Musical Cryptography. Empirical Analysis of Algorithms

Inhalt

1. INTRODUCTION
1.1 CRYPTOGRAPHY
1.2 TYPES OF CRYPTOGRAPHY
1.2.1 SYMMETRIC KEY
1.2.2 ASYMMETRIC KEY
1.2.3 HASH FUNCTIONS
1.3 MUSICAL CRYPTOGRAPHY
1.4 HINDUSTANI MUSIC

2. LITERATURE SURVEY

3. RAGAS
3.1 AAROH & AVROH
3.2 VADI & SAMVADI
3.3 DEERGHA & ALPA NOTES
3.4 NOTES
3.5 WESTERN MUSIC NOTES
3.6 RAAG BHEEMPALASI
3.7 RAGA BAGESHREE
3.8 RAGA MALKAUNS
3.9 RAGA YAMAN

4. METHODOLOGY
4.1 SEMI-NATURAL COMPOSITION
4.2 MARKOV CHAIN
4.3 TRANSITION PROBABILITY MATRIX (TPM)
4.4 SEMI-NATURAL COMPOSITION ALGORITHM (SNCA)
4.5 BAGESHREE RAGA
4.6 ENCRYPTION
4.7 BHEEMPALASI RAGA

5. ANALYSIS OF RAGA
5.1 EMPIRICAL ANALYSIS
5.1.1 BAGESHREE RAGA
5.1.2 BHEEMPALASI RAGA
5.1.3 MALKAUNS RAGA

6. IMPLEMENTATION AND RESULTS
6.1 THEORETICAL ANALYSIS
6.2 EMPIRICAL ANALYSIS
6.3 EXPERIMENTAL RESULTS

7. CONCLUSION

BIBLIOGRAPHY

APPENDIX

ABSTRACT

With an onset of electronic commerce and portable devices for communication, cryptology has become an exceedingly important science in the present day. The diversity of applications in which crypto-algorithms have to operate have increased and hence the requirement for the efficient algorithms have grown. Confidential information of a government or private agency or department is secured through the use of Cryptography.

Musical properties, for example, notes of which the music is made are not consistent and shift from one arrangement to another. Same tune played by various composers shows a variety in the succession of notes utilized along with different qualities of a musical organization, for example, term of each note and the recurrence at which each note is played. Such a variety can be utilized to encode the message. In this work, we have joined the utilization of Hindustani (North Indian) melodic notes to encode messages and used this method on three ragas to test the robustness of the algorithm with different input size. We have utilized a semi-natural composition procedure to produce note successions of Indian music which would then be able to be utilized as a device for message stowing away. This from the outset place guarantees that the message is avoided the interloper and second it gives another irregular arrangement of notes each time same message is sent. So the very motivation behind a Cryptographic calculation is served. The scrambled message as melodic notes is at that point sent to the planned beneficiary as a melodic structure which helps in opposing the gatecrasher of detecting any classified data that is being sent over the correspondence channel.

Mathematics Subject Classification: 94A60

Key Words: Musical Cryptography; raga; semi-natural composition

1. INTRODUCTION

In today’s world where the security of the information is a primary necessity not only for military-diplomatic messages but also for private messages. Today's scenario of communication has increased the importance of financial data exchange, image processing, e-commerce transactions which in turn has made data security an important issue for the world. With the onset of these features, cryptology has become exceedingly important science for privacy protection. Cryptology is defined as the science which is concerned for the communication in a secure format. Cryptology consists of cryptography and cryptanalysis. The aim of cryptology is the construction of such schemes, which can maintain the required security, even after malicious attempts.

1.1 CRYPTOGRAPHY

Cryptography is a method of protecting information and communications through the use of codes so that only those for whom the information is intended can read and process it. The prefix "crypt-" means "hidden" or "vault" -- and the suffix "- graph" stands for "writing.

Cryptography is a field of computer science and mathematics that emphasizes techniques for the secure transmission of information between two parties while a third party is present. The message which is being sent is called a plain text whereas a disguised message which is encrypted while sending to a receiver is known as ciphertext. A process of disguising a message in such a way that it hides the actual message is known as encryption. A process of turning back disguised message or ciphertext into a plain text is known as decryption.

