# Comparison Of Quantum Cryptography And Classical Cryptography Computer Science Essay

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Cryptography is the science of hiding information and protecting data. The ultimate aim of cryptography is to convert the readable data into a form which is not readable by unauthorized parties. The authorized parties will be able to retain the original data from the scrambled data. In the past scientists used to work on increasing the computational capability of a method to hide the information, but recently a new method has been invented known as Quantum cryptography which uses the laws of physics and far different from the traditional Classical cryptography which uses the mathematical techniques for the secure communication. [4]

With quantum cryptography, the third party cannot read data without altering it. And whenever the third party alters data, authorized parties who are in the communication will get to know about the alteration. Now the question is, whether quantum cryptography will be able to replace classical cryptography? Which one is the ultimate solution? In this paper we discuss the deficiencies of the quantum cryptography and the diversity of classical cryptography. The primary objective of the paper is to present the loop holes in the concept of quantum cryptography and the potential of the classical cryptography. We also present the best known application of quantum cryptography, quantum key distribution.[1]

Quantum cryptography is a technique, which is used for providing secure communication between different parties in a communication network by applying the phenomena of quantum physics. It mainly depends on two important elements of the quantum mechanics, the Heisenberg uncertainty principle and the principle of photon polarization. The Heisenberg principle is one of the important concepts of quantum physics, which states that, it is impossible to measure the state of a system without disturbing it. Data is presented in the form of "qubits" in quantum cryptography. According to the principle of photon polarization, any eavesdropper cannot copy the states of unknown qubits, that is he cannot clone the qubits as the quantum cryptography is based on No-cloning theorem.[6]

In quantum cryptography, the qubits not only have two states, '0' or '1', but also their superposition. Whenever a unauthorized third party tries to intercept the communication between two authorized parties then the data will be disturbed and an alert will be sent to the two parties.[3] Two eigenstates associated with logical value '0' or '1' can be mathematically represented as:

1 = 0 =

Quantum key distribution (QKD) is a technique based on the quantum cryptography, which is used to distribute the keys that are used for encryption between two authorized parties. Whenever a key is successfully created and shared between two parties using QKD, that key cannot be cracked or intercepted by a hacker as the QKD is based on the quantum principles. And QKD creates the key by converging the random operations that are performed at the sender and receiver side. [2]

Let us consider three parties Alice, Bob and Eve. QKD uses quantum cryptography to distribute shared key (secret key) between Alice and Bob, in such a way that the third party Eve will not be able to learn anything about the key, even if Eve tries to eavesdrop the communication between Alice and Bob. This can be achieved by performing some operations at both Alice and Bob's side.

The sequence of operations that are performed are:

Alice encodes the bits into quantum data i.e., polarized photons, by passing them through the polarization filters.

Polarized data is transferred to Bob's side.

After receiving the data, Bob again sends his polarized photons to Alice for the verification, as it doesn't know whether it has received the correct data.

Alice verifies the data, and tells Bob which are the correct states that form the shared or secret key.

This can be shown in a tabular form as:

0

1

2

3

4

5

6

7

1

0

0

1

1

1

0

1

Bit sequence :

Alice's sequence :

After polarization :

Bob's polarized states :

Bob's correct states :

Alice tells Bob regarding

which states form the key:

or represents a logical '0'. Or represents a logical '1'.

## Fig:1 The sequence of operations[1]

Quantum cryptography is mainly used in key distribution, which just is a part of providing security. There are much more like cryptographic algorithms, digital signatures which are required to provide the integrity and repudiability. Even QKD has its own limitations, there needs some modifications to be done, to use it properly.

