Author: Milica Djekic

Spies, communication, and secret codes! Cryptography is the art of encrypting and decrypting messages. It has existed as long as people have distrusted each other and looked for the forms of secure communication. Cryptographic techniques have evolved over the centuries. The aim is always the same – the code-makers work to stay ahead of the code-breakers. Today’s most common encryption methods are threatened by the potential creation of the quantum computer. In other words, quantum cryptography promises more secure communication than any existing technique.

Introduction

Quantum cryptography is focused on the unique behavior of microscopic objects which enable users to securely develop secret keys. The work on quantum cryptography was begun by Stephen J. Wiesner in the late 1960’s. The first protocol for sending a private key using quantum techniques is published in 1984 by Bennett and Brassard. The development of quantum cryptography is based on “public-key

As companies and individuals increasingly use wireless technologies for their significant communications, they also must be assured of security using proper cryptographic algorithms. The major fields of applications are mobile e-commerce transactions, e-mails and corporate data transaction. On the other hand, as wireless systems grow in popularity and carry valuable information, hackers are directing their attacks on these novel targets. The need for secure wireless transport of audio, video and data across wide area networks has become crucially important for almost everyone. This is a great issue because wireless devices were not originally designed with security as a top priority. Nowadays, wireless security is becoming a very important and challenging area of research and development. In this article we discuss the potentials of wireless security protocols (WEP, WPA and WPA2/802.11i) used today and security aspects of wireless communication systems as well.

Introduction

Mobility and broadband media services are two crucial demands of modern telecommunication networks. The fast progress in wireless communication systems, smart card technologies and personal communication systems provides new opportunities and challenges for scientist and engineers working on the security problems of new communication systems and technologies. In general, public-key cryptography offers a lot of solutions to many of concerning security problems in communication systems. However, big computational requirements have limited the use of public-key cryptography on wireless communication systems.

Encryption mechanisms can be classified as: symmetric or asymmetric. The both are of static state. A new approach follows the stream key generation mechanism, which involves time dimension into the key generation and brings up dynamic keys, one per each data record. The symmetric key is taken into consideration, but in a dynamic streaming environment. A static key is generated once and stored at location for performing encryption later. On the other hand, a dynamic key is initialized by a central authority.

In WLANs, privacy is obtained by data protected with encryption. Without encryption, any other standard wireless device can read all traffic in network. There are three major generations of security approaches:

(1)   WEP (Wired Equivalent Privacy),
(2)   WPA (Wi-Fi Protected Access),
(3)   WPA2/802.11i (Wi-Fi Protection Access, Version 2).

Each of these protocols can have name that is personal and enterprise template. In this article, it will be listed and explained the main sorts of wireless protocols.

Wired Equivalent Privacy (WEP)

Wired Equivalent Privacy (WEP) is a security algorithm for IEEE 802.11 wireless networks. Introduced in September 1999, its intention was to provide data confidentiality comparable to that of a traditional wired network. WEP is recognized thanks to the key of 10 or 26 hexadecimal digits. It is widely in use and is frequently the first security option given to users by router configuration tools.

In the sender side, WEP uses four operations to encrypt the data (plaintext). Firstly, the secret key used in WEP algorithm is 40-bit long and has a 24-bit Initialization Vector (IV). This vector is focused to acting as the encryption/decryption key. At second, the resulting key behaves as the seed for a Pseudo-Random Number Generator (PRNG). Thirdly, the plaintext is put into a integrity algorithm and focuses using the plaintext again. Fourthly, the result of key sequence and IV will go to RC4 algorithm. In other words, a final encryption message is made by attaching the IV in front of the Cipher text.

In the recipient side, WEP uses five operations to decrypt the received side (IV + Cipher text). Firstly, the Pre-Shared Key and IV are used to form a secret key. At second, the Cipher text and Secret Key go to CR4 algorithm and as a result there is a plaintext. At third, the IV and plaintext will separate. Fourthly, the plaintext goes to Integrity Algorithm to make a new IV and finally the new IV compared to original IV.

Two methods of authentication may be applied to WEP: Open System authentication and Shared Key authentication. Here will be discussed WEP authentication in the Infrastructure mode which is between a WLAN client and an Access Point. All this can be applied to the Ad-Hoc mode as well. In Open System authentication, the WLAN client need not provide its credentials to the Access Point during authentication. Any client can authenticate with the Access Point and then attempt to associate. In fact, no authentication happens. WEP keys can be used for encrypting data frames. The client must have the correct keys.

