习For/Next循环语句。 学情分析 教学对象为高一的学生，对程序的接触不太多，前面的课程只讲了程序中的基本元素，初步了解了流程图的画法，但没有通过实际的编程来上机实践。所以，本节课从简单的实例着手，让学生搞清楚什么情况下要去使用循环结构，怎么样来使用它。 教学目标1、知识技能目标： ①掌握For/Next循环语句的格式 ②理解For/Next循环语句的功能和执行步骤 2、过程方法目标： ①能够分析简单的For/Next循环语句功能，尝试编写简单的For/Next 循环程序 ②培养学生分析问题，解决问题的能力。 3、情感态度目标： 感受用计算机程序解决问题的魅力，激发学生学习程序设计的兴趣。 重点掌握For/Next循环语句的格式与执行步骤 难点运用For/Next循环语句编制简单的计算机程序解决实际问题 教学方式讲授法、任务驱动法、小组协作 教学准备多媒体网络教室、PPT 教学过程 教学环节教师活动学生活动设计意图 复习编制计算机程序解决问题的基本过 程：分析问题→算法设计→编写程序 →调试运行→检测结果 回答问题 唤起学生记忆，为 新课做铺垫
VLOOKUP函数是Excel中几个最重函数之一，为了方便大家学习，兰色幻想特针对VLOOKUP函数的使用和扩展应用，进行一次全面综合的说明。本文为入门部分 一、入门级 VLOOKUP是一个查找函数，给定一个查找的目标，它就能从指定的查找区域中查找返回想要查找到的值。它的基本语法为： VLOOKUP（查找目标，查找围，返回值的列数，精确OR模糊查找) 下面以一个实例来介绍一下这四个参数的使用 例1：如下图所示，要求根据表二中的，查找所对应的年龄。 公式：B13 =VLOOKUP(A13,$B$2:$D$8,3,0) 参数说明：
1 查找目标：就是你指定的查找的容或单元格引用。本例中表二A列的就是查找目标。我们要根据表二的“”在表一中A列进行查找。 公式：B13 =VLOOKUP(A13,$B$2:$D$8,3,0) 2 查找围（VLOOKUP(A13,$B$2:$D$8,3,0) ）：指定了查找目标，如果没有说从哪里查找，EXCEL肯定会很为难。所以下一步我们就要指定从哪个 围中进行查找。VLOOKUP的这第二个参数可以从一个单元格区域中查找，也可以从一个常量数组或存数组中查找。本例中要从表一中进行查找，那么围我们要怎么指定呢？这里也是极易出错的地方。大家一定要注意，给定的第二个参数查找围要符合以下条件才不会出错： A 查找目标一定要在该区域的第一列。本例中查找表二的，那么所对应的表一的列，那么表一的列（列）一定要是查找区域的第一列。象本例中，给定的区域要从第二列开始，即$B$2:$D$8，而不能是$A$2:$D$8。因为查找的“”不在$A$2:$D$8区域的第一列。 B 该区域中一定要包含要返回值所在的列，本例中要返回的值是年龄。年龄列（表一的D列）一定要包括在这个围，即：$B$2:$D$8，如果写成$B$2:$C$8就是错的。 3 返回值的列数（B13 =VLOOKUP(A13,$B$2:$D$8,3,0)）。这是VLOOKUP 第3个参数。它是一个整数值。它怎么得来的呢。它是“返回值”在第二个参数 给定的区域中的列数。本例中我们要返回的是“年龄”，它是第二个参数查找围$B$2:$D$8的第3列。这里一定要注意，列数不是在工作表中的列数（不是第4
For... Next循环语句 For…next循环简称为For循环。它是一种指定循环次数（事先知道循环次数）的循环程序结构。在这种结构中，使用了一个称为循环变量的特殊变量作为计数器，指定它的初始数值，然后每重复执行一次循环，循环变量就会自动增加或减少一个指定的数值(称为步长值)，直到循环变量的改变达到最终的指定值，循环才停止执行。 1．For …Next语句的语法格式 For <循环变量>=<初值> To <终值> [Step步长] [语句块] [Exit For] Next [循环变量] 功能：用来控制重复执行一组语句。