Modern cryptography concerns itself with the following four objectives:

- Confidentiality – only the authorized recipient should be able to extract the content of the cipher.
- Message Integrity – the information or message cannot be altered during transmission.
- Authentication – the sender and receiver should confirm each other’s identity and the origin or destination of the information.
- Non- repudiation – creator/sender information cannot deny at a later stage his or her intentions in the creation or transmission of the information

1.2 TYPES OF CRYPTOGRAPHY

There are three types of cryptography:

- Symmetric Key
- Asymmetric Key
- Hash Functions

1.2.1 SYMMETRIC KEY

It deals with a single key for encryption and decryption of messages. Symmetric key cryptography is faster and simpler. The problem with these types of systems is that the sender and receiver have to exchange the keys one way or another in a secure manner. The most popular symmetric key cryptography is Data Encryption System (DES).

1.2.2 ASYMMETRIC KEY

It deals with two types of keys for encryption and decryption. A public key is for encryption purposes and a private key is for decryption purpose. The advantage of using an asymmetric key is even if the public key is known to everyone the intended receiver can only decode the message because the private key is known to an only specific person. RSA algorithm is asymmetric key cryptography.

1.2.3 HASH FUNCTIONS

In this type of cryptography algorithm, no key is involved. Hash functions have a hash value with a fixed length which is calculated as per the plain text. This makes it impossible for the contents of a message or plain text to be recovered. Hash functions are used by many operating systems to encrypt passwords.

1.3 MUSICAL CRYPTOGRAPHY

The two terms music and cryptography, normally independent, sometimes do converge and when they do it is of interest. The patterns encrypted and decrypted in this context turned out to be progressively set apart in the later long stretches of the twentieth century. The combinative force originated from the two sides: cryptography and music. Cryptographers have consistently endeavoured to make their music-figures however much like genuine music as could reasonably be expected to upgrade their adequacy as a figure. A few writers, on the other hand, may well have felt that their music was improved by a prudent admixture of cryptographic components. The utilization of figure subjects appears to have started with J.C. Faber and may well have proceeded with Michael Haydn, Schumann, and Elgar. The undisguised use continued in France with Ravel, Poulenc, Honegger, and others, and finished in Messiaen. In any case, as Norman Cazden asserted in 1961, current scores present unmatched open doors for encipherments of various types, and no uncertainty there are undeclared types of undisclosed figure strategies of the melodic piece.

Musical cryptography refers to a cryptographic sequence of musical notes that can be taken to allude to an extra-melodic content by some 'sensible' relationship, for the most part between note names and letters. The most well-known and most popular models result from writers utilizing figured forms of their own or their companions' names as topics or themes in their synthesis.

A lot rarer is the utilization of music documentation to encode messages for reasons of undercover work or individual security called steganography.

1.4 HINDUSTANI MUSIC

Hindustani classical music is an Indian classical music tradition that took shape in northern India in the 13th and 14th centuries A. D. Its beginnings lie in existing strict, people, and dramatic execution rehearses. The beginnings of Hindustani music can be found in the Samaveda (wherein Sāman signifies "song" and Veda signifies "information"). The Samaveda comes next in the typical request of the four Vedas. Samaveda comprises of an assortment (Samhita) of songs and sections or explicitly demonstrated tunes called Samagana that were sung by the clerics while offering drinks to different divinities.

Hindustani music is based on the raga system. Hindustani music raga is a melodic scale, including notes from the essential seven- Sa, Re, Ga, Ma Pa, Dha, and Ni. Based on notes remembered for it, each raga achieves an alternate character. The type of the raga is additionally dictated by the specific example of high and low of the notes, which may not be carefully direct.

In Hindustani (North Indian) classical music, the most common way to classify a raga is under ten parent scales (called thaat). A thaat is a seven-note scale including one each of the seven notes Sa, Re, Ga, Ma Pa, Dha,Ni.. Of these, the notes Re Ga Ma Dha and Ni each have two variants (natural vs. flat, or natural vs. sharp), so there can be 32 different thaats, but 10 occur very commonly in Hindustani music.Given the notes they use, most Hindustani ragas can be characterized under one of these ten scales. The parent size of a raga capacity, basically, as its key mark. For example, if we realize that a raga has a place with the Kalyan scale, at that point you realize that it utilizes Ma.

