Cryptography Tutorial

This tutorial covers the basics cryptography Tutorial the science of cryptography. It explains how programmers and network professionals can use cryptography to maintain the privacy of computer data. Starting with the origins of cryptography, it moves on to explain cryptosystems, various traditional and modern ciphers, public key encryption, data integration, message authentication, and digital signatures.

Audience This tutorial is meant for students of computer science who aspire to learn the basics of cryptography. It will be useful for networking professionals as well who would like to incorporate various cryptographic algorithms to ensure secure data communication over their networks. Prerequisites This tutorial has been prepared with the view to make it useful for almost anyone who is curious about cryptography. A basic knowledge of computer science and a secondary level of mathematics knowledge is sufficient to make the most of this tutorial.

January 2015

The Java enum tutorial has been updated with several new sections, including a video version. The Java lambda expression tutorial has been updated quite a bit, and now includes a video version too. The Java Cryptography API enables you to encrypt and decrypt data in Java, as well as manage keys, sign and authenticate messages, calculate cryptographic hashes and much more. The term cryptography is often abbreviated to crypto, so sometimes you will see references to Java crypto instead of Java Cryptography.

The two terms refer to the same topic though. In this Java Cryptography tutorial I will explain the basics of how to use the Java Cryptography API to perform the different tasks needed for secure encryption. This Java Cryptography tutorial will not cover the underlying cryptography theory. You will have to look elsewhere for that for now. The Java Cryptography Extension is also sometimes referred to vi the abbreviation JCE.

The Java Cryptography Extension has been part of the Java platform for a long time now. The JCE was initially kep separate from Java because the US had some export restrictions on encryption technology. Therefore the strongest encryption algorithms were not included in the standard Java platform. US encryption export rules have been eased a lot. Therefore most of the world can benefit from the international encryption standards via Java JCE. JCA is structured around some central general purpose classes and interfaces. The real functionality behind these interfaces are provided by providers.

You can implement and plugin your own providers too, but you should be careful with that. Implementing encryption correctly without security holes is hard! Unless you know what you are doing, you are probably better off using the builtin Java provider, or use a well established provider like Bouncy Castle. The most commonly used of these classes are covered throughout the rest of this Java Cryptography tutorial. In order to use the Java crypto API you need a Provider set.

The Java SDK comes with its own cryptography provider. If you don’t set an explicit cryptography provider, the Java SDK default provider is used. However, this provider may not support the encryption algorithms you want to use. One of the most popular cryptography providers for the Java cryptography API is called Bouncy Castle. A cipher can be used to both encrypt and decrypt data. This example creates a Cipher instance which uses the AES encryption algorithm internally. String identifying which encryption algorithm to use, as well as a few other configurations of the algorithm.

In the example above, the CBC part is a mode the AES algorithm can work in. The PKCS5Padding part is how the AES algorithm should handle the last bytes of the data to encrypt, if the data does not align with a 64 bit or 128 bit block size boundary. The first parameter specifies whether the Cipher instance should encrypt or decrypt data. The second parameter specifies they key to use to encrypt or decrypt data with.

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Please note that the way the key is created in this example is not secure, and should not be used in practice. This Java cryptography tutorial will describe how to create keys more securely in sections later. To initialize a Cipher instance to decrypt data you have to use the Cipher. Symmetric keys are used for symmetric encryption algorithms. Symmetric encryption algorithms use the same key for encryption and decryption.

Asymmetric keys are used for asymmetric encryption algorithms. Asymmetric encryption algorithms use one key for encryption, and another for decryption. The public key – private key encryption algorithms are examples of asymmetric encryption algorithms. Somehow the party that needs to decrypt data needs to know the key needed to decrypt the data. If the party decrypting the data is not the same as the party encrypting it, somehow these two parties need to agree on a key, or exchange the key. This is referred to as key exchange. The example in the previous section about the Cipher class used a very simple, hardcoded key.

This is not a good idea in practice. If they key is easy to guess, it is easy for an attacker to decrypt the encrypted data and possibly create fake messages herself. It is important to make a key hard to guess. Thus, a key should consist of random bytes. The more random, the better, and the more bytes, the harder to guess because there are more possible combinations. Private and public keys are used in asymmetric encryption.