指定循环变量以步长为增量，从初值到终值依次取值，并且对于循环变量的每一个值，把语句块执行一次。 说明： （1）关键字For和Next成对出现，For是循环语句的开始，Next是循环语句的终端，必须出现在For语句的后面。在关键字For和Next之间的语句块叫循环体，它们将被重复执行指定的次数，执行的次数由初值、终值、步长值决定。 （2）初值、终值和步长值都是数值表达式，步长值可以是正数，也可以为负数。如果步长值为1，可以省略不写，即系统默认步长值为1。 （3）<循环变量>为必要参数，是用作循环计数器的数值变量，这个变量不能是数组元素。在循环体内，一般不提倡再给循环变量另外赋值。循环变量从初值开始，逐次按照步长值增加或减少而改变，直到超过终值，这时循环停止执行。这里所说的“超过”有两种含义：即大于或者小于。 （4）<初值>和<终值>也都是必要参数。当初值小于终值时，<步长值>必须是正数；反过来，如果初值大于终值，则步长值必须为负数。 （5）如果循环体中安排了Exit For 语句，当程序执行到该语句时直接跳出循环结构，不再执行循环体中Exit For的后续语句（如果有），而是转到Next后面的其他指令继续执行。 （6）Next语句中的[<循环变量>]可以省略。 2. For... Next语句的执行过程： 进入For...Next循环后，程序按照以下步骤执行： （1）若初值、终值和步长值为表达式，求出它们的值，并保存起来：
vlookup函数使用方法 Lookup_value为需要在数据表第一列中进行查找的数值。Lookup_value 可以为数值、引用或文本字符串。当vlookup函数第一参数省略查找值时，表示用0查找。 Table_array为需要在其中查找数据的数据表。使用对区域或区域名称的引用。 col_index_num为table_array 中查找数据的数据列序号。col_index_num 为 1 时，返回table_array 第一列的数值，col_index_num 为2 时，返回table_array 第二列的数值，以此类推。如果col_index_num 小于1，函数VLOOKUP 返回错误值#VALUE!;如果col_index_num 大于table_array 的列数，函数VLOOKUP 返回错误值#REF!。 Range_lookup为一逻辑值，指明函数VLOOKUP 查找时是精确匹配，还是近似匹配。如果为FALSE或0，则返回精确匹配，如果找不到，则返回错误值#N/A。如果range_lookup 为TRUE或1，函数VLOOKUP 将查找近似匹配值，也就是说，如果找不到精确匹配值，则返回小于lookup_value 的最大数值。应注意VLOOKUP函数在进行近似匹配时的查找规则是从第一个数据开始匹配，没有匹配
到一样的值就继续与下一个值进行匹配，直到遇到大于查找值的值，此时返回上一个数据(近似匹配时应对查找值所在列进行升序排列)。如果range_lookup 省略，则默认为1。 一.VLOOKUP的语法 1.括号里有四个参数，是必需的。最后一个参数range_lookup是个逻辑值，我们常常输入一个0字，或者False;其实也可以输入一个1字，或者true。两者有什么区别呢?前者表示的是完整寻找，找不到就传回错误值#N/A;后者先是找一模一样的，找不到再去找很接近的值，还找不到也只好传回错误值#N/A。 2.Lookup_value是一个很重要的参数，它可以是数值、文字字符串、或参照地址。我们常常用的是参照地址。用这个参数时，有三点要特别提醒: A)参照地址的单元格格式类别与去搜寻的单元格格式的类别要一致，否则的话有时明明看到有资料，就是抓不过来。特别是参照地址的值是数字时，最为明显，若搜寻的单元格格式类别为文本格式，虽然看起来都是123，但是就是抓不出东西来的。 而且格式类别在未输入数据时就要先确定好，如果数据都输入进去了，
