Introduction to Network Security – Part 8

NOTIFICATION: These examples are provided for educational purposes. The use of this code and/or information is under your own responsibility and risk. The information and/or code is given ‘as is’. I do not take responsibilities of how they are used. You are welcome to point out any mistakes in my posting and/or leave a comment.

In security, we use a system of key in order to work on encryption and decryption. The most common system used are the Symmetric Key Encryption and the Public Key Encryption

Symmetric Key Encryption

In a symmetric  system, one key is used for the encryption of a plaintext to a ciphertext and for the decryption of the ciphertext to a plaintext.

The key must be distributed in a secure way to the sender and the receiver making sure that the key is not disclose since then the communication could be compromised. The possible disclose of the key is one of the disadvantages of this system.

Another disadvantages of this system are:

  1. There is no way to prove the message was send by the original sender and not from an intruder.
  2. The recipient could change the message and say it came from the sender.

Public-key Encryption

In the public key system, normally two keys are generated (pair keys). One key is used to encrypt the message and another key is generated to decrypt the message.

The key that was used for the encryption of the message cannot be used for the decryption and the key used for the decryption of the message cannot be used for the encryption of the plaintext.

One key is the public key which is going to be used for the encryption of the plaintext to the ciphertext and for the verification of the signatures.

The other key is the private key which is going to be used for the decryption of the ciphertext to a plaintext and the generation of signatures.

This system can be used for:

  1. Authentication: Verify that the message came from the corresponding sender and the message is received to the corresponding receiver
  2. Confidentiality: Create a message that cannot be decrypt by an attacker
  3. Authentication and Confidentiality

However, this system still have some main issues such as:

  1. Key distribution: In the same way that the symmetric key encryption, there have to be a secure way to distribute keys.
  2. Digital Signatures: The way to verify that the message is coming for the sender and not an attacker.

The public-key encryption is considered to be an asymmetric system. This means that those who encrypt the plain-text and/or verify the signatures cannot decrypt the message or create signatures.

In order for a public key encryption to be feasible, it must:

  1. Make harder for an attacker to find the key used for the decryption of the ciphertext by just knowing the algorithm and the key used for the encryption of the plaintext.
  2. To provide an easy way to decrypt the ciphertext when the key for decryption is used.
  3. To provide a way in which either, the private key or public key, can be used for the encryption and the other key used for the decryption of the message. System that implement this policy is called RSA.

This is the way that normally pubic key works:

  1. Each user generate a pair of key that will be use for the encryption and decryption.
  2. Each user place one key (the public key) to a public register while holding the private key to themselves (the private key is never distributed).
  3. In case the private key is change, then the user must generate a new public key that will replace the older public key.

Symmetric Key Encryption Versus Public-Key Encryption

Before we go in deep comparing both encryption systems let clarify some points:

  1. The security of both system depend directly on the key/s length. The largest is the key, the harder is to break the cipher.
  2. While the public key may provide more security than symmetric key, it produce an overhead. This is the main reason that symmetric key is not considered obsolete with the apparition of the public key encryption.

Here are the differences between symmetric key (conventional) and public key:

  1. Symmetric key: Same algorithm using the same key is used for encryption and decrytion.
    Public-key: One algorithm is used for encryption and decryption but a pair of keys are generated. One key is used for the encryption, another is used for the decryption.
  2. Symmetric key: Sender and receiver must use the same algorithm and share the same key.
    Public-key: Sender and receiver must use the same algorithm, but each user must create a pair key. One of those keys (the public key) must be distributed from the receiver to the sender. The other key (private-key), the receiver must kept this key and make sure it doesn’t not get distributed.

Things that need to be resolve from the point of view of security:

  1. Symmetric key: The shared key must be kept in secret
    Public-key: One of the two keys (normally the private key) must be kept in secret.
  2. Symmetric and Public-key: It should be very hard for an attacker to decipher a message if there is no information available.
  3. Symmetric key: Even do the attacker may have knowledge of the algorithm and have possession of the ciphertext, it should be very hard to obtain the plaintext and/or the shared key.
    Public-key: Even do the attacker may have knowledge of the algorithm, samples of the ciphertext, and the public key, it should be very hard to obtain the plaintext and the other key.