2. LITERATURE SURVEY

From early days music and melodic documentation have been utilized for cryptographic purposes. Musical cryptography has emerged as a new genre to send messages without the insight of intruders. In the fifteenth century, Tractus varii medicinales 7 developed a framework involving five distinct pitches and utilized them in five distinct manners which yielded 25 images to make an alphabetic figure, each pitch was given certain documentation and the stem headings and the note esteems were changed in five different ways. Before the finish of sixteenth-century numerous varieties of complex frameworks were presented which utilized 9 pitches and were proficient to create 72 distinct images. Garrison 8 used to send messages utilizing ringing chimes in prearranged ways. Athanasius Kircher 9 utilized the possibility of the ensemble by apportioning four unique notes every one of six distinctive melodic instruments, this yielded 24 unique notes. Hooper and Kluber 10, 11 utilized a figure wheel, which had notes, what's more, comparing letters composed round in two circles.

The gadget utilized by Hooper and Kluber allowed visit resetting consequently creating various documentations on various occasions. In the late eighteenth and mid-nineteenth century, it was an issue of discussion for age melodic figures with genuine music. Leibniz 12 gave a thought of counterfeit language containing tones and spans. Leibniz in 1817 utilized seven unique images and joined five at a time, the request and stress were additionally changed. Bach 13, 14 utilized melodic documentation to compose names in melodic style. Elgar 15 utilized melodic documentation to compose messages to his companions, one of his messages to his significant other Dorabella is still unbreakable.

In the paper 5 a multiple note substitution algorithm is proposed this algorithm is used to overcome the drawbacks of using only a limited number of letters in the plaintext message. The application of the algorithm is to produce an obscure message that helps sequestered from everything the message in the melodic notes and diminishes the opportunity of being perceived as the figure. In the encryption, all the conceivable outcomes of the melodic notes of letters in the plaintext are found with the help of the key matrix.

An algorithm is utilized which changes over the plaintext into a melodic piece with supplanting the characters of plaintext by produced melodic notes separately. Specific character grouping of the plaintext message has its succession of the melodic notes which emulates the melodic example present. The sender sends this melodic example to the collector as a music record. Encryption/Decryption key has seed esteem which is moved utilizing lopsided calculation that is RSA in which the keymaps the letters to the relating melodic notes. An n x n framework is utilized as an encryption key. The framework will be created with the assistance of the seed estimation of the key on both the sides that is sender and receiver. 6

In this paper 4 fuzzy logic algorithm is discussed for musical cryptography. Fuzzy logic is being used in musical cryptography to create the melodic grouping which is difficult to distinguish as the figure. To overcome the traditional algorithm which used simple substitution cipher which produced musical sequences, a fuzzy logic-based algorithm is proposed in this paper 4. An asymmetric key substitution cipher is used which uses one of the n candidates notes to encrypt a particular character 4. This application of fuzzy logic produces a musical sequence that is difficult to suspect.

In this paper 2 a new cipher system is used for safe transmission of a message. This paper used seminatural composition on Indian raga for this purpose. This paper introduced a new algorithm known as SNCA (algorithm). In this algorithm, each time a new set of random is generated and with the help of this random number a soothing raga is formed. This type of encryption will help in defying the intruder of sensing information that is sent or received.

3. RAGAS

An octave has 12 notes. A scale is a musical theme created by choosing a specific set of notes from within these 12 notes. Indian classical music (ICM) has two broad forms: North Indian or Hindustani and South Indian or Carnatic music. In either form, the nucleus is the raga. A raga is a melodic structure with fixed notes and a set of rules that characterize a particular mood conveyed through performance 1.

3.1 AAROH & AVROH

When ascend or rise of raga occurs then it is called Aaroh whereas the descend of the raga is called avroh. Aaroh and Avroh of raga greatly influence the structure of the raga.

3.2 VADI & SAMVADI

All ragas have what is called a "Vadi" note, which stands out above the others as the most prominent note in that raga. This is the note that seems to wrap the raga around itself 3.

The samvadi is not as important as the Vadi, but it is the focal point in its region of the octave. So, between the vadi and samvadi, there are two focal points for balance. Additionally, the samvadi can mirror some of the note patterns of the vadi, lending a pleasing sense of symmetry 3.

3.3 DEERGHA & ALPA NOTES

Deergha is known as a strong note whereas Alpa is known as a weak note. The elongated notes is known as a Deergha note.

Example: For example, Re (2) and Dha (6) are Deergha in Raag Bhimpalasi, which gives them a strong presence despite being used only used in descending sequences 3.

By contrast, Dha is absent in Dhani, and Re is used infrequently and without emphasis. This gives Re a weak presence in Dhani, making it an alpa note in this raga 3.