In Shared Key authentication, the WEP key is used for authentication in a four step challenge-response handshake:

1.   The client sends an authentication request to the Access Point.

2.   The Access Point replies with a clear-text challenge.

3.   The client encrypts the challenge-text using the configured WEP key, and sends it back in another authentication request.

4.   The Access Point decrypts the response. If this matches the challenge-text the Access Point sends back a positive reply.

After all this, the pre-shared WEP key is also used for data frames encryption using RC4. At first glance, it might seem that Shared Key authentication is more secure than Open System authentication, although the latter offers no real authentication. But, it is quite the opposite. It is possible to derive the key-stream used for the handshake by capturing the challenge frames in Shared Key authentication. It has been advised to use Open System authentication for WEP authentication, rather than Shared Key authentication.

The major weaknesses and enhancements of WEP protocol are given in reference [1] and are as follows:

1.   WEP does not prevent forgery of packets.
2.   WEP does not prevent replay attacks. An attacker can simply record and reply packets as desired and they will be accepted as legitimate.
3.   WEP uses RC4 improperly. The used keys are very weak and can be brute-forced on standard computers quickly using freely available software.
4.   WEP re-uses IVs. Many cryptanalytic methods can decrypt data without knowing the encryption key.
5.   WEP allows an attacker to undetectably modify a message without knowing the encryption key.
6.   Key management is lack and updating is poor.
7.   Problem in the RC4 algorithm.
8.   Easy forging of authentication messages.

Implemented non-standard fixes of WEP protocol are as follows:

I. WEP2

This stopgap enhancement to WEP was present in some of the early 802.11i drafts. It was implementable on some (not all) hardware not able to handle WPA or WPA2, and extended both the IV and the key values to 128 bits. It was hoped to eliminate the duplicate IV deficiency as well as stop brute force key attacks. After it became clear that the overall WEP algorithm was deficient (and not just the IV and key sizes) and would require even more fixes, both the WEP2 name and original algorithm were dropped. The two extended key lengths remained in what eventually became WPA’s TKIP.

II. WEP plus

WEP plus, also known as WEP+, is a proprietary enhancement to WEP by Agere Systems (formerly a subsidiary of Lucent Technologies) that enhances WEP security by avoiding “weak IVs”. It is only completely effective when WEP plus is used at both ends of the wireless connection. As this cannot easily be enforced, it remains a serious limitation. It also does not necessarily prevent replay attacks, and is ineffective against later statistical attacks that do not rely on weak IVs.

III. Dynamic WEP

Dynamic WEP refers to the combination of 802.1x technology and the Extensible Authentication Protocol. Dynamic WEP changes WEP keys dynamically. It is a vendor-specific feature provided by several vendors such as 3Com. The dynamic change idea made it into 802.11i as part of TKIP, but not for the actual WEP algorithm.

Wi-Fi Protected Access (WPA)

Wi-Fi Protected Access (WPA) and Wi-Fi Protected Access II (WPA2) are two security protocols and security certification programs developed by the Wi-Fi Alliance to secure wireless computer networks.

WPA became available in 2003. The Wi-Fi Alliance intended WPA as an intermediate measure to take the place of WEP pending the availability of the full IEEE 802.11i standard. WPA could be implemented through firmware upgrades on wireless network interface cards designed for WEP. Since the changes required in the wireless access points (APs) were more extensive than those needed on the network cards.

The WPA protocol implements much of the IEEE 802.11i standard. Specifically, the Temporal Key Integrity Protocol (TKIP) was adopted for WPA. WPA also includes a message integrity check. This is designed to prevent an attacker from capturing, altering and/or resending data packets. This replaces the cyclic redundancy check (CRC) that was used by the WEP standard. WPA uses a message integrity check algorithm called Michael to verify the integrity of the packets.