How to Use Public Key Encryption

The public-key encryption can be used to provide:

  1. Confidentiality: Prevent attackers to know the content of the message
  2. Integrity: Prevent attackers for modifying the original message
  3. Authentication: To verify that the sender and/or receiver is not an attacker disguising as the sender and/or receiver
  4. Digital Signature:  To verify that the message is send by the sender and not the attacker

Confidentiality (secrecy):

  1. For a plaintext X where X = [X1, X2, …, Xn]
  2. User A will generate two keys: Public key (PUa) and Private key (PUb)
  3. User B will generate two keys: Public key (PUb) and Private key (PUa)
  4. For A to send a message to B, A will receive the public key (PUb) from B.
  5. User A will encrypt the plaintext (X) using the public key (PUb) from user B with the encryption algorithm (E) to generate the ciphertext (Y).
    Y = E(PUb, X)
  6. User B will receive the ciphertext (Y). Using private key (PRb) with the decryption algorithm (D), user B will obtain the plaintext (X).
    X = D(PRb, Y)

Authentication:

  1. User A generate a plaintext for user B. User A encrypt the plaintext (X) using the private key (PRa) and the encryption algorithm (E) then user A send the ciphertext (Y) to user B.
    Y = E(PRa, X)
  2. User B receive the ciphertext (Y) and using the public key (PUa) with the decryption algorithm (D), user B obtain the plaintext (X).
    X = D(PUa, Y)

Even do this provide authentication and provide safety against the alteration of the message, it does not provide confidentiality because:

  1. This Authentication do not prevent from eavesdropping.
  2. An attacker can decrypt the ciphertext (Y) using user A public key (PUa).

Since tthe message can be prepare only for user A because it was encrypted by using user A’s private key (PUa). this message can be used for the purpose of digital authentication (we can assure the message comes from user A since he provide the public key), and it provide data integrity ( prevention against alteration of the message) since it is impossible to alter the message without the private key (PRa).

Confidentiality and Authentication:

By using the the properties of Confidentiality and Authentication, we can create a scheme that provide more security.

  1. User A generates a pair of keys (PUa and PRa) while user B also generates a paid of keys (PUb and PRb)
  2. Sending the message: User A uses the private  key (PRa) with the encryption algorithm (E) to encrypt the plaintext (X) to a ciphertext (Y). Then user A uses the public key (PUb) from user B with the encryption algorithm (E) to encrypt the ciphertext again to a new ciphertext (Z).
    Z = E(PUb, E(PRa, X))
  3. Receiving the message: User B receive the ciphertext (Z) from user A. User B uses the decryption algorithm (D) with the private-key (PRb) with the ciphertext (Z) to produce ciphertext (Y). Then user B uses the public key (PUa) from user A with the decryption algorithm (D) to decrypt the ciphertext (Y) to the plaintext (X).
    X = D(PUa, D(PRb, Z))

Requirements for Public Key Encryption

  1. It should be easy for user A to generate a pair of keys: Public key (PUa) and private key (PRa).
  2. It should be easy for user B to generate a pair of keys: Public key (PUb) and private key (PRb).
  3. It should be easy for user A to encrypt the plaintext (M) to a ciphertext (C) using the public key (PUb) from user B.
    C = E(PUb, M)
  4. It should be easy for user B to decrypt the ciphertext (C) to the plaintext (M) using the private key (PRb).
    M = D(PRb, C)
    Since C  = E(PUb, M) then M = D(PRb, E(PUb, M))
  5. It should be very hard for an attacker while knowing the public key (PUb) from user B to guess correctly the private key (PRb) of user B.
  6. It should be very hard for the attacker while knowing the public key (PUb) from user B and the ciphertext (C) encrypted with the public key (PUb) to obtain the plaintext (M) send by user A to user B
  7. Both keys should be able to be used in either order for the encryption and decryption:
    M = D(PUb, E(PRb, M)) = D(PRb, E(PUb, M))

Algorithm such as RSA follow these requirements.

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Introduction to Network Security – Part 5

NOTIFICATION: These examples are provided for educational purposes. The use of this code and/or information is under your own responsibility and risk. The information and/or code is given ‘as is’. I do not take responsibilities of how they are used.

Symmetric Encryption

In the symmetric encryption, the same key (normally a single-key) is used to perform the encryption and decryption of the ciphertext.