A public key can have an associated certificate. A certificate is a document that verifies the identity of the person, organization or device claiming to own the public key. A certificate is typically digitally signed by the verifying party as proof. Secret keys are used in symmetric encryption. The Keytool comes with the Java installation.

The Keytool is described in more detail in the tutorial about the Java Keytool. A common solution is to calculate a message digest from the data before it is encrypted, and then encrypt both the data and the message digest and send that across the wire. A message digest is a hash value calculated from the message data. If a byte is changed in the encrypted data, the message digest calculated from the data will change too. When receiving encrypted data, you decrypt it and calculate the message digest from it, and compare the calculated message digest to the message digest that was sent along with the encrypted data.

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There are several different message digest algorithms available. The term MAC is short for Message Authentication Code. A MAC is similar to a message digest, but uses an additional key to encrypt the message digest. You create a Java Mac instance by calling the Mac. Before you can create a MAC from data you must initialize the Mac instance with a key.

When data is signed a digital signature is created from that data. The signature is thus separate from the data. The encrypted message digest is called a digital signature. To create a Signature instance you call the Signature. Once the Signature instance is initialized it can be used to sign data.

Hill in 1929, the Hill cipher is a polygraphic substitution cipher based on linear algebra. Hill used matrices and matrix multiplication to mix up the plaintext. To counter charges that his system was too complicated for day to day use, Hill constructed a cipher machine for his system using a series of geared wheels and chains. However, the machine never really sold. Hill’s major contribution was the use of mathematics to design and analyse cryptosystems.

It is important to note that the analysis of this algorithm requires a branch of mathematics known as number theory. For a guide on how to break Hill ciphers, see Cryptanalysis of the Hill Cipher. This example will rely on some linear algebra and some number theory. The key for a hill cipher is a matrix e.

Assume we want to encipher the message ATTACK AT DAWN. To encipher this, we need to break the message into chunks of 3. This process is performed for all 3 letter blocks in the plaintext. The plaintext may have to be padded with some extra letters to make sure that there is a whole number of blocks. Now for the tricky part, the decryption.

We need to find an inverse matrix modulo 26 to use as our ‘decryption key’. If our 3 by 3 key matrix is called K, our decryption key will be the 3 by 3 matrix K-1, which is the inverse of K. To find K-1 we have to use a bit of maths. It turns out that K-1 above can be calculated from our key. A lengthy discussion will not be included here, but we will give a short example. Let K be the key matrix. Let d be the determinant of K.

The simplest way of doing this is to loop through the numbers 1. 25 and find the one such that the equation is satisfied. Once K-1 is found, decryption can be performed. The case here is restricted to 2×2 case of the hill cipher for now, it may be expanded to 3×3 later. The ‘key’ should be input as 4 numbers, e. Cryptanalysis is the art of breaking codes and ciphers.

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When attempting to crack a Hill cipher, frequency analysis will be practically useless, especially as the size of the key block increases. For a guide on how to break Hill ciphers with a crib, see Cryptanalysis of the Hill Cipher. For the case of a 2 by 2 hill cipher, we could attack it by measuring the frequencies of all the digraphs that occur in the ciphertext. In standard english, the most common digraph is ‘th’, followed by ‘he’.

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If it is not, we could try other combinations of common ciphertext digraphs until we get something that is correct. In general, the hill cipher will not be used on its own, since it is not all that secure. Some modern ciphers use a matrix multiplication step to provide diffusion e. AES and Twofish use matrix multiplication as a part of their algorithms. Further reading We recommend these books if you’re interested in finding out more.

Leave a comment on the page and we’ll take a look. The first step in any automatic speech recognition system is to extract features i. The main point to understand about speech is that the sounds generated by a human are filtered by the shape of the vocal tract including tongue, teeth etc. This shape determines what sound comes out.

If we can determine the shape accurately, this should give us an accurate representation of the phoneme being produced. They were introduced by Davis and Mermelstein in the 1980’s, and have been state-of-the-art ever since. We will give a high level intro to the implementation steps, then go in depth why we do the things we do. Towards the end we will go into a more detailed description of how to calculate MFCCs.

