The document discusses using the RSA algorithm to provide data security in cloud computing. It begins with an objective to ensure security and optimize encryption/decryption time using RSA. It then provides background on cloud computing and the need for security. It describes the RSA algorithm, including key generation, encryption, and decryption. It also discusses a proposed method to improve data security and decrease execution time by increasing key length.

1. DATA SECURITY IN CLOUD USING
RSAALGORITHM
-Lakshmi Teja .S

2. CONTENTS
 OBJECTIVE
 INTRODUCTION
 WHAT IS RSA?
 BLOCK DIAGRAM
 LITERATURE REVIEW
 CRITICAL ANALYSIS
 PROBLEM IDENTIFICATION
 PROPOSED METHOD
 PROGRESS OF THE WORK

3. OBJECTIVE
To ensure the security and to
optimize the time of execution of the encryption
and decryption of the cloud based data using
RSA algorithm.

4. INTRODUCTION
 Cloud computing is emerging technology which
gives open sources on the internet, it denotes
sharing of resources rather than having local
servers to handle applications.
 The major drawback is security in providing data
over the internet, So as to enhance the security
we use an algorithm called RSA

5. WHAT IS CLOUD ?
 Common implies multi-tenancy, not single or isolated tenancy
 Location-independent
 Online
 Utility implies pay-for-use pricing
 Demand implies ~infinite, ~immediate, ~invisible scalability

6. WHAT IS CLOUD AND ITS PROS AND CONS

7. LITERATURE REVIEW
S.NO Title of the paper Name of Authors Year Remarks
1
A Study And
Performance Analysis
Of RSAAlgorithm
M. Preetha,
Computer Science
& Application &
Periyar University,
India.
M. Nithya, CSA,
Periyar University,
India
2013
security aspects are
addressed.
2
RSA Public Key
Cryptography
Algorithm – A
Review
Shireen Nisha,
Mohammed Farik
2015
Strengths and
weaknesses are
addressed.
3
Data Encryption
and Decryption
Using RSA
Algorithm in a
Network
Dheeb Al Bashish,
Malik Braik,
Sulieman Bani-
Ahmad. Deot. Of
IT,
2017
Emphasizes on data
security between
computers sharing
some resources and
their private and

8. CLASSIFICATION OF ENCRYPTION ALGORITHMS
Encryption
Algorithms
Symmetric or
Secret Key
Encryption
Asymmetric or
Public Key
Encryption
DES
RSA

9. WHAT IS RSA..?
• RSA is an algorithm used by modern computers to encrypt
and decrypt messages
• It is an asymmetric cryptographic algorithm.
• It is included as a part of the web browsers from Microsoft and
Netscape.
• It is also part of Lotus Notes ,Intuit’s Quicken and many other
products

10. RSA CONTD
 RSA is the first practical public-key cryptosystems and is
widely used for secure data transmission
 Every number has a prime factorization and it is hard to
find if the number is very large. The time complexity is
also very high. But on the other hand the multiplication
is easy and time complexity is also not very high.
 The RSA algorithm involves three steps: key generation,
encryption and decryption

11. BLOCK DIAGRAM

12. RSA KEY SETUP
 each user generates a public/private key pair by:
 selecting two large primes at random - p, q
 computing their system modulus N=p*q
 note ø(N)=(p-1)(q-1)
 selecting at random the encryption key e
 where 1<e<ø(N), gcd(e,ø(N))=1
 solve following equation to find decryption key d
 e.d=1 mod ø(N) and 0≤d≤N
 publish their public encryption key: KU={e,N}
 keep secret private decryption key: KR={d,p,q}

13. RSA BLOCK DIAGRAM

14. CONFIDENTIALITY
 protecting the information from disclosure to
unauthorized parties
 ensures that only the right people (people
who knows the key) can read the information.

15. AUTHENTICATION
 The sender and receiver can confirm each other’s identity
and origin/destination of the information

16. RSA EXAMPLE
1. Select primes: p=17 & q=11
2. Compute n = pq =17×11=187
3. Compute ø(n)=(p–1)(q-1)=16×10=160
4. Select e : gcd(e,160)=1; choose e=7
5. Determine d: de=1 mod 160 and d < 160 Value is d=23
since 23×7=161= 10×160+1
6. Publish public key KU={7,187}
7. Keep secret private key KR={23,17,11}

17. RSA EXAMPLE CONTD
 Sample RSA encryption/decryption is:
 Given message M = 88 (nb. 88<187)
 Encryption:
C = 887 mod 187 = 11
 Decryption:
M = 1123 mod 187 = 88

18. HOW RSA WORKS
 because of Euler's Theorem:
 aø(n)mod N = 1
 where gcd(a,N)=1
 in RSA have:
 N=p.q
 ø(N)=(p-1)(q-1)
 carefully chosen e & d to be inverses mod ø(N)
 hence e.d=1+k.ø(N) for some k
 hence :
Cd = (Me)d = M1+k.ø(N) = M1.(Mø(N))q =
M1.(1)q = M1 = M mod N

