Reed-Muller Code Based Symmetric Key Fully Homomorphic Encryption Scheme

Challa, Ratnakumari; Gunta, VijayaKumari

doi:10.1007/978-3-319-49806-5_29

Cited by 2 publications

(6 citation statements)

References 20 publications

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“…In the proposed scheme, Reed Muller encoding and decoding operations have been used. The decoding algorithm used here is similar to the decoding used in the RMC-based FHE scheme (27). In encryption step, the novel method is adopted to expand the message by prepending a random binary string of zeros and ones in order to generate a new (nondeterministic) codeword for same message if the same message encoded multiple times, which will provide one-many mapping between message and codeword.…”

Section: Proposed Fully Homomorphic Encryption Schemementioning

confidence: 99%

“…But same thing doesn't hold true for homomorphic component wise 2 multiplication. To overcome this problem, one more step of de-noising has been added to multiplication operation to nullify the error introduced as discussed in the RMC-based FHE scheme (27).…”

Section: Overview Of the Schemementioning

confidence: 99%

“…Retrieve the codeword, = ( 0 , 1 , … , −1 ) from by collecting from the locations as specified by the key 2. Compute the -bit expanded plaintext message (27) eliminates the additional noise generated during multiplication and decryption of resulting cipher produces 1 . 2 .…”

Section: Algorithmsmentioning

confidence: 99%

“…( 2 ) and ( ) for encryption and decryption respectively and at ( ) for the homomorphic addition and multiplication operations. Anew Reed-Muller Code (RMC)-based FHE scheme, based on the scheme presented by Armknecht et al (2011), has been proposed with a de-noising step which nullifies the error terms produced during each homomorphic multiplication (27). This is, in one way, the ciphertext refreshing or post-processing idea similar to bootstrapping step in the Gentry's blueprint (9).…”

Section: Introductionmentioning

confidence: 99%

“…The underlying codeword in the ciphertext at the fixed positions, as specified by the secret key, might be computed through Chosen Plaintext Attack (CPA). Present work is the modification to the RMC-based FHE scheme (27) by padding mechanism in order to give one-to-many mapping between message and codeword which will improve its security against CPA. The scheme is proved CPA secure and is thoroughly analyzed with respect to the changes and new techniques suggested to show that the proposed scheme is secure against all the known attacks.…”

Section: Introductionmentioning

confidence: 99%

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A Modified Symmetric Key Fully Homomorphic Encryption Scheme Based on Read-Muller Code

Challa

Gunta

2021

Baghdad Sci.J

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Homomorphic encryption became popular and powerful cryptographic primitive for various cloud computing applications. In the recent decades several developments has been made. Few schemes based on coding theory have been proposed but none of them support unlimited operations with security. We propose a modified Reed-Muller Code based symmetric key fully homomorphic encryption to improve its security by using message expansion technique. Message expansion with prepended random fixed length string provides one-to-many mapping between message and codeword, thus one-to many mapping between plaintext and ciphertext. The proposed scheme supports both (MOD 2) additive and multiplication operations unlimitedly. We make an effort to prove the security of the scheme under indistinguishability under chosen-plaintext attack (IND-CPA) through a game-based security proof. The security proof gives a mathematical analysis and its complexity of hardness. Also, it presents security analysis against all the known attacks with respect to the message expansion and homomorphic operations.

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Section: Proposed Fully Homomorphic Encryption Schemementioning

confidence: 99%

Section: Overview Of the Schemementioning

confidence: 99%

Section: Algorithmsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Modified Symmetric Key Fully Homomorphic Encryption Scheme Based on Read-Muller Code

Challa

Gunta

2021

Baghdad Sci.J

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Towards the Construction of Reed-Muller Code Based Symmetric Key FHE

Challa¹,

Gunta²

2021

ISI

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Homomorphic encryption (HE) schemes became popular cryptographic primitives and very useful in variety of security applications. Homomorphic encryption based on coding theory have the advantages of faster computations due to the structural properties of the codes used. Several schemes are supporting unlimited Mod2 addition operations in literature. The present paper introduces Reed-Muller (RM) code based Mod2 multiplication operation thereby making RM code based HE scheme fully homomorphic. The representation of the codeword with necessary adaption to support unlimited number of Mod2 multiplication operations is presented along with the scheme first. The correctness proof of the homomorphic operations along with experimental evaluation is also presented to demonstrate the practical aspects of the proposal.

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Reed-Muller Code Based Symmetric Key Fully Homomorphic Encryption Scheme

Cited by 2 publications

References 20 publications

A Modified Symmetric Key Fully Homomorphic Encryption Scheme Based on Read-Muller Code

A Modified Symmetric Key Fully Homomorphic Encryption Scheme Based on Read-Muller Code

Towards the Construction of Reed-Muller Code Based Symmetric Key FHE

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