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Frame the signal into short frames. For each frame calculate the periodogram estimate of the power spectrum. Apply the mel filterbank to the power spectra, sum the energy in each filter. Take the logarithm of all filterbank energies.

Take the DCT of the log filterbank energies. Keep DCT coefficients 2-13, discard the rest. There are a few more things commonly done, sometimes the frame energy is appended to each feature vector. Delta and Delta-Delta features are usually also appended.

Liftering is also commonly applied to the final features. Why do we do these things? We will now go a little more slowly through the steps and explain why each of the steps is necessary. This is why we frame the signal into 20-40ms frames. The next step is to calculate the power spectrum of each frame. Our periodogram estimate performs a similar job for us, identifying which frequencies are present in the frame. In particular the cochlea can not discern the difference between two closely spaced frequencies.

This effect becomes more pronounced as the frequencies increase. For this reason we take clumps of periodogram bins and sum them up to get an idea of how much energy exists in various frequency regions. Once we have the filterbank energies, we take the logarithm of them. This is also motivated by human hearing: we don’t hear loudness on a linear scale. Generally to double the percieved volume of a sound we need to put 8 times as much energy into it. This means that large variations in energy may not sound all that different if the sound is loud to begin with.

This compression operation makes our features match more closely what humans actually hear. Why the logarithm and not a cube root? The final step is to compute the DCT of the log filterbank energies. There are 2 main reasons this is performed. Because our filterbanks are all overlapping, the filterbank energies are quite correlated with each other. The DCT decorrelates the energies which means diagonal covariance matrices can be used to model the features in e.

But notice that only 12 of the 26 DCT coefficients are kept. The Mel scale relates perceived frequency, or pitch, of a pure tone to its actual measured frequency. Humans are much better at discerning small changes in pitch at low frequencies than they are at high frequencies. Incorporating this scale makes our features match more closely what humans hear. Frame the signal into 20-40 ms frames.

The first 400 sample frame starts at sample 0, the next 400 sample frame starts at sample 160 etc. If the speech file does not divide into an even number of frames, pad it with zeros so that it does. The next steps are applied to every single frame, one set of 12 MFCC coefficients is extracted for each frame. A short aside on notation: we call our time domain signal . This is called the Periodogram estimate of the power spectrum.

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We take the absolute value of the complex fourier transform, and square the result. We would generally perform a 512 point FFT and keep only the first 257 coefficents. Each vector is mostly zeros, but is non-zero for a certain section of the spectrum. To calculate filterbank energies we multiply each filterbank with the power spectrum, then add up the coefficents. Take the log of each of the 26 energies from step 3. This leaves us with 26 log filterbank energies. 26 log filterbank energies to give 26 cepstral coefficents.

For ASR, only the lower 12-13 of the 26 coefficients are kept. In this section the example will use 10 filterbanks because it is easier to display, in reality you would use 26-40 filterbanks. Good values are 300Hz for the lower and 8000Hz for the upper frequency. Of course if the speech is sampled at 8000Hz our upper frequency is limited to 4000Hz. Using equation 1, convert the upper and lower frequencies to Mels. In our case 300Hz is 401. 25 Mels and 8000Hz is 2834.

For this example we will do 10 filterbanks, for which we need 12 points. This means we need 10 additional points spaced linearly between 401. 70, 8000 Notice that our start- and end-points are at the frequencies we wanted. We don’t have the frequency resolution required to put filters at the exact points calculated above, so we need to round those frequencies to the nearest FFT bin. This process does not affect the accuracy of the features.

The first filterbank will start at the first point, reach its peak at the second point, then return to zero at the 3rd point. The second filterbank will start at the 2nd point, reach its max at the 3rd, then be zero at the 4th etc. This filterbank starts at 0Hz and ends at 8000Hz. This is a guide only, the worked example above starts at 300Hz. I have implemented MFCCs in python, available here. Use the ‘Download ZIP’ button on the right hand side of the page to get the code.