Symmetric Cipher Model: This model is performed by performing transformations and substitutions on the plaintext. A secret key, independent from the plaintext and the algorithm, is used to cipher the plaintext. After, the ciphertext plus the secret key is used with the decryption algorithm to obtain the original plaintext.

Symmetric Encryption is the opposite to the concept of public key distribution which will be explained in future postings.

Requirements:

  1. The cipher model must be mathematical expression:
    (E: Encryption, D: Decryption, X: plaintext, Y: ciphertext, K: secret key)

    Y = E(K, X)
    X = D(K, Y)
    
  2. Assumption that the encryption algorithm is known to the attacker.
  3. A strong encryption algorithm which in case the attacker would obtain or know some examples of the ciphertext and the plaintext produced from the ciphertext, the attacker would still be not able to obtain the key. This means that if the attacker would obtain the ciphertext, the attacker would not be able to obtain the secret key or the plain text.
  4. Secret key should be known only by the sender and the receiver of the ciphertext.
  5. The distribution of the secret key must be done in a secure fashion. For example, the use of a third party that would generate and provide in a secure way the key to the sender and the receiver.

Substitution Ciphers

In classical substitution ciphers, all the letters in the plaintext will be replaced by another letter, number, and/or symbol.

Caesar Cipher

History explains that Julius Caesar <http://www.roman-empire.net/republic/caesar-index.html> came up with a substitution cipher that he used in his campaigns for military affairs.

The cipher works in the following way:

  1. We use the alphabet of 26 letters:
    
    
  2. Under this alphabet, we will rewrite the alphabet by picking a letter as a starting point.
    Lets say our key indicate the starting point such as K = 4 so we begin with the letter ‘E’ then:
  3. This means that if we wish to send a plaintext (P) that says HELLO, the ciphertext (C) would be LIPPS, and the key (K) would be 4
  4. The mathematical way to represent this cipher will be the follows:
    1. Give each letter of the alphabet a number:
      A = 1, B = 2, C = 3, D = 4, E = 5,F = 6, G = 7, H = 8, J = 9, K = 10, L = 11, M = 12, N = 13, O = 14,P = 15, Q = 16, R = 17, S = 18, T = 19, U = 20, V = 21, W = 22, X = 23, Y = 24, Z = 25.
    2. Encryption Algorithm:
      E: Encryption, Ct: Ciphertext, Pt: Plaintext, K: secret key

      Ct = E(Pt)
         = (Pt + K) mod 26
    3. Decryption Algorithm:
      D: Decryptor, Ct: Ciphertext, Pt: Plaintext, K: secret key

      Pt = D(Ct)
         = (26 + (Ct - K)) mod 26
  5. The weakness of this cipher is that it can be broken by brute force. We just need to test the 25 combinations of different keys  until we find the key that reveals the message.

Monoalphabetic Cipher

The mono-alphabetic cipher instead of shifting the alphabet a number of letters, its substitute each letter arbitrarily by mapping the plaintext letter map to a random arranged ciphertext. The only requirement for the ciphertext is that the letters must not be repeated.

Since we are using 26 letters of the alphabet the arrangement of the cipher can permute a total of 26! permutations.

If we wish to encode the word “HELLO”, we would obtain “NERRS”

Lets assume we wish to cipher a plaintext:

Plaintext = “THIS IS A SECRET MESSAGE ENCODED IN MONOALPHABETIC”

Ciphertext = “XNMW MW E WIGBIX OIWWEJI IPGSCIC MP OSPSERUEDIXMG”

The following website let you play a little with monoalphabetic cipher by randomizing for you the ciphertext:
<http://www.simonsingh.net/The_Black_Chamber/generalsubstitutionWithMenu.html>

The only problem is that this cipher can be exploited by doing regularities analysis over the frequency of the letters. Base on the language rules some letters are used more than others. For example, in English, the letter ‘E’ is the most common used in words, followed by A, I, O, N, R, S, T. Others letters such as K, J, Q, X, Z are less used than the rest.

The largest is the message, the most chances that the attacker can decrypt the message.
Just in this message “XNMW MW E WIGBIX OIWWEJI IPGSCIC MP OSPSERUEDIXMG” we have:

  • W = 6 letters
  • E = 4 letters
  • M = 4 letters
  • S = 3 letters
  • P = 2 letters
  • ….