19. PUBLIC KEY CRYPTOGRAPHY

20. PUBLIC KEY CHARACTERISTICS
 computationally infeasible to find private key knowing
only algorithm & public key
 computationally easy to en/decrypt messages when the
relevant (private/public) key is known
 either of the two related keys can be used for encryption
and other is used for decryption

21. PUBLIC KEY APPLICATIONS
 encryption/decryption(provide Confidentiality)
 digital signatures (provide authentication or proof)

22. RSA SECURITY PROBLEMS
 Three approaches to attack RSA:
 Brute force key search (infeasible given size of numbers)
 Mathematical attacks (based on difficulty of computing ø(N), by
factoring modulus N)
 Timing attacks (on running of decryption)

23. MODIFIED RSA ALGORITHM USING ‘N’ PRIME
NUMBERS
Using more than two factors in the modulus of RSA
cryptosystem that the arthimetic advantage that the private key
computations can be speeded up using Chinese remaindering.
At the same time with the proper choice of parameters one does
not have to work with a larger modulus to achieve the same level
of security in terms of the difficulty of integer factorization
problem

24. ADVANTAGES OF RSA
•
•
Very fast, very simple encryption and verification.
Easier to implement than Elliptical curve
cryptography(ECC).
•
•
Easier to understand.
Widely deployed, better industry support.
DISADVANTAGES OF RSA
•
•
Very slow key generation.
Slow decryption, which is slightly tricky to implement
securely.
• Two-part key is vulnerable to GCD attack if poorly
implemented.

25. CRITICAL ANALYSIS
 Though the execution time of the RSA is more it is widely applied in
many fields because it provides more security as it adds complexity for
the intruders and also provides authentication .
 It is used:
-to protect web traffic, in the SSL protocol
(Security Socket Layer),
-to guarantee email privacy and authenticity in
Pretty good privacy.
- to guarantee remote connection in SSH(Secure Shell).
-also in digital data information and telephone security

26. PROBLEM IDENTIFICATION
 At present, 1024 bit keys are considered weak, 2048
bit keys are probably secure enough for most
purposes, and 40 bit keys are likely to remain
secure for decades.
 RSA is very vulnerable to chosen plaintext attacks.
There is also a new timing attack that can be used to
break many implementations of RSA.
 The RSA algorithm is believed to be safe when used
properly, but one must be very careful when using it
to avoid these attacks.

27. PROPOSAL METHOD
 To improve the Data Security and to decrease the
execution time for the existing algorithm by increasing the
length of the key.

28. PROGRESS OF THE WORK
 Encryption of the plain text using RSA algorithm
using MATLAB software has been performed
successfully.
 The comparison of the time of execution for various
plain texts.

29. FUTURE SCOPE
The future will focusing on –
More strong security algorithms and implement a better
version of RSA .
New security techniques need to be developed and older
security techniques needed to be radically tweaked to be able
to work with the clouds architecture.
As the development of cloud computing technology is still
under R&D, there will be more better understanding of
the design challenges of cloud computing, and pave the way
for further research in this area.

30. CONCLUSION
 Security is a major requirement in cloud computing
while we talk about data storage. There are number of
existing techniques used to implement security in cloud.
So in this presentation, It discussed the popularly
used asymmetric algorithms of cloud encryption
techniques.

31. REFERENCES
 Coutinho, S. C. The Mathematics of Ciphers: Number Theory and RSA Cryptography. Wellesley,
MA: A K Peters, 1999.
 Flannery, S. and Flannery, D. In Code: A Mathematical Journey. Profile Books, 2000.
 Honsberger, R. Mathematical Gems III. Washington, DC: Math. Assoc. Amer., pp. 166-173, 1985.
 Meijer, A. R. "Groups, Factoring, and Cryptography." Math. Mag. 69, 103-109, 1996.
 Rivest, R. L. "Remarks on a Proposed Cryptanalytic Attack on the MIT Public-Key
Cryptosystem." Cryptologia 2, 62-65, 1978.
 Rivest, R.; Shamir, A.; and Adleman, L. "A Method for Obtaining Digital Signatures and Public-
Key Cryptosystems." MIT Memo MIT/LCS/TM-82, 1977.
 Rivest, R.; Shamir, A.; and Adleman, L. "A Method for Obtaining Digital Signatures and Public
Key Cryptosystems." Comm. ACM 21, 120-126, 1978.
 RSA Laboratories. "The RSA Factoring
Challenge" http://www.rsa.com/rsalabs/node.asp?id=2092.
 Simmons, G. J. and Norris, M. J. "Preliminary Comments on the MIT Public-Key
Cryptosystem." Cryptologia 1, 406-414, 1977.

32. RESULTS
SNO P Q FILE SIZE TIME TAKEN
1 53 59 4KB 3.05 s
2 1021 1031 8KB 37s
3 10163 10169 8KB 1.83 s
SNO P Q R FILE SIZE TIME
TAKEN
1 5 6 7 12KB 0.004s
2 51 53 61 12KB 2.14s
3 10163 10169 10177 12KB 0.0003s