Coding & Cryptography

Front 1

Parity bit

Back 1

Added to o messages to check for errors.

The parity bit can be either even or odd

Front 2

Cyclic redundancy check

Back 2

Much more powerful way of creating a check. Instead of a single parity bit, it will produce a string of bits as its check.

Front 3

How can XOR be used to create backup discs?

Back 3

There are 2 drives on a computer, each contain binary data.

A backup drive is created by taking the XOR of the 2 drives.

If an of the 3 drives fail, you can recover the by taking the XOR of the other 2 drives.

Front 4

Hamming(7,4) code

Back 4

Code that consists of blocks of 7 bits, 4 of which is the actual data and the other 3 are parity bits.

It is an error correcting code or that can detect up to 2 errors, but can only correct any 1 error.

Front 5

Rate of a code

Back 5

The message length/block length

e.g. hamming(7,4): 4/7

Hamming codes are considered perfect because of their high code rates.

A code with the best rate that can possibly be achieved for a code of a certain length with a specified error I correcting abilities is called a perfect code

Front 6

Prefix-free codes

Back 6

A set of codewords where no codeword appears at the beginning of any other codeword. No codeword is a prefix of another.

This set {10, 11,101} is not a prefix-free code because 10 appears at the beginning of 101.

But this set {11, 10, 001} is prefix free

Front 7

Linear codes

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The combination (via XOR) of any 2 codewords gives another possible codeword.

Also any linear codeword must contain the all-zero codeword

Front 8

Cyclic codes

Back 8

Are linear and every cyclic permutation of a codeword is also a valid codeword.

Front 9

Linear feedback shift

Back 9

To take certain predefined digits of this keyword, perform an operation like XOR on them, and then put the output on the left of the keyword, shifting everything in the keyword one place to the right, so the last digit falls off and disappears.

Front 10

Practical issues for linear feedback shift register

Back 10

Highly useful for generating pseudo-random sequences

Useful in various applications e.g. generating a model of white noise in a communication channel.

Used heavily in digital transmissions especially for scrambling of data.

Appear in applications like DAB radio and NICAM sound

Also used in applications like GPS and Bluetooth

Commonly used due to their simplicity.

Front 11

Secret key and public key crypt

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Secret key can be likened to boxes and locks.

With secret key cryptography both Alice and Bob have identical keys that unlock the box with the message.

But with public key Bob has the only decryption key.

Advantages of public key

Bob has the only key so if the messages is intercepted before it gets to bob, it cannot be cracked.

Disadvantages

Bob cannot verify who the message came from, and if the key gets lost then the message can't be decrypted.

Advantage of secret key

Both bob and alice have the same key so they can both decrypt the message.

Disadvantage of secret key

Someone might be able to get the key while it is being transmitted.

Somebody might also pretend to be your partner and ask for the key

Front 12

Primitive root

Back 12

A set of numbers mod (n) for some n. A number g in this set is called a primitive root (mod n) if g, g^2,....g^(n-1) are all different (mod n) e.g. 5 mod 7.

5 is a primitive root (mod 7)

Front 13

Elliptic Curve

Back 13

An equation of the form:

y^2=x^3+ax+b

Many cryptographic algorithms can be adapted to use elliptic curve groups rather than the multiplicative group (mod p)

The Diffie-Hellman elliptic curve key exchange scheme is an example of an elliptic curve method.

Front 14

Steganography

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Historical steganography was when the head of a trusted slave was shaved and a message was tattooed on it. The hair grew back to hide the message and the slave was sent to dispatch the message. The person on the receiving end shaves the slaves head to read the message.

Modern day steganography is when documents are hidden within digital images.

Front 15

Digital signature

Back 15

A mathematical technique used to validate the authenticity and integrity of a message or digital documents

Front 16

Digital signature picture

Back 16

Alice takes her message m and applies some hashing algorithm to it to obtain the hash h .

Alice then encrypts the hash h using her private key to obtain her signature s

She then encrypts the message using bobs public key and send the encrypted message to bob.

Bob decrypts the message using his private key and obtains the message and the signature s

Bob decrypts the signature s using Alice's public key to obtain the hash h

Finally bob applies the agreed hashing algorithm to m. If everything is in order then he should obtain the same hash h as in the previous step.

Front 17

Certificate authority

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A designated body that can authorise a user.

Digital certificates contain details of the public key, the algorithm uses to obtain it, details of the user requesting the certificate and the authority issuing it.

They contain a valid from date, and an expiry date.

Widely used certificate authority:

Venisign

Comodo

GeoTrust

Thawte

Digisign

Front 18

P.A.I.N

Back 18

Privacy

recipient.

Authentication

Privacy The need to keep the data secret from anyone other than the intended recipient. Authentication Ensuring that who you think you are communicating with is actually that person. Integrity Making sure that the message received is the actual message sent. Non-repudiation Once a transaction has taken place neither party can later deny it.

The need to keep the data secret from anyone other than the intended recipient. Authentication Ensuring that who you think you are communicating with is actually that person. Integrity Making sure that the message received is the actual message sent. Non-repudiation Once a transaction has taken place neither party can later deny it.

person.

Integrity

Ensuring that who you think you are communicating with is actually that person. Integrity Making sure that the message received is the actual message sent. Non-repudiation Once a transaction has taken place neither party can later deny it.

person. Integrity Making sure that the message received is the actual message sent. Non-repudiation Once a transaction has taken place neither party can later deny it.

Non-repudiation

Making sure that the message received is the actual message sent. Non-repudiation Once a transaction has taken place neither party can later deny it.

Non-repudiation Once a transaction has taken place neither party can later deny it.

Once a transaction has taken place neither party can later deny it.

Front 19

Does a public key infrastructure address all of these issues?

Back 19

Privacy

No-one apart from bob can recover the message as it was sent using his public key, so only his private key can decrypt it.

Authentication

The signature was created by Alice's private key so no-one else can create the same signature, since no one knows this private key.

Integrity

If the message is changed during transmission then the hashes will not match. This could be a problem with authentication (bob can't confirm Alice's identity) or integrity (the message has changed)

Bob will notice the hashes don't match and so he knows something went wrong.

Non-Repudiation

The signature acts as confirmation that this transaction really happened and was signed for by Alice so she can't later deny it happened.

Yes a public key infrastructure addresss all of these issues.

Front 20

Quantum cryptography

Back 20

Is based on physics and quantum mechanics. It is an entirely different approach to cryptography