And continue counting.

As you may notice the letter ‘W’ of the encrypted message have the most counts, so we could  assume that this is the letter E of the plaintext.

If you are interested to know the frequency of letters in English you can go to the following website:
<http://www.cryptograms.org/letter-frequencies.php>

For more information about attacking mono-alphabetic cipher, there is a good example on this website:
<http://unsecure.co.uk/attackingmonoalphabeticciphers.asp>

Playfair Cipher

Playfair is one way to improve the security of mono-alphabetic cipher by encrypting multiple letters.

Playfair Encryption

  1. Create a playfair key matrix:
    1. Create a matrix of letters based on a keyword. For this example, the matrix should be 5 by 5
    2. Fill in the letters of the keyword from left to right and from top to bottom. Make sure that there are not duplicate letters
    3. Fill the rest of the matrix with the other letters that are not in the keyboard, making sure to not duplicate letters.
    4. As a rule, the letter I and J count as one letter.
      • I am not sure the reason for this rule, except the following:
        • First, it make it harder to decrypt the message since one letter is missing.
        • Second, in some languages, the J and I would have the same pronunciation.
          For example, my last name Carlstein was originally written as Karlštejn.
      • In case you know the real reason, please let me know and give me a reference to verify (thanks).
    5. Example of playfair key matrix:
      1. Let use the keyword: “EDUCATOR”
      2. The table should looks like this:
      3. Notice that I and J are counted as one letter
  2. The next step is to encrypt the plaintext taking two letters at the time.
    1. In case a two letters are the same (repeated), we must insert a filler letter (use the letter X as the filler). For example:
      HELLO → HE LX LO
    2. In case two letters are in the same row, replace each letter with the letter to the right. In case the letter is at the last column, pick the letter of the first row (the table is considerate to be circular). For example, lets say we have the letters D and A:

      1. D → U and A → E
      2. Therefore DA became UE
    3. In case two letters are in the same column, replace each letter with the letter below. In case the letter is at the last row, pick the letter of the first row (the table is considerate to be circular). For example, lets say we have the letters T and V:

      1. T → G and V → E
      2. Therefore TV became GE
    4. In case two letter are in different row and column, the first letter will be replaced with another letter of the same row on the column of the second letter. The second letter will be replaced with another letter of the same row on the column of the first letter. For example lets say we have the letters O and Q:

      1. To replace the letter O:
        1. This means that O → B
      2. To replace the letter Q:
        1. This means that Q → N
      3. Therefore OQ became BN

Playfair Decryption:

  1. Decrypt two letters at a time:
    1. In case two letters are in the same row, replace each letter with the letter to the left. In case the letter is at the last column, pick the letter of the first row (the table is considerate to be circular). For example, lets say we have the letters U and E:

      1. U → D and E → A
      2. Therefore UE became DA
    2. In case two letters are in the same column, replace each letter with the letter above. In case the letter is at the last row, pick the letter of the first row (the table is considerate to be circular). For example, lets say we have the letters G and E:

      1. G → T and E → V
      2. Therefore GE became TV
    3. In case two letter are in different row and column, the first letter will be replaced with another letter of the same row on the column of the second letter. The second letter will be replaced with another letter of the same row on the column of the first letter. For example lets say we have the letters B and N:

      1. To replace the letter B:
        1. This means that O → B
      2. To replace the letter Q:
        1. This means that Q → N
      3. Therefore OQ became BN
  2. After you will finish with the final message. You must remove any extra X that do not make sense in the message:
    HE LX LO → HELLO
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Introduction to Network Security – Part 4

NOTIFICATION: These examples are provided for educational purposes. The use of this code and/or information is under your own responsibility and risk. The information and/or code is given ‘as is’. I do not take responsibilities of how they are used.