For/next语句 一、教材分析 For/next语句是《算法与程序设计》中一个重点，也是后面学习面向对象程序设计的一个基础，如何有效教学，跨越这个门槛是我头痛之处，经了解，学生在数学上学习过循环结构，于是，通过整合数学资源实现突破。 二、学情分析 本节课教学对象是高二学生，通过一段时间的学习，学生已经具备了一定的抽象逻辑思维能力，并处于不断发展的阶段；积累了用计算机编程解决现实中的问题的初步经验。在此基础上学习for/next语句，再加上我校学生基础好，学习态度端正，习惯好。学好本节课内容不算什么难事。 三、教学目标 1、知识与技能： （1）、掌握For/Next语句的格式，理解For/Next循环语句的功能和执行步骤 （2）、能够分析简单的For/Next循环语句功能，尝试编写简单的For/Next 循环程序 2、过程与方法 首先，通过绘制同心圆的问题，让学生发现绘制不同半径的同心圆，反复使用circle函数所带来的麻烦，从而引出for/next语句，进而解决代码重复所带来的麻烦。让学生感到欣喜的同时，渴望知识。其次，通过任务设置进一步掌握for/next语句的使用方法，为学习双层循环做准备。最后，通过打印九九乘法表达到掌握双重循环的目的。 3、情感价值观 通过信息技术对其他学科的整合，提高学生学习算法的兴趣，激发学生编程的热情，同时也培养了学生的细心和耐心，加深了对计算机这一工具的认识，也增强了用计算机编程来解决一些无法用人工来计算的问题的信心。 四、教学重点与难点 For/next语句的使用方法和功能以及执行步骤。 根据实际情况，确定for/next语句的循环变量条件和循环体。 五、教学策略 本节课首先采用问题探究方法，引导学生发现问题，进而引出for/next语句；其次通过讲授for语句的使用方法和功能，增强学生对for语句的理解；最后通过实践任务的设置来巩固所学，达到学以致用的效果。 六、教学环境 多媒体机房 七、教学过程
Vlookup函数使用方法 Vlookup函数可以通过区域查找的方式，把你需要匹配的记录的某一列字段反馈回来，具体使用方法如下 Vlookup（需要查找的内容，查找的区域，反馈区域某一列的列排序编号，查找方式） 1、查找的区域可以跨文件进行查找； 2、反馈区域某一列的列排序编号：填写的反馈列为你查找区域中的列排序，假设查找的范 围冲B至F，需要反馈E的数据，则填写列排序编号为4； 3、查找方式：查找方式只存在两个参数，true和false。True为近似查找，匹配查找内容及 查找的区域精准度不高，近似的值都反馈查找结果。false为精确查找，必须查找内容与查找区域完全相同才反馈查找结果。 示例： 1、目前有两个excel文件，《附件10-柳州供电局2013年固定资产投资调整计划表.xls》和 《02柳州样式表.xml》两个文件 2、打开两个文件夹，现在我需要在《02柳州样式表.xml》把符合项目编码的项目的建设性 质在附件《10-柳州供电局2013年固定资产投资调整计划表.xls》进行查找匹配出来《02柳州样式表.xml》如下：
《10-柳州供电局2013年固定资产投资调整计划表.xls》如下： 4、在《02柳州样式表.xml》的建设性质上使用vlookup函数，具体设置如下： =VLOOKUP(B3,'[附件10-柳州供电局2013年固定资产投资调整计划表.xls]附件10-1-1 10千伏城网'!$C:$G,5,FALSE) 因为项目编码是唯一的，则需要匹配两个表的项目编码即可比对出是否存在该项目，现在就 查找第一个项目的排序编码B3,； 第二个参数选取的范围为《10-柳州供电局2013年固定资产投资调整计划表.xls》中的C-G （选取匹配的范围必须包括你需要匹配的列和需要反馈值的列），则第三个参数根据选定区域反馈列的信息为第五列，则设置第三个参数为5；设置第四个参数为false，则进 行精确查找。
