Public key infrastructure based cryptographic algorithms are usually considered as slower than their corresponding symmetric key based algorithms due to their root in modular arithmetic. In the RSA public-key security algorithm, the encryption and decryption is entirely based on modular exponentiation and modular reduction which are performed on very large integers, typically 1024 bits. Due to this reason the sequential implementation of RSA becomes compute-intensive and takes lot of time and energy to execute. Moreover, it is very difficult to perform intense modular computations on very large integers because of the limitation in size of basic data types available with GCC infrastructure. In this topic, we are looking into the possibility of improving the performance of proposed parallel RSA algorithm by using two different techniques simultaneously, first implementing modular calculation on larger integers using OpenMP on the GCC infrastructure. I have also analyzed the performance gained by computing the sequential version with the parallel version of RSA running on the GCC infrastructure.

1. Presentation
On
An Efficient Parallel Algorithm for
Secured Data
Communication Using RSA Public Key
Cryptography Method
Presented by: Harshal Solao

2. Outline
• Introduction
• Motivation
• Literature Review
• Mathematical Model
• RSA Algorithm with Example
• Parallelization of RSA
• Methodology
• Advantages and Limitations
• Application
• Conclusion
• Future Scope
• References

3. Introduction
• The need of spectrum is increasing
exponentially in wireless networking due to
increasing demand for new wireless services
and application.
• Routing is challenging problem due to fitful
availability of Spectrum and incomplete
knowledge of environment.
• Reinforcement learning is generic method for
resource utilization in Dynamic environment.

4. Motivation
• Public-key infrastructure based cryptographic algorithms
are usually considered as slower than their corresponding
symmetric key based algorithms due to their root in
modular arithmetic.
• Sequential implementation of RSA becomes compute-
intensive and takes lot of time and energy to execute.
• Difficulties in performing intense modular computation on
very large integer because of the limitation in size of basic
data types available with GCC infrastructure.
• Required algorithm that provide efficient parallel
implementation of RSA to be executed on multi-core
machine.

5. Conventional Vs Public key Encryption

6. Literature survey
Title Author Publication Findings
Handbook of
applied
cryptography.
Menezes, Alfred
J., Paul C. Van
Oorschot, and
Scott A
CRC press, 2010. How RL use to opportunistically
route the packet even in the
absence of Reliable knowledge
about channel statistic and network
model.
"New directions in
cryptography.”
Die, Whiteld, and
Martin E.
Hellman.
Information
Theory, IEEE
Transactions on
22.6 (1976): 644-
654.
It show the impact of PU activities
on the operation of OCR in channel
sensing, relay selection and data
transmission.
"An efficient
implementation of
RSA digital
signature
algorithm."
Cao, Ying-yu, and
Chong Fu.
Intelligent
Computation
Technology and
Automation (ICICTA),
2008 International
Conference on. Vol. 2.
IEEE, 2008.
Mapping of spectrum selection
metrics and local PU interference
observation to a packet forwarding
delay over the control channel.

7. Literature survey
Title Author Publication Findings
"A method for
obtaining digital
signatures and
public-key
cryptosystems."
Rivest, Ronald L.,
Adi Shamir, and Len
Adleman.
Communication
s of the ACM
21.2 (1978):
120-126.
The real time information exchange
inside the neighborhood and
adaptation to the CR very dynamic
spectrum opportunities.
Fast multiplication:
algorithms and
implementation.
Bewick, Gary W. Diss. Stanford
University,
1994.
Uses a distributed protocols to
collect some key parameters related
to paths from source to destination
"Constant-
optimized quantum
circuits for modular
multiplication
and
exponentiation."
Markov, Igor L., and
Mehdi Saeedi.
Quantum
Information
Computation
12.5-6 (2012):
361-394.
An Artificial ANT colony system can
be used for discovering, observing
and learning of routing strategies by
guided ants communication in an
indirect way.

8. Mathematical Modeling
• Markov Decision Process
A Markov process is a stochastic process with the
following properties:
• Outcomes or states is finite.
• The outcome at any stage depends only on the
outcome of the previous stage.
• The probabilities are constant over time

9. RSA Algorithm with Example

10. Proposed Work

11. Methodology
• Temporal Difference : TD(0) procedural form
Initialize V(s) arbitrarily, π to the policy to be evaluated
Repeat (for each episode):
Initialize s
Repeat (for each step of episode):
a← action given by π for s
Take action a; observe reward, r and next state, 𝒔′
𝑉 𝑠 ← 𝑉 𝑠 + 𝛼[𝑟 + 𝛾𝑉 𝑠′ − 𝑉(𝑠)]
s ← 𝑠′
Until s is terminal

12. Advantages and Disadvantages
• Advantages
– Parallel RSA perform fast computation that save
energy and time of execution.
– Their is no limitation of size of basic data types
available in GCC with this algorithms because of
GNU's MP Library.
– Performance gain due to parallelization on multiple
cores of system with the help of OpenMP Library.
– Provide fast execution with respect to sequential
version.
– Public-key systems can provide digital signatures
that cannot be repudiated.

13. Application
• It is useful to Data signature and
encryption application.
• Protocols supporting e-commerce today.
• Fast computation for data security

14. Conclusion
• The parallel RSA gives the improved result
using OpenMP in combination with GCC
infrastructure and GNU's MP library.
• The parallel RSA are more efficient than that
of the sequential version of it in terms of time
and energy.

15. Future Scope
• The programs used are executed in dual
quad core environment which are based on
repeated square and multiply method. They
could be performed with other modular
exponentiation methods and improving
upon synchronization issues which will
further improve the run-time.

16. References
1. Menezes, Alfred J., Paul C. Van Oorschot, and Scott A. Vanstone.
Handbook of applied cryptography CRC press, 2010.
2. Die, Whiteld, and Martin E. Hellman. "New directions in
cryptography." Information Theory, IEEE Transactions on 22.6
(1976): 644-654.
3. Cao, Ying-yu, and Chong Fu. "An ecient implementation of RSA
digital signature algorithm." Intelligent Computation Technology and
Automation (ICICTA), 2008 International Conference on. Vol. 2. IEEE,
2008.
4. Rivest, Ronald L., Adi Shamir, and Len Adleman. "A method for
obtaining digital signatures and public-key cryptosystems."
Communications of the ACM 21.2 (1978): 120-126.
5. The gnu multiple precision arithmetic library edition 2002
6. Chandra, Rohit, ed. Parallel programming in OpenMP. Morgan
Kaufmann, 2001.

17. References
7. Pieprzyk, Josef, and David Pointcheval. "Parallel authentication and
public-key encryption." Information Security and Privacy. Springer
Berlin Heidelberg, 2003.
8. Barrett, Paul. "Implementing the Rivest Shamir and Adleman public
key encryption algorithm on a standard digital signal processor."
Advances in cryptologyCRYPTO86. Springer Berlin Heidelberg, 1987.
9. Viot, Diego, et al. "Modular Multiplication Algorithm For PKC."
Universiadade Federal do Ceard, LESC (2008).
10. Cohen, Henri, Gerhard Frey, Roberto Avanzi, Christophe Doche,
Tanja Lange, Kim Nguyen, and Frederik Vercauteren, eds. Handbook
of elliptic and hyperelliptic curve cryptography. CRC press, 2010
11. Bewick, Gary W. Fast multiplication: algorithms and
implementation. Diss. Stanford University, 1994.
12. Markov, Igor L., and Mehdi Saeedi. "Constant-optimized quantum
circuits for modular multiplication and exponentiation." Quantum
Information Computation 12.5-6 (2012): 361-394.

18. •Thank You !!