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The scrambling of electronic information being stored and sent so that if someone wrongly receives such information it will not be readable.
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Simultaneously, character position information showing how far the encrypted character is located from the beginning character is embedded into the corresponding ciphertext.
The characteristics of homomorphic encryption are for some operations in plaintext and then encryption effect is equivalent to some operation directly in the ciphertext [26-30].
Next, Boyen and Waters [3] proposed an anonymous IBE scheme to guarantee receiver's privacy, where the ciphertext does not leak the identity of the recipient.
Our scheme satisfies following two properties: 1) only receivers can decrypt ciphertexts.
k] the k ciphertexts which encode the k richest parties' indices.
2] of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and define semi-functional keys and semi-functional ciphertexts in the following manner.
Within these constraints, we need an algorithm that will encrypt data by permuting strings in a given format to different strings in the same format, will not leak information to an attacker that has access to a large number of ciphertexts, and will survive the exposure of a reasonable number of plaintext/ciphertext pairs.
However, not all combinations are possible, as for example a public key should not be used to turn secret data into public ciphertexts.
However even with a limited set of linearly independent known plaintexts, all ciphertexts belonging to the linear subspace generated by these can be found.
mathematical expression not reproducible]) which are associated with ciphertexts, the attributes in leafs are stored in the form of plaintext.
When an attribute revocation happens, the secret keys and ciphertexts corresponding to that particular attribute need to be updated.
The ciphertexts and private keys are of constant size, but the public key grows linearly in the number of users.