Now let us consider the limitations of the quantum cryptography:

## Paper clip : A powerful weapon

The bits after encoded into photons need to be transferred to receiver's side. These photons travel in an optical fiber several kilometers to reach the destination. A couple of paper clips can be pinched to the optical fiber, which changes the refractive index of the fiber. This in turn results in the change in polarization of photons, which ultimately leads to the incorrect interpretation of key. [2]

## Paucity of digital signatures

Digital signatures are generally used in cryptography for providing origin integrity, data integrity and non-repudiability to the receiver. Digital signatures involve different steps. First the key is generated, then the data is signed and finally the key is verified. Each step needs different algorithm to be implemented. It is difficult to implement algorithms with quantum cryptography. So, digital signatures cannot be implemented with quantum cryptography. This one major disadvantage with quantum cryptography.

## Plight due to photon sources

All the photons that are emitted from a source should have varying phase coherence. This requires a special design of phase modulator that will change the consecutive photons' phase in a random and rapid manner.

## Dedicated channel is required

For transferring the photons between two parties, devoted channels are required in quantum key distribution. Moreover multiplexing is not supported in quantum principles. So, if at all the sender wishes to send data to multiple parties, separate dedicated channels are required for each party, which results in high cost. This is one of the major disadvantage of QKD.[1]

## Lower distances

By using QKD, we can transfer photons only to a maximum distance of 250 kilometers at a speed of 16 bits per second. Repeaters can be used to transfer the photons to longer distances. This again increases the overall cost of system. This is another disadvantage with QKD.

## Problems caused by the length of medium

Probability of absorption or depolarization of a photon increases relatively with the length of a optical fiber. This cause the following two problems:

The number of attempts required to transfer a photon without any absorption or depolarization increases exponentially with the length of fiber

When a photon arrives successfully to the receiver's side, the state of photons will not be same as the initial state. The intensity of photon decreases along the length of the optical fiber

## Even Cloning of qubits is possible

One of the primary advantages of using quantum cryptography is, the state of qubits cannot be used to create a exact replica or clone. But stimulated emission has later resulted in the approximate generation of the qubits. And another way is, by using the bunching properties of the light fields we can generate the optimal clones by adjusting the output of a beam splitter.[1]

## Classical cryptography

Classical cryptography makes use of mathematical techniques to keep the data secret. These algorithms mainly depend on the computational complexity. The only disadvantage with these algorithms is, if a hacker is assumed to have infinite computational power, then he can crack the secret code, which known as cipher text. The table below provides details of some of the popular cryptographic algorithms and their feature:

## Key Management

Symmetric Encryption

Yes

No

No

Yes

Public Key

Yes

Yes

No

Yes

Digital Signature

No

Yes

Yes

No

Key Agreement Algorithms

Yes

Optional

No

Yes

One way Hash Function

No

No

Yes

No

Message Authentication Codes

No

Yes

Yes

No

Table1: Some of the famous algorithms and their features [1]

The classical cryptographic algorithms can be mainly classified into two categories as symmetric key algorithms and asymmetric key algorithms.

## Symmetric key Algorithms

Symmetric key algorithms, also known as shared key, secret key or one key algorithms use the same key for both the encryption and decryption. The secret key will be pre shared between the two communicating parties, before the communication begins. The key will be shared by a key distribution center. Encryption and decryption in symmetric cryptography can be shown as:

Ek (M) = C Dk (C) = M

E= Encryption, M=Plain Text, C= Cipher Text, K=shared key

In these algorithms, key is applied to plain text just to shift some bits or to perform simple transformations. They are classified as substitution ciphers, transposition ciphers and product ciphers. Some of the symmetric key algorithms are:

Rail fence cipher: This is an example for a transposition cipher, where the letters in plain text are rearranged to produce the cipher text.

Caesar cipher: This is an example for a substitution cipher, where characters of a plain text are changed to produce a cipher text.

Vigenere cipher : This is similar to Caesar cipher, but uses a phrase as the key.