Before we begin talking about encryption, decryption, and ciphers related topic, let go over some terminologies to have in account:

  • Cipher: An algorithm used for encryption.
    Link reference: <http://www.merriam-webster.com/dictionary/cipher>
  • Ciphertext: The encrypted(coded) message.
    Link reference: <http://cryptnet.net/fdp/crypto/crypto-dict/en/crypto-dict.html>
  • Cryptanalysis: Study of the principles and methods of deciphering a ciphertext without having the required key.
    Link reference: <http://en.wikipedia.org/wiki/Cryptanalysis>
  • Cryptography: Study of the principles and methods of encryption.
    Link reference: <http://en.wikipedia.org/wiki/Cryptography>
  • Cryptology: The study of cryptanalysis and cryptography.
    Link reference: <http://www.britannica.com/EBchecked/topic/145058/cryptology>
  • Deciphering: Also known as decryption. The act of transforming a ciphertext to the original plaintext.
    Link reference: <http://www.merriam-webster.com/dictionary/deciphering>
  • Decryption: Also known as deciphering. The act of transforming a ciphertext to the original plaintext.
  • Enciphering: Also known as encryption. The act of transforming a plaintext to a ciphertext.
    Link reference: <http://www.merriam-webster.com/dictionary/enciphering>
  • Encryption: Also know as enciphering. The act of transforming a plaintext to a ciphertext.
  • Plaintext: the original message to be encrypted.
    Link reference: <http://en.wikipedia.org/wiki/Plaintext>
  • Product: stages of transposition and substitutions performed.
    Link reference: <http://www.britannica.com/EBchecked/topic/477942/product-cipher>
  • Secret key: An input required for the encryption and/or decryption algorithms.
  • Substitution: Map each element in a plain text to another element.
    Link reference: <http://substitution.webmasters.sk/>
  • Transposition: Rearrange the elements in the plaintext
    Link reference: <http://mw1.meriam-webster.com/dictionary/transposition%20cipher>

Cryptography

A cryptographic system is characterized by the use of encryption operations, number of keys used for encryption and decryption, and the way in which the plain text is processed.

Encryption Operations: In order to encrypt a plaintext to a chipertext is required to perform multiple stages of transposition and substitution, also known as product.

  • Substitution: We take each element from the plaintext and mapped them to another element
  • Transposition: We  take each element in the plaintext and rearrange its order in such a way that it differ from the original plaintext.

To perform encryption and decryption, we use a key reference. We can categorize the encryption techniques as  symmetric, single, asymmetric, double, and/or public.

The plaintext can be processed by using a method of streams or blocks:

  • Stream: The plaintext is processed as a continuous set of elements in which each element is encrypted one at a time.
  • Blocks: The plaintext is divided in a set of blocks in which each block is encrypted one at a time.

Cryptanalysis

As explained in the terminology list, Cryptanalysis is purpose of decrypt an encrypted ciphertext without the knowledge of the key used for the encryption. One way is to attack the encryption system and recover the key used for the encryption instead of recovering the plaintext from a single ciphertext.
Cryptanalysis attacks are divided in two categories:

  1. Brute-force Attack: Every combination of a possible key is tested on the chipertext until the plaintext is obtained.
  2. Cryptanalytic Attack: The use of knowing some characteristic of the original plaintext such as some used keywords, language, format, plaintext to ciphertext pairs examples, and  knowledge of the possible algorithm used to decrypt the ciphertext.

Unconditional Security

We call unconditional security when a cipher cannot be broken by using a ciphertext and the plaintext that produced the ciphertext regardless of the computational power and time available. Up to day, there are no encryption algorithm that can be unconditional secure with the exception of the one-time pad encryption algorithm <http://www.ibm.com/developerworks/library/s-pads.html> which will be explained in the following postings.

Computational Security

Base on the cost-benefit of braking a cipher, a cipher may not be broker due:

  1. The cost of braking the cipher is greater than the value of the plaintext encrypted
  2. The time required to breaking the cipher exceed the usefulness lifetime of the plaintext encrypted
  3. Depending of the complexity of the cipher, there would be a limitation of computing resources and time.

Brute Force Search

As explained before, we call brute force to try every key combination possible to decrypt the ciphertext into plaintext. Before obtaining success, the attacker must try at least 50 percent of the possible keys; therefore, the probability of success may be proportional to the size of the key.

Lets assume we wish to have to option of using:

  1. DES encoding (56-bit) <http://groups.csail.mit.edu/cag/raw/benchmark/suites/des/README.html>.
  2. Triple DES (168-bit) <http://en.wikipedia.org/wiki/Triple_DES>
  3. AES (Greater than 128 bits) <http://www.aescrypt.com/>

Depending of which encryption we use, the time required to find the right key by brute force could be:

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