Wi-Fi Protection Access, Version 2 (WPA2)

WPA2 has changed WPA. WPA2 demands testing and certification by the Wi-Fi Alliance and uses the mandatory elements of IEEE 802.11i. In particular, it introduces CCMP, which is a new AES-based encryption mode with strong security. After only several years, WPA2 certification is mandatory for all new devices to bear the Wi-Fi trademark. The Wi-Fi Alliance intended it as an intermediate measure in anticipation of the availability of the more secure and complex WPA2. WPA2 became available in 2004 and is common shorthand for the full IEEE 802.11i (or IEEE 802.11i-2004) standard.

Conclusion

Wireless and mobile networks are rapidly extending their capabilities. In addition to their increasing bandwidth and because of their flexibility and freedom they are becoming the communication infrastructure of choice. Wireless communication provides a user the capability of conducting commerce at anytime, with nearly anyone, from anywhere, using a mobile communication channel. This mobile communication channel can also be used as an access method to the Internet.

References:

1.   Cryptography and Network Security: Principles and Practice, William Stallings, Prentice-Hall, Inc., New Jersey, 1999.
2.   Designing and Developing 802.11n Wireless Networks, Jim Geler, Cisco Systems, Inc., 2010.
3.   Wireless Mesh Networking: Architectures, Protocols and Standards, Yan Zhang, Jijun Luo, Honglin Hu, Auerbach Publications, Taylor & Francis Group, New York, 2007.

We continue with the series of articles about cryptography. More precisely, this one can be defined as a brief review of its history and the most significant ciphering device of ancient world. The initial post about this topic can be found here.

Going back through time, the Mankind always had the need to transform the message and to keep the information hidden. One of the oldest cryptography tools was a Spartan scytale. It is a tool used to perform a transposition cipher, consisting of a cylinder with a strip of parchment wound around it on which is written a message. The ancient Spartans and Greeks, in general, are told to have used this cipher to communicate during military campaigns.

 

The idea of the scytale ciphering is as follows. The recipient uses a rod of the same diameter on which he wraps the parchment to read the message. It has the advantage of being fast and not prone to mistakes which is a necessary characteristic when on the battlefield. If not, it can be easily broken. Since the strip of parchment hints strongly at the method, the ciphertext would have to be transferred to something less suggestive.

From indirect evidence, the scytale was first mentioned by the Greek poet Archilochus who lived in the 7th century B.C. The ancient Greeks used this cipher to communicate during military campaigns. Sender and recipient each had a cylinder of exactly the same radius. The sender wound a narrow ribbon of parchment around his cylinder. Then he wrote on it lengthwise. After the ribbon is unwound, the writing could be read only by a person who had a cylinder of exactly the same circumference.

Imagine that each column wraps around the dowel one time that is the bottom of one column is followed by the top of the next column.

For instance, the original message can be: kill king tomorrow midnight

Wrapped message:

k i l l k i n g
t o m o r r o w
m i d n i g h t

Encoded message: ktmioi lmd lon kri irg noh gwt

The key parameter in the scytale encryption is the number of letters that can be recorded on one wrap ribbon around the dowel. In the example, the maximum is 3, since there are 3 rows in the wrapped message. The last row was covered with blank spaces before the message was encoded. It is called the wrap parameter. If you don’t know the wrap parameter you cannot decode a message.

In conclusion, the Spartan scytale is one of the earliest encryption devices in the history. It was used by the Spartan Military for encoding message sent between commanders. In modern cryptography techniques, the scytale can be replaced with appropriate matrix system. Using the similar approach, the message can be ciphered using that method.

Cryptography is the practice and study of techniques for secure communication in the presence of third parties. More generally, it is about constructing and analyzing protocols that overcome the influence of third parties and which are related to various aspects in information security such as data confidentiality, data integrity, authentication, and non-repudiation. Modern cryptography intersects the disciplines of mathematics, computer science, and electrical engineering. Applications of cryptography include ATM cards, computer passwords, and electronic commerce. In this article I introduce the Symmetry Law which can be useful for symmetric encryption of information.

The Symmetry Law

The symmetry of the set of the encrypted information is the characteristic that separates the set of such ciphered information into two identical or symmetric or mirrored parts. In binary logics, the symmetry is the property of XOR and XNOR functions. Some algorithms based on these two functions can produce the symmetric result. In the coming theorems all this will be explained and proved.

Firstly, let start with the logic function XOR and XNOR and let prove their symmetry.

Later, I will show how some ciphering algorithms based on these two functions or their combinations can be used for constructing the set of symmetric encrypted information.

