homomorphic

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ho·mo·mor·phic

(hō'mō-mōr'fik),
Denoting two or more structures of similar size and shape.
[homo- + G. morphē, shape, appearance]
Farlex Partner Medical Dictionary © Farlex 2012

ho·mo·mor·phic

(hō'mō-mōr'fik)
Denoting two or more structures of similar size and shape.
[homo- + G. morphē, shape, appearance]
Medical Dictionary for the Health Professions and Nursing © Farlex 2012
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References in periodicals archive ?
To evaluate homomorphically a mod-Q arithmetic circuit, one can use the FHE scheme with message space [Z.sup.Q] directly, or one can firstly convert the arithmetic circuit to a Boolean one and carry out all the computation using an FHE scheme with binary message space.
The usual technique for squashing the decryption circuit amounts to homomorphically evaluating a large integer sum of the form Z01 [[summation].sub.[THETA].sub.i=1][s.sub.i][z.sub.i], where the [s.sub.i] are secret bits and the [z.sub.i] are public constants computed from the original ciphertexts and public parameters.
Therefore, any circuit C with efficient description can be evaluated homomorphically. However, this somewhat fully homomorphic scheme (SWHE) is not perfect.
If both G [right arrow] H and H [right arrow] G, then G and H are said to be homomorphically equivalent.
Since M is non-empty, the subgraph consisting of only e maps homomorphically to M, so mcM(N,w) [greater than or equal to] 1/|E(N)|.
However, his scheme relies on relatively stronger cryptographic assumptions on ideal lattices (ideal lattices are a special breed that we know relatively little about) and can only evaluate "low degree" polynomials homomorphically without "bootstrapping."
If there is computation that needs to be carried out on the ciphertext, the decryption circuit of the targeted ciphertext will be evaluated homomorphically to re-encrypt the plaintext under the FHE scheme.
Therefore, the somewhat homomorphic encryption scheme is constructed, which can homomorphically evaluates arithmetic circuits of limited depth.
As for the first round, we encode the original broadcast message as a polynomial [m.sub.i] = [m.sub.s] whose coefficients belong to {0, 1} for sender [v.sub.s] and assign polynomials [m.sub.i] = 0 to any other nodes [v.sub.i] (i [not equal to] s), thus all nodes can trivially figure out their inputs as [E.sub.PK] ([m.sub.i + [k.sup.1.sub.i]) by homomorphically combining [E.sub.PK]([m.sub.i]) with [E.sub.PK] ([k.sup.1.sub.i]).
[5] studied how to calculate edit distance of encrypted gene data homomorphically. Yasuda et al.
Also, Gentry gave a construction framework [12] that an FHE scheme can be easily transformed by applying the bootstrapping theorem regularly from a somewhat HE scheme, which can merely evaluate low-degree polynomials homomorphically. However, to support bootstrappable encryption, Gentry's framework has to squash the decryption circuit that results in the inefficiency of the construction.
Then, Gentry's key idea, called bootstrapping, consists in homomorphically evaluating this decryption polynomial on encryptions of the secret key bits, resulting in a different ciphertext (refreshed ciphertext) associated with the same plaintext with possibly reduced noise.