3.4 NOTES

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3.5 WESTERN MUSIC NOTES

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3.6 RAAG BHEEMPALASI

Description:

Bheempalasi is a very sweet and pleasant raga. The Raga (also called Raag) is started with an Alaap this gives the Raga mood which is then carried into waves and Taans. It is expanded freely in all three octaves.18

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3.7 RAGA BAGESHREE

Description:

This is a popular raga of the late-night, this raga is meant to portrait the emotion of a woman waiting for reunion with her lover. It is said that this raga was first sung by Mian Tansen, who is among the 9 ratans of the courtyard of Emperor Akbar in the sixteenth century.

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3.8 RAGA MALKAUNS

Description:

This raga is one of the oldest ragas of Hindustani Music. It is believed that this raga is created by goddess Parvati to calm Shiva when the lord Shiva was outraged and was not calming down after Tandavin rage of Sati’s sacrifice.

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3.9 RAGA YAMAN

Description:

Yaman is considered to be one of the most fundamental ragas in the Indian Classical Raga tradition. Yaman came from the parent musical scale known as Kalyan.

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Ragas of Hindustani Classical Music are based on, or a variation of ten basic Thaats (frameworks or musical scales) – Bhairav, Bilawal, Todi, Asavari, Kalyan, Khamaj, Poorvi, Marwa, Kafi, Bhairavi 1.

Here, I discussed four Ragas, Malkauns, Bheempalasi, Bageshree, and Yaman.

- Malkauns framework is on Bhairavi thaat
- Bheempalasi musical notes are based on Kafi thaat.
- Bageshree is also based on Kafi thaat.
- Yaman is based on Kalyan thaat.

4. METHODOLOGY

The methodology comprises the theoretical analysis of the methods and all the principles that are associated with a branch of knowledge. In the proposed work, the empirical analysis of algorithms used in musical cryptography is done. This work emphasized more on Semi-Natural Composition Algorithm (SNCA).

4.1 SEMI-NATURAL COMPOSITION

Music composition can be natural, artificial, or semi-natural 1. Natural music composition refers to a composition where a human being decides what to play and how to play whereas, artificial music composition refers to a composition where a computer is trained to achieve the “what to play” and “how to play” aspects and then comes semi-natural composition which suggests that computer will decide what to play while a human being will decide how to play. The semi-natural composition is formally discussed in Chakraborty et. al 1 and has been recently used in the context of cryptography successfully in 2. The semi-natural composition as used in 1-2 and the present work assumes a first-order Markov Chain to generate the sequence of the raga.

4.2 MARKOV CHAIN

A Markov chain is a stochastic model describing a sequence of possible events within which the probability of every event depends only on the state attained within the previous event. In continuous-time, it's called a stochastic process. It is named after the Russian mathematician Andrey Markov.

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So, the sequence of random variables X 1, X 2, X 3, … .The trials are independent and the result of the trial does not depend on the previous trials in any circumstances. The random variables are independent 16. The states of the outcomes are called the states of the Markov Chain 16.

4.3 TRANSITION PROBABILITY MATRIX (TPM)

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Here, P is a stochastic matrix.

This is known as the transition probability matrix of transition probabilities which is also called as TPM of the Markov Chain.

4.4 SEMI-NATURAL COMPOSITION ALGORITHM (SNCA)

SNC Algorithm is based on the first-order Markov chain. The Markov Chain is used to generate the sequence of any raga 1. The state here signifies a particular note at any particular instance. SNCA also makes use of conditional probability. P (R/S) is the conditional probability that the next note will be R on S being the present note. This is calculated by dividing the number of times S followed by R by the total number of times S occurring in the sequence. However, if note S is found to be the last note in the sequence, we subtract the total number of S by 1 as we do not have any knowledge of the next possible transition in the sequence.1

ALGORITHM

- Step 1: We take the note at instance 1 to be Sa (S), without any loss of generality.
- Step 2: Construct a Transition Probability Matrix (TPM) with the notes of the sequence.
- Step 3: Construct a Class Matrix from the TPM as the cumulative sum.
- Step 4: Generate a continuous uniform variates X in the range [0, 1].
- Step 5: Contingent upon the class (from the Class Matrix) in which X falls, simulate the following note as any of the twelve notes of Hindustani Music.
- Step 6: Take the note chose in Step 5 as the new occasion from where reproduction is to be finished.
- Step 7: Repeat from stage 3 to stage 6 till the finish of the persistent uniform variates X is reached.

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