Field of the invention
The present invention relates generally to secure communication and document
identification over computer networks or other types of communication systems
to have a secure user identification technique and digital signature techniques
based on an algorithm.
Background of the invention
Enterprise data loss costs business nearly $105 billion last year. Nearly 220 million
records have been breached since January 2005. According to primary rights
clearing house a non profit consumer information and advocacy organisations.
With the enormous volume of data that is transmitted electronically throughout the
world, methods for securing the privacy of that data are crucial to the economy.
Before the 1970s, senders and recipients would need to agree on some sort of
secret key in order to encrypt messages such that they could not be deciphered by
unauthorized third parties but could still be read by the intended recipient. This sort
of symmetric cryptography alone is inconvenient in the Internet age, where it is not
always easy to arrange a meeting to exchange a secret password that will allow for
future secure communications. Fortunately, public key cryptography was
developed in the last few decades by Diffie, Hellman, Rivest, Shamir, and
Adelman among others.
Public key cryptography allows for the secure exchange of information between
senders and recipients without the necessity that the two parties first exchange a

secret key. The recipient simply makes his public key available, which can be used
by anyone to encrypt a message to him. Once a message is encrypted using the
recipient's public key, only the private key can be used to restore the message to its
original state. Only the recipient knows his private key, so messages encrypted
with the public key are secure.
The standard methods for public key cryptography were developed by Rivest,
Shamir, and Adelman (RSA), described in U.S. Pat. No. 4,405,829. RSA and its
variants provide for encryption of data using a public key and decryption using a
private key.
In 1991 The National Institute of Standards and Technology(NIST) proposed the
Digital Signature algorithms (DSA) for frderal digital signature applications. To
propose new Digital Signature Standard(DSS) uses a public-key signature scheme
to verify to a recipient the integrity of data received and the identity of the sender
of the data. DSA provides smartcard applications for digital signature. Key
generation in DSA is faster than in RSA. Signature generation has the same level
of speed as RSA, but signature verification is much slower than RSA. The
decryption algorithm is exactly identical to the encryption algorithm except that the
round keys are used in the reverse order. Since the encryption keys for each round
are Ki, K2, K3 ., Kj6 , the decryption keys for each round are K)6 , Kj5,...., KL
Therefore, the same algorithm works for both encryption and decryption.
Public-key cryptosystems were invented with some help from the development of
complexity theory around that time. It was observed that based on a problem so
difficult that it would need thousands of years to solve, and with some luck, a
cryptosystem could be developed which would have two keys, a private key and a

"public key. With the public key one could encrypt messages, and decrypt them
with the private key. Thus the owner of the private key would be the only one
who could decrypt the messages, but anyone knowing the public key could send
privately.
Another idea that was observed was that of a key exchange. In a two-party
communication it would be useful to generate a common secret key for bulk
encryption using a secret-key cryptosystem (for example, some block cipher).
Indeed, Whitfield Diffie and Martin Hellman used ideas from number theory to
construct a key exchange protocol that started the era of public-key
cryptosystems. Shortly after that Ron Rivest, Adi Shamir, and Leonard Adleman
developed a cryptosystem that was the first real public-key cryptosystem capable
of encryption and digital signatures.
Later several public-key cryptosystems followed using many different underlying
ideas (for example, knapsack problems, different groups on finite fields, and
lattices). Many of them were soon proven to be insecure. However, the Diffie-
Hellman protocol and RSA appear to have remained two of the strongest up to
now.
Summary of the Invention
The present invention is directed to and provides systems and methods for secure
communication. The system and methods provided according to the present
provide for signing and verifying a digital document.

The main embodiment of the present invention is to provide secure
communication and document identification over computer networks or other
types of communication systems to have a secure user identification technique
and digital signature techniques based on algorithm.
Another embodiment of the invention is to provide atleast one processor based
subsystem wherein the processor selects the element in the number system
which can be treated as public key.
Yet another embodiment of the present invention is plaintext is converted into
ciphertext with the help of a conventional encryption and the key for conversion
is decided upon mutual agreement wherein the key may be transmitted to the
receiver through a secured channel with the help of a secret algorithm.
Yet another embodiment of the present invention is ciphertext is further
encrypted to a new set of digit and this set of digit is transmitted to the receiver
either through a secured channel or an unsecured channel.
Yet another embodiment of the present invention is the receiver can have
another module stored in his machine to check the authenticity of the message
which enables to check the timeliness, and authenticity of the message sent by
the sender.
Brief description of the drawings
Fig.l illustrates the flow diagram showing steps included in a method for key
generation according to the present invention.