Exclusive-OR or XOR function

Exclusive-OR or XOR function can be defined as follows. A true output (1) results if one, and only one, of the inputs to the gate is true (1). On the other hand, if both inputs are false (0) or both are true (1), a false output (0) results. Its behavior is summarized in the truth table. A way to remember XOR is “one or the other but not both”.

The truth table of XOR function:

The logic gate of XOR function is given in Figure 1.

Figure 1. XOR gate drawn in Logic Circuit software

As it is obvious from the truth table, an XOR function gives a set of symmetric output results for the different input combinations. That leads to conclusion that the XOR function is a symmetric function.

Exclusive-NOR or XNOR function

Exclusive-NOR or XNOR function is the inverse of the exclusive-OR or XOR function. It behaves according to its truth table. A high output (1) results if both of the inputs to the gate are the same. On the other hand, if one but not both inputs are high (1), a low output (0) results.

The truth table of XNOR function:

The logic gate of XNOR function is shown in Figure 2.

Figure 2. XNOR gate designed in Logic Circuit software

Theorem 1:

Let assume that we observe a set of a-bit binary information, where a ≥ 3. The set of information contains 2ª different combinations of 0s and 1s. In that case, the source message can be represented using the weight coefficients. This is given in Equation (1).

Where:

n – the highest value of the weight coefficient for the message; n ≥ 2,

f – the weight coefficient for the message.

Let also assume that an encrypted message or a cipher can be presented as array of the weight coefficients, where number of digits for the message and number of digits for the cipher are the same. This is shown in Equation (2).

Where:

n – the highest value of the weight coefficient for the cipher; n ≥ 2,

g – the weight coefficient for the cipher.

If the following algorithm (3) is applied, as a result the symmetric or mirrored set of encrypted or ciphered information will be gotten.

The Proof:

The law will be proved using the case of the set of 4-bit binary information.

The set of 4-bit binary information:

Let observe the set of 4-bit binary information, which consists of 4 bits of information and has 2ª = 16 combinations. In this case, a number of bits or digits is a = 4. These combinations cover the set of the following decimal numbers: from 0 to 2ª – 1 = 15. All these combinations are given in Table 1 as follows.

Table 1.

Solution:

The results of such a provided ciphering process are given in Table 2. It is obvious that the set of the encrypted information is completely symmetric or mirrored, which is the consequence of the symmetric nature of XOR logic function. Table 2 is shown as follows.

Table 2.

Theorem 2:

Let assume that we observe a set of a-bit binary information, where a ≥ 3. The set of information contains 2ª different combinations of 0s and 1s. In that case, the source message can be represented using the weight coefficients. This is given in Equation (3).

Where:

n – the highest value of the weight coefficient for the message; n ≥ 2,

f – the weight coefficient for the message.

Let also assume that an encrypted message or a cipher can be presented as array of the weight coefficients, where number of digits for the message and number of digits for the cipher are the same. This is shown in Equation (4).

Where:

n – the highest value of the weight coefficient for the cipher; n ≥ 2,

g – the weight coefficient for the cipher.

If the following algorithm (5) is applied, as a result the symmetric or mirrored set of encrypted or ciphered information will be gotten.

The Proof:

The law will be proved using the case of the set of 4-bit binary information.

The set of 4-bit binary information:

Let observe the set of 4-bit binary information, which consists of 4 bits of information and has 2ª = 16 combinations. In this case, a number of bits or digits is a = 4. These combinations cover the set of the following decimal numbers: from 0 to 15. All these combinations are given in Table 3 as follows.

Table 3.

 

The results of such a provided ciphering process are given in Table 4. It is obvious that the set of the encrypted information is completely symmetric or mirrored, which is the consequence of the symmetric nature of XNOR logic function. Table 4 is illustrated as follows.

Table 4.

Conclusions

This article provides a brief review of the results the author got during her research. The author plans to continue her research and to publish her findings into this magazine. The initial step has been made and the facts about the Symmetry Law have been shared with the audience. This is not the final version of the law, only the initial step. As research goes further, the author will be that free to publish the results.

Reference:

1.   Digital Systems – Principles and Applications, Ronald J. Tocci & Neal S. Widmer, Prentice-Hall International, Inc., 1998.