A Practical Quantum Public-Key Encryption Model

Name: Muhammad

Azeem Iqbal Awan

Class: CS-7 (M)

Roll no: BCS–

F14-13

Submitted to:

Ma’am Nadia Mumtaz

Abstract:

In this paper Quantum Public Key Encryption(QPKE) model is proposed

by studying the related recent techniques of QPKE. This model is proposed such

that changing in one module does not affect the whole model. Each module of

model is independent. The proposed model explicit stipulation on the

generation, authentication, distribution and usage of secrets key. Moreover, it

encapsulates the process of encryption and decryption for users.

Introduction:

Practical model of quantum public key encryption (QPKE) is

suggested by visualizing older QPKE schemes. The QPKE model consists of;

1.Black box-

D/E adapter

2. QPKDC-

quantum publication key distribution center

3. CA-

certification authorities

Methods:

1.Quantum trapdoor one-way function (OWF):

Consider a set

Z which includes numbers and a set Q which includes quantum states of a

physical system. Quantum OWF is a map i.e Z–›Q. It is easy to perform but its

inversion is difficult. If inversion of Z–›Q is possible with the help of some

trapdoor information than it is quantum trapdoor OWF.

2. The Holevo bound:

Assume a party

(Alice) prepares a domain px where x= 0,1, 2…, n

And its probabilities are (p0, p1, p2,

…, pn) respectively. Another party (Bob)

Carry out a computation explained by POVM elements i.e

{E4} ? {E0, E1, … En}

on that states with their calculations their result is Y. The holevo bound

method explains for such calculations that bob do;

H (X: Y) ? S (?) – ?x px S(?x)

Where P = ? px?x and S (?) ? -tr (? log ?)

Represented by Von Neuman entropy of quantum state. This is very

useful method to access information which plays important role in numerous

prosecutions of quantum information theory.

3.Information theoretic security:

It is a QPKE

plan (E, G) for quantum memo. For every positive polynomial (P) and a large (n)

any of two quantum memos ?, ? ? Hm satisfy

D (?kpk?k(?), ?kpk?k(??))

? 1/p(n)

Where pk(?) and pk(??)

are quantum ciphers of ? using QE algorithm and Pk is QPK and we take it as possibility of public

key pk generation from

quantum algorithm G and ? k=k pk =1. Left side of above

equation is 1/p(n) in this p(n) is a random polynomial, we are unable to distinguish

ciphers by quantum orbit of any magnitude.

Description of QPKE model:

Symmetric

cryptosystem i.e (one time pad) provides more introvert and arbitrary key which

is distributed between two groups.

Recently, this

is done by quantum key distribution method. It offers solution to key

allocation issues in the phantom of congent opponents. But key organization is

the main downside of symmetric encryption plan. A solution to this issue is the

use of uttered trusted third part or carol so that it behaves as a PKDC but

disadvantage of this is that PKDC becomes a striking objective.

In this model PKDC

is concerned only with public keys and private keys are under the control of

authorized employs. A more better solution to key allocation and handling issue

is by the use of quantum public key asymmetric cryptosystem which has one way property.

This one way feature is based on the basic rules of quantum mechanics. In QPKE authorized

users uses arbitrary key to make public key which is related to private key. In

this way multiple private keys are manufactured and are in the access of sender

in the legal way i.e PKDC.

1.

Alice and Bob communicators get their verification from CA and

obtain a data block of quartet (ID, CAID,skca,GenAlgsk

).

2.

Customer shows GenAlgsk

algorithm provided by CA with their own identity and get a range

of private key pair (n,si) and n, si are unique arbitrary

numbers.

3.

Customer selects any type of quantum one way trapdoor function F(.)

And express it by si or (n.si) to get respective quantum

public key.

4.

Customer is registered with KDC for all the quantum public keys

related to private key pair (n,si). Then PKDC connects to CA for

verification and in case of verification register the customer.

5.

For Alice to send data to Bob, Alice question for Bob’s ID to CA

and if Bob’s ID is recovered and verified from CA (chip value ? holevo x) PKDC send quantum public key

state to Alice.

6.

Alice code his data on his D/E adapter by quantum public key state

recommended by PKDC.Actual data is not in the form of simple memos but in the

form of quantum domains.

Ø After Bob

receive data from Alice,he enquire to CA center for Alice verification.

Ø QUADRUPLE

DESCRIPTION:

1.(a) ID-

user’s identification no.

(b)

CAID- user’s certificate

(c) GenAlgsk- generator of private key

(d) skCA- user’s private key.

2. Every D/E adapter can accomplish quantum state encryption and

decryption process and can also exhibit GenAlgsk for private key

generation.

3. For execution of authorized use of quantum public key the

customer’s adapter will compute its Holevo bound as the total no.Of copies

issued by PKDC.

4. To verify the validity of encrypted data received by receiver,

both customer and PKDC have a buffet of beginning value of holevo x.when

PKDC sends a public key its buffet is decreased by one.

5. This

model can be used for point to point communication.

DISCUSSION:

The main

purpose of an opponent wire tapper is to redeem the plain text from cipher

text. Opponent can only get information from public key when its multiple

copies are produced. So QPKE should analyze security issue related to size of public

and private keys.

Recently, it is shown that QPKE should have randomness for secure

communication. QPKE is also used as a black box to make new arbitrary

bit-encryption plan.

Focus of this model is;

·

Private key pair created by GenAlgsk should be random.

·

Quantum public key must be 1 to 1 or 1 to many.

·

CA is related to authentication and PKDC to control and

preservation of public keys.

·

User can replace quantum trapdoor OWF and encryption/decryption at

algorithms at any interval.

·

CA and PKDC perform major role in this model.

CONCLUSION:

We purposed QPKE model by the integration of recent QPKE

plans and older PKE theory. Major part of model are CA,PKDC and customer’s

encryption/decryption process(black box).private key creation occurs by means

of CA/customer. Quantum public key is generated by trapdoor OWF which is

effective and easy to measure. Recent work is on Blockchain technology which

can replace CA and PKDC and solve decentralization issue but this is not nubile

yet.