"Fig.2 illustrates the flow diagram showing steps included in a method for
encryption and decryption according to the present invention.
Detailed description of the invention
While the invention will be described in connection with a particular
embodiment, it will be understood that the intent is not to limit it to that
embodiment. To the contrary, the intent is to cover all the alternatives,
modifications, and equivalents as may be included within the spirit and scope of
the invention. Each entity A has a public key e and a corresponding private key d.
In secure systems the task of computing d given e is computationally infeasible.
The public key defines an encryption transformation Ee, while the private key
defines the associated decryption transformation Dd. Any entity B wishing to send
a message m to A obtains an authentic copy of A's public key e, uses the
encryption transformation to obtain the cipher text c= Ee (m), and transmits c to
A. To decrypt c, A applies the decryption transformation to obtain the original
Wherein the public key is not kept secret but is widely available such that A is the
only party who knows the corresponding private key.
For the present invention the term digital signatures is defined as a message
signed with a sender's private key can be verified by anyone who has access to
the sender's public key, thereby proving that the sender had access to the private

"key. The term Public key encryption is defined as a message encrypted with a
recipients public key cannot be decrypted by anyone except a possessor of the
matching private key.
The present invention provides a system and method for secure communication.
The present invention provides a system for establishing cryptographic
communications including:
A method for signing and verifying a digital document D, comprising of at least
one processor based subsystem by selecting an element in the number system by
generating subsequent elements which can be treated as publickeys.
The method comprises of steps where s is an element of S derived from a
function:

Wherein A,B,C,D,E/F,G,H and a are all being either positive integers or negative
integers.
The method also comprises of a specified condition on digital signature M that is a
quantity derived from s and p satisfies a specific relation generated from a
specific algorithm as detailed:

Wherein I,J,K,L,M,N,O,P and b are all being either positive integers or negative
integers.

The method also comprises of the specific condition on the digital signature as
detailed:
If u is an element of U derived from a function
Wherein l,J;K,L,M,N,0,P and b are all being either positive integers or negative
integers.
The method also comprises of the specific condition on the digital signature as
detailed:

Wherein Q,R,S,T,U and c are all being either positive integers or negative integers.
Preferably systems and method of the present invention provides that the original
intelligible message referred to as plaintext is converted into apparently random
nonsense referred to as ciphertext with the help of conventional encryption and
the key for conversion is decided upon mutual agreement wherein the key may
be transmitted to the receiver through a secured channel with the help of a secret
algorithm.
Wherein the ciphertext is represented by Z.
In systems and methods of the present invention, a plaintext message is
encrypted into ciphertext message Z using any method that produces a value
equivalent to Z

'Preferably system and methods of the present invention performs all of the
function as detailed:

Wherein the right hand side of all the above functions can generate the ciphertext
Z which is further encrypted to a new set of digit. This digit is transmitted to the
receiver either through a secured channel or an unsecured channel.
Wherein the functions of the present invention consists of positive integers,
negative integers, decimals and fractions.
In systems and methods of the present invention the receiver when receives the
function of the form as in eq.(l) performs V(Z+u) - u when u is already stored
with the receiver as the decryption key and generates the value equivalent to Z.
After getting Z the receiver once again performs a function with the help of
conventional encryption and the key for conversion has been decided upon the
mutual agreement wherein the key has been transmitted to the receiver through
a secured channel with the help of a secret algorithm.

In systems and methods of the present invention the receiver when receives the
function of the form as in eq.(2) performs V(Z-u) + u when u is already stored
with the receiver as the decryption key and generates the value equivalent to Z.
After getting Z the receiver once again performs a function with the help of
conventional encryption and the key for conversion has been decided upon the
mutual agreement wherein the key has been transmitted to the receiver through
a secured channel with the help of a secret algorithm.
In systems and methods of the present invention the receiver when receives the
function of the form as in eq.(3) performs V(u -Z) -u when u is already stored
with the receiver as the decryption key and generates the value equivalent to Z.
After getting Z the receiver once again performs a function with the help of
conventional encryption and the key for conversion has been decided upon the
mutual agreement wherein the key has been transmitted to the receiver through
a secured channel with the help of a secret algorithm.
In systems and methods of the present invention the receiver when receives the
function of the form as in eq.(4) performs mV(u.Z) when u is already stored with
the receiver as the decryption key and generates the value equivalent to Z.
After getting Z the receiver once again performs a function with the help of
conventional encryption and the key for conversion has been decided upon the
mutual agreement wherein the key has been transmitted to the receiver through
a secured channel with the help of a secret algorithm.

