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I am a beginner to homomorphic encryption scheme. As far as I think, it is just a kind of concealing real value without using standard encryption algorithms such as AES,DES or RSA. For example , for concealing value of $3$, it expresses $6$ where ($6=2 \times 3$). Decryption is done successfully if user knows $2$ (secret value). Is it correct or not?

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  • $\begingroup$ Couldn't you cast RSA, for example, in this same light? You are concealing the message $m$ as $m^e\bmod{n}$. You can only decrypt if you know the secret $d$, which cancels out the $e$. $\endgroup$ – mikeazo Apr 15 '16 at 14:51
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    $\begingroup$ In other words, I'm having a hard time understanding what your question really is. $\endgroup$ – mikeazo Apr 15 '16 at 14:53
  • $\begingroup$ My real intention is just to conceal message without using standard algorithm. Just wanna use light function. $\endgroup$ – astyst Apr 15 '16 at 14:59
  • $\begingroup$ So your real intention has nothing to do with homomorphic encryption? What is your definition of a "light function"? There are light-weight ciphers, do you mean something that can be done by pen and paper in reasonable time? $\endgroup$ – Thomas M. DuBuisson Apr 15 '16 at 18:10
  • $\begingroup$ Your last comment means that you simply want a very simple encryption scheme. But it unfortunately follows that the security of your scheme would be very low or negligible. Cf. the ubiquitous Principle of No Free Lunch. Extending the example that you have provided yourself, a permutation polynomial mod 2**n could be of use to you, since it bijectively maps blocks of n bits. However, the secret key hereby involved, namely the coefficients of the permutation polynomial, could be recovered by the adversary, if he manages to know a correspondingly small number of pairs of plaintext and ciphertext. $\endgroup$ – Mok-Kong Shen Apr 17 '16 at 9:48
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Homomorphic encryption allows you to perform operations on the ciphertext that are reflected in the plaintext. These operations are not used to keep the plaintext confidential, that's performed by the homomorphic encryption itself.

Homomorphic encryption usually has little to do with obfuscation techniques, which is probably what you're looking for. "just looking for a light version" as you explain in your comments probably rules out homomorphic encryption techniques to accomplish obfuscation.

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    $\begingroup$ Allow me a nit-picking: There are connections between homomorphic encryption and software obfuscation. See B. Barak, "Hopes, fears, and software obfuscation", CACM, vol. 59, no.3, 2016 and S. Garg et al., "Hiding secrets in software: a cryptographic approach to program obfuscation", CACM, vol.59, no.5, 2016. $\endgroup$ – Mok-Kong Shen May 16 '16 at 15:02
  • $\begingroup$ @Mok-KongShen Interesting, I'll remember those references! $\endgroup$ – Maarten Bodewes May 16 '16 at 15:18

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