For-Next循环语句--(第1课时) 【适用教材】广东教育出版社《信息技术》册 【适用年级】初二年级 一、教学内容分析 本节课讲授的是For-Next循环语句，因为之前学生学习过顺序结构，分支结构中的条件语句，对编程有了一定的基础，但是循环语句相对于条件语句来说，语法和语句的工作流程都复杂了，所以在讲述For-Next循环语句时，可以让学生分析程序的具体执行过程，引导学生分析For-Next 循环语句是如何实现程序的循环功能的，加深学生对循环功能的实现方法的理解。 二、教学对象分析 本节课的教学对象是初二学生，因为初二学生的理解能力有限，而这节课涉及的循环语句比较抽象，较难理解，因此在教学中宜比较自然地引入循环语句的功能、格式以及使用方法。并且为了学生更好地理解For-Next语句，尽可能使用程序与流程图结合的方法进行讲解。 三、教学目标 ．初步理解循环结构的定义和作用； ．初步掌握循环语句的一般格式； ．结合For-Next循环语句的执行流程图理解循环结构
程序的执行过程。 四、教学重点以及教学难点 理解及初步掌握For-Next循环语句。 五、教学过程设计 复习程序的顺序结构 前面我们讲过程序的顺序结构，计算机最基本的结构。计算机在执行程序时，按照从上往下的顺序依次执行语句，这样的结构称为顺序结构。 复习程序的分支结构 有时候处理问题时，比如判断一个年份是否闰年，需要根据某个条件进行判断，然后再决定程序的执行过程，这种程序结构称为分支结构。前面我们所学过的If-Then-Else 条件语句就可实现条件的判断。 格式：条件语句的执行过程： IfThen Else EndIf 讲述新 引入： 有时，在解决一些问题时，经常需要重复执行一些操作，
VLOOKUP函数的使用方法(高级篇) VLOOKUP是按列查找，最终返回该列所需查询列序所对应的值;与之对应的HLOOKUP是按行查找的。下面Yjbys给大家推荐一下高级的VLOOKUP函数的使用方法! 一、字符的模糊查找 在A列我们知道如何查找型号为“AAA”的产品所对应的B列价格，即： =VLOOKUP(C1,A:B,2,0) 如果我们需要查找包含“AAA”的产品名称怎么表示呢?如下图 表中所示。 公式=VLOOKUP("*"&A10&"*",A2:B6,2,0) 公式说明：VLOOKUP的第一个参数允许使用通配符“*”来表示包含的意思，把*放在字符的两边，即"*"&字符&"*"。 二、数字的区间查找 数字的区间查找即给定多个区间，指定一个数就可以查找出它 在哪个区间并返回这个区间所对应的值。 在VLOOKUP入门中我们提示VLOOKUP的第4个参数，如果为0 或FALSE是精确查找，如果是1或TRUE或省略则为模糊查找，那么 实现区间查找正是第4个参数的模糊查找应用。 首先我们需要了解一下VLOOKUP函数模糊查找的两个重要规则： 1、引用的数字区域一定要从小到大排序。杂乱的数字是无法准确查找到的。如下面A列符合模糊查找的前题，B列则不符合。
2、模糊查找的原理是：给一定个数，它会找到和它最接近，但比它小的那个数。详见下图说明。 最后看一个实例： 例：如下图所示，要求根据上面的提成比率表，在提成表计算表中计算每个销售额的提成比率和提成额。 公式：=VLOOKUP(A11,$A$3:$B$7,2) 公式说明： 1、上述公式省略了VLOOKUP最后一个参数，相当于把第四个参数设置成1或TRUE。这表示VLOOKUP要进行数字的区间查找。 2、图中公式中在查找5000时返回比率表0所对应的比率1%，原因是0和10000与5000最接近，但VLOOKUP只选比查找值小的那一个，所以公式会返回0所对应的比率1%。 三、VLOOKUP的反向查找。 一般情况下，VLOOKUP函数只能从左向右查找。但如果需要从右向右查找，则需要把区域进行“乾坤大挪移”，把列的位置用数组互换一下。 例1：要求在如下图所示表中的姓名反查工号。 公式：=VLOOKUP(A9,IF({1,0},B2:B5,A2:A5),2,0) 公式剖析： 1、这里其实不是VLOOKUP可以实现从右至右的查找，而是利用IF函数的数组效应把两列换位重新组合后，再按正常的从左至右查找。