Data Encryption Standard, Triple DES and Advanced Encryption Standard are some more symmetric key algorithms.[5]

## Asymmetric key algorithms

The problem with symmetric key algorithms is, before the communication begins we need to share the private key between the two parties. The sharing process becomes difficult in potentially large networks. If the private key falls in the hands of a hacker, then he will be able to intercept and modify the encrypted data that is shared between two authorized parties. To overcome this situation, asymmetric key algorithms were introduced. In asymmetric key or public key algorithms, two different keys are used for encryption and decryption. Public key is generally shared with all other parties who want to send messages to that party and private key is kept secret. If a plain text is encrypted by using the public key, then the resultant cipher text can only be decrypted by using the equivalent private key and same algorithm that was used for encryption. This can be shown as:

Decryption

EncryptionPlain Text Cipher Text Plain Text

EncEnc

public key private key

Fig:2 picture illustrating the public key cryptography

Some of the public key cryptographic algorithms are:

Diffie Helman : This is the first asymmetric key algorithm proposed. In this algorithm, a common secret key is computed by using a symmetric key exchange protocol.

RSA Algorithm : RSA is another public key algorithm . This algorithm depends on finding the prime numbers relative to a large number n, i.e., in finding the totient(n). [5]

## Advantages of Classical Cryptography (CC) over Quantum Cryptography

As stated earlier, CC purely depends on computational prowess. The more complex u design the algorithm the more safe your data will be. In QC U discretise your data into many packets and send them over a cable medium. The more discretisations you make, the more safer your data will be.

But the main challenge here is the medium through which the data travels. One can use only optical cable medium here to send data from one place to another whereas in CC one can use any form of communication which is physically feasible. The one major advantage of CC lies in this area.

## Unique Security

With advantage of digital signatures on the rise, if one uses such kind of digital signatures while sending the data, the receiver always knows from whom the data is coming and this he can verify by cross checking. This almost makes any interference impossible

## Use of Science

With computational power growing day by day and the advancements made in the computational domain and taking into consideration of the fact that" Forward computations is easy than recursive computation" the design of the algorithm can be made keeping in mind that the algorithm will work in the near future also. With this we are increasing the lifetime of the algorithm which is not possible in QC.

## Expected lift time

Triple key DES

112

Through 2030

256-bit AES

256

Beyond 2030

DSA(p=7680,q=384)

192

Beyond 2030

DSA(p=2048,q=224)

128

Through 2030

SHA - 512

256

Beyond 2030

SHA - 224

112

Through 2030

Table 2 : Life expectancy of different CC algorithms[1]

## Communication Range

In QC the data can travel over only upto 250 km. CC does not have any such limitations as , we have seen earlier that CC does not depend only one (optical fiber) medium. One can send data irrespective of distance with enhanced security using CC.

## No courier related issues

Having a safe courier is not mandatory for CC as it is coded over a complex algorithm. Even when the hacker gets his and on the data, he has to understand what the algorithm is and run the complex computation involved in it to decipher it which is not easy.

## Simpler key exchange

Exchange of data in networks is very easy with the use of CC . As many systems will be interlinked in the same network, the data sent using CC will be more safer and not that easy to be understood in the network other than sender and receiver.

## Quantum computer a reality

It is estimated that, to break a 1024 bit RSA key we need 3000 qubits. Currently the quantum computers have just 10 qubits. So, public key cryptography is safe for atleast 30 years from now. If at all quantum computers become reality, then situation will be analogous to the life expectancy of algorithms, which we have discussed, in "the use of science". Use the computational resource of the quantum computers to generate complex algorithms, which makes it impossible for the other quantum computer to crack the algorithm. If two parties are using RSA, large prime numbers can be generated by a quantum computer, and use them immediately for the transfer of cipher text. These prime numbers will be large enough which makes the cracking difficult for the other hacker quantum computer. [1]

## Conclusion:

Even though CC has its own shortcomings, (very limited) has its own upper hand over QC as seen earlier. The main problem with QC is the limitation of designing and implementing an appropriate algorithm. In CC one can develop his own algorithm depending upon the computational proficiency. Even when we assume that this limitation of QC will be overcome in the near future, the dependency of QC over QKD will not be separated from QC. Even though QKD has a small part in the security of the data, it plays an important role in it. Thus CC will always remain the best possible available source for sending data over long distances without worrying much about the security. [1]