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Ensuring Data Security Using Homomorphic Encryption in Cloud Computing

explanatory Essay
1063 words
1063 words
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Homomorphic Encryption allows access to highly scalable, inexpensive, on-demand computing resources that can execute the code and store the data that are provided to them. This aspect, known as data outsourced computation is very attractive, as it alleviates most of the burden on IT services from the consumer. Nevertheless, the adoption of data outsourced computation by business has a major obstacle, since the data owner does not want to allow the un trusted cloud provider to have access to the data being outsourced. Merely encrypting the data prior to storing it on the cloud is not a viable solution, since encrypted data cannot be further manipulated. This means that if the data owner would like to search for particular information, then the data would need to be retrieved and decrypted a very costly operation, which limits the usability of the cloud to merely be used as a data storage centre. Homomorphic Encryption systems are used to perform operations on encrypted data without knowing the private key (without decryption), the client is the only holder of the secret key. When we decrypt the result of any operation, it is the same as if we had carried out the calculation on the raw data. Definition: An encryption is homomorphic, if: from Enc(a) and Enc(b) it is possible to compute Enc(f (a, b)), where f can be: +, ×, ⊕ and without using the private key. For plaintexts P1 and P2 and corresponding ciphertext C1 and C2, a homomorphic encryption scheme permits meaningful computation of P1 Θ P2 from C1 and C2 without revealing P1 or P2.The cryptosystem is additive or multiplicative homomorphic depending upon the operation Θ which can be addition or multiplication. A homomorphic encryption scheme consists of the followi... ... middle of paper ... ...S: [1] Vic (J.R.) Winkler, “Securing the Cloud, Cloud Computer Security, Techniques and Tactics”, Elsevier, 2011. [2] Pascal Paillier. Public-key cryptosystems based on composite degree residuosity classes. In 18th Annual Eurocrypt Conference (EUROCRYPT'99), Prague, Czech Republic, volume 1592, 1999 [3] Julien Bringe and al. An Application of the Goldwasser-Micali Cryptosystem to Biometric Authentication, Springer-Verlag, 2007. [4] R. Rivest, A. Shamir, and L. Adleman. A method for obtaining digital signatures and public key cryptosystems. Communications of the ACM, 21(2):120-126, 1978. Computer Science, pages 223-238. Springer, 1999. [5] Taher ElGamal. A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Transactions on Information Theory, 469-472, 1985. [6] Craig Gentry, A Fully Homomorphic Encryption Scheme, 2009.

In this essay, the author

  • Explains that the output-a tuple (sk, pk) consisting of the secret key and public key.
  • Explains input-a public key, circuit with inputs and a set of ciphertext.
  • Explains that a homomorphic encryption scheme consists of all algorithms and an extra one. the correctness-condition for the conventional part is identical.
  • Describes the paillier cryptosystem, which is an additive homomorphic encryption scheme based on the intractability hypothesis.
  • Explains that two large prime numbers p and q are chosen randomly and independently of each other. this property is assured if both primes are of equal length.
  • Explains that n divides the order of g by checking the existence of the following modular multiplicative inverse.
  • Explains that rsa is an algorithm for public-key cryptography based on the presumed difficulty of factoring large integers.
  • Explains that rsa involves a public and private key. the public key can be known to everyone and is used for encrypting messages.
  • Explains that the integers p and q should be chosen at random, and of similar bit-length, for security purposes.
  • Explains that n is used as the modulus for both the public and private keys. its length is the key length.
  • Explains that e and (n) are coprime integers.
  • Explains that e having a short bit-length and small hamming weight results in more efficient encryption – most commonly 216 + 1 = 65,537.
  • Explains that d is the multiplicative inverse of e (modulo (n)).
  • Describes how alice transmits her public key (n, e) to bob and keeps the private key secret. bob then wishes to send message m to alice.
  • Explains that bob transmits c to alice using the method of exponentiation by squaring.
  • Explains alice can recover m from c by using her private key exponent d via computing.
  • Explains that cloud computing security based on homomorphic encryption is a new concept of security which enables providing results of calculations on encrypted data without knowing the raw data on which the calculation was carried out.
  • Presents pascal paillier's paper on public-key cryptosystems based on composite degree residuosity classes.
  • Explains julien bringe's application of the goldwasser-micali cryptosystem to biometric authentication, springer-verlag, 2007.
  • Explains r. rivest, a. shamir, and l. adleman's method for obtaining digital signatures and public key cryptosystems.
  • Explains taher elgamal's public key cryptosystem and a signature scheme based on discrete logarithms in ieee transactions on information theory.
  • Explains that homomorphic encryption allows access to highly scalable, inexpensive, on-demand computing resources that can execute the code and store the data that are provided to them.
  • Explains that the notation a/b does not denote the modular multiplication, but rather the quotient of the largest integer value v>=0 to satisfy the relation.
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