In systems and methods of the present invention the receiver when receives the
function of the form as in eq.(5) performs rV(Z/u) when u is already stored with
the receiver as the decryption key and generates the value equivalent to Z.
After getting Z the receiver once again performs a function with the help of
conventional encryption and the key for conversion has been decided upon the
mutual agreement wherein the key has been transmitted to the receiver through
a secured channel with the help of a secret algorithm.
In systems and methods of the present invention the receiver when receives the
function of the form as in eq.(6) performs vV(u/Z) when u is already stored with
the receiver as the decryption key and generates the value equivalent to Z.
After getting Z the receiver once again performs a function with the help of
conventional encryption and the key for conversion has been decided upon the
mutual agreement wherein the key has been transmitted to the receiver through
a secured channel with the help of a secret algorithm.
Preferably, in the systems and methods according to the present invention, the
receiver can check the authenticity of the message by another module stored in
its machine to check the timeliness and authenticity of the message sent by the
sender.
The systems and methods of the present invention provides that the receiver part
is dependent on the specific algorithm wherein a secondary type of protection at

"the receiving end is being performed by the functions (a+b), (a-b), (b-a), (a.b),
(a/b), (b/a) completely at the discretion of the sender but easily available to the
receiver by selecting any of the options and where a is considered to be equal to Z
and b is any of the above mentioned functions.
The present invention provides a system and methods for secure communication
wherein the security of the cryptosystem is based on the fact that the private key
can be computed from the public key only by solving the difficult computational
problem.
For the present invention the term algorithm is defined as an explicit description
of how a particular problem can be performed. The efficiency of an algorithm can
be measured as the number of elementary steps it takes to solve the problem
wherein the asymptotic running time has been settled which can be expressed as
0(f(n), if its worst case running time divided by f(n) is bounded by a fixed(positive)
constant as the input size n increases. The term computational complexity is
defined as a problem is polynomialitime or in P if it can be solved by an algorithm
which ntakes less than O(n') steps, where t is some finite number and the variable
n measures the size of the problem instance. If the solution to a can be verified in
polynomial time then the problem is said to be in NP (non-deterministic
polynomial time).
Wherein integer factorization of problem has been included to the set of large
number of problems that lie in NP.

The present invention provides a system and methods for the secure
communication wherein the message in the form of plaintext, data or transaction
is to be sent to receiver. The message is converted into digits with the help of any
known or secret procedure and is expressed as ciphertext Z.
The present invention provides a system and methods wherein the trusted third
party TTP or the certifying authority can verify, authenticate, repudiate and
validate any transfer of message with the help of a function named as Parabolic
Curve Cryptography. TTP can also determine the level of certification.
Advantages of the invention
The main advantage of the present invention is it does not depend on the prime
numbers which are used worldwide. Also it uses all three types of integers i.e. odd
digits (prime and non prime numbers) and even digits. It also uses all the available
digits in number system i.e. positive integers, negative integers, fractions and
decimals. The present invention reduces the processing speed in execution in
comparision to known methods. Also hardware cost is minimum. In the digital
signature all the functions of a) Authentication, b) Validation, c) Repudiation, d)
Certification are being uniquely and excellently performed. The sender part and
the receiver part is dependent on a specific algorithm. In the present invention a
secondary type of protection at the receiving end is being performed by the
functions (a+b), (a-b), (b-a), (a.b), (a/b), (b/a) completely at the discretion of the

"sender but easily available to the receiver by selecting any of the options. In the
present invention no bit function has been used but any user may apply any sort
of prevalent bit function with a view to have greater height of data security.
The present invention also provides secure communication and document
identification over computer networks or other types of communication systems
to have a secure user identification technique and digital signature based on an
algorithm not yet used by anyone and obviously quite unique in nature.
The invention also has application to communication providing legal recognition
to transactions carried out through electronic communications for providing a
secure environment for e-Governance and e-commerce. Moreover it can be used
for promoting the use of Public Key Cryptography based Digital Signature for
variety of applications in e-Commerce and e-Governance in a secure manner.
It is a fact that some of the most critical e-Governance applications in India rely on
Digital Signature Certificates issued by various Certifying Authorities in the Indian
Public Key Infrastructure for authentication of digitally signed electronic
transitions which is the basis of a Public Key Infrastructure is the trust in a
presented Digital Signature Certificate. In order for a relying party to trust a
Digital Signature Certificate and process it, the application is required to carry out
number of operations.

vVe claim:
1. A method for establishing cryptographic communications for signing and
verifying a digital document comprising the steps of : generation of public
key in the form of subsequent elements by using at least one processor
based subsystems; converting plain text into ciphertext Z, wherein the
key(s) are operable for encryption and can be transmitted to the receiver;
receiving the message and providing private key to decrypt the message,
thereby providing a secure system for cryptographic communications.
2. The method of claim 1, further including the steps of generation of
subsequent elements such that these elements can be treated as public
keys wherein,
S is an element of S derived from a function

where A,B,C,D,E,F,G,H and a are all being either positive integers or
negative integers.
3. The method of claim 1, wherein a specified condition on the digital
Signature M is that a quantity derived from s and p satisfies a specific
relation generated from a specific algorithm as described below:
If p is an element of P derived from a function

Where l,J,K,L,M,N,0,P and b are all being either positive integers
Or negative integers.

