A take it as possibility of public key

 

 

 

 

 

 

 

A Practical Quantum Public-Key Encryption Model

 

 

Name:             Muhammad
Azeem Iqbal Awan

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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.

 

 

 

 

 

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