4. The method of claim 1, wherein a specified condition on digital signature M
Is:

Where \,},K,LM,N,Q,P and b are all being either positive integers
Or negative integers.
5. The method of claim 1, wherein a specified condition on digital signature
Mis:

Where Q, R, S, T, U and c are all being either positive integers or negative
integers.
6. The method of claim 1, wherein the key may be transmitted to the
receiver through a secured channel with the help of a secret algorithm.
7. The method of claim 1, wherein the function is performed as:
8. The method of claim 1, wherein the function is performed as:
9. The method of claim 1, wherein the function is performed as:


10. The method of claim 1, wherein the function is performed as:

11. The method of claim 1, wherein the function is performed as:

12. The method of claim 1, wherein the function is performed as:
13. The method of claim 1, wherein after receiving the message as claimed in
claim 7, the receiver performs V(Z+u) - u(already stored with the
receiver as the decryption key as generated in the aforementioned one-
way function) and as such gets Z.
14. The method of claiml3, wherein after getting Z the receiver once again
performs a function with the help of conventional encryption and the key
for conversion has earlier been decided upon mutual agreement where the
key has been transmitted to the receiver through a secured channel with
the help of a secret algorithm.
15. The method of claim 1, wherein after receiving the message as claimed in
claim 8, the receiver performs V(Z-u) + u (already stored with the
receiver as the decryption key as generated in the aforementioned one-
way function) and as such gets Z.

16. The method of claiml5, wherein after getting Z the receiver once again
performs a function with the help of conventional encryption and the key
for conversion has earlier been decided upon mutual agreement where the
key has been transmitted to the receiver through a secured channel with
the help of a secret algorithm.
17. The method of claim 1, wherein after receiving the message as claimed in
claim 9, the receiver performs V(u -Z) -u (already stored with the
receiver as the decryption key as generated in the aforementioned one-
way function) and as such gets Z,
18. The method of claiml7, wherein after getting Z the receiver once again
performs a function with the help of conventional encryption and the key
for conversion has earlier been decided upon mutual agreement where the
key has been transmitted to the receiver through a secured channel with
the help of a secret algorithm.
19. The method of claim 1, wherein after receiving the message as claimed in
claim 10, the receiver performs V(u.Z) (already stored with the receiver
as the decryption key as generated in the aforementioned one-way
function) and as such gets Z.
20. The method of claiml9, wherein after getting Z the receiver once again
performs a function with the help of conventional encryption and the key
for conversion has earlier been decided upon mutual agreement where the
key has been transmitted to the receiver through a secured channel with
the help of a secret algorithm.

21. The method of claim 1, wherein after receiving the message as claimed in
claim 11, the receiver performs rV(Z/u)(already stored with the receiver
as the decryption key as generated in the aforementioned one-way
function) and as such gets Z.
22. The method of claim21, wherein after getting Z the receiver once again
performs a function with the help of conventional encryption and the key
for conversion has earlier been decided upon mutual agreement where the
key has been transmitted to the receiver through a secured channel with
the help of a secret algorithm.
23. The method of claim 1, wherein after receiving the message as claimed in
claim 12, the receiver performs vV(u/Z) (already stored with the receiver
as the decryption key as generated in the aforementioned one-way
function) and as such gets Z.
24. The method of claim23, wherein after getting Z the receiver once again
performs a function with the help of conventional encryption and the key
for conversion has earlier been decided upon mutual agreement where the
key has been transmitted to the receiver through a secured channel with
the help of a secret algorithm.
25. The method of claim 1, wherein the receiver if wants to check the
authenticity of the message can have another module stored in his
machine which enables to check the timeliness, and authenticity of the
message sent by the sender.

26. The method of claim 1, wherein Right Hand Side of the functions only can
generate the ciphertext Z.
27. The method of claim 1, wherein cipher text is further encrypted to a new
set of digits and this set of digit is transmitted to the receiver through a
secured channel or an unsecured channel channel.
28. The method of claim 1, wherein a secondary type of protection at the
receiving end is being performed by the functions (a+b), (a-b), (b-a),
(a.b), (a/b), (b/a) completely at the discretion of the sender but easily
available to the receiver by selecting any of the options.
29. The method of claim 7, wherein the functions of the method uses
Positive integers, negative integers, decimals and fractions.
30. The method of claim 1, wherein the method uses discrete
Mathematics and can apply any sort of bit functions for example: 32-64-

128-256 etc.

A method for establishing cryptographic communications based on a unique
one way function for signing and verifying a digital document comprising the
steps of: generation of public key in the form of subsequent elements by using
at least one processor based subsystems; converting plain text into ciphertext
Z, wherein the key(s) are operable for encryption and can be transmitted to
the receiver; receiving the message and providing private key to decrypt the
message, thereby providing a secure system for cryptographic communication.