Cryptography Paper.docx - HOMOMORPHIC CRYPTOGRAPHY ABSTRACT In this study we focused on the development of Homomorphic Encryption to support the

Cryptography Paper.docx - HOMOMORPHIC CRYPTOGRAPHY ABSTRACT...

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HOMOMORPHIC CRYPTOGRAPHY
ABSTRACTIn this study, we focused on the development of Homomorphic Encryption to support the learning of Cryptographic methods. Homomorphic Encryption allows mathematical operations on data to be carried out in ciphertext, instead of on the actual data itself. The cipher text is an encrypted version of the input data. We also demonstrate the first working types of homomorphicalgorithms, the different levels of homomorphism, and the steps needed to render them fully homomorphic. We then also discuss the benefits of homomorphic encryption, along with potential drawbacks, and improvements being made to lessen said drawbacks. We end with looking at the future of homomorphic encryption, and a potential time horizon for when its use can be considered viable outside of academia.INTRODUCTIONHomomorphic encryption is a method of encryption that allows computations manipulation to be performed on encrypted data without needing to decrypt it. When the final result is decrypted, it will match the result as the same computations were performed on plaintext(Crane, 2019). When it comes to manipulating sensitive data, typically data needs to be encrypted first, which opens up potential lines of attack for cybercriminals (Crane, 2019). With homomorphic encryption, even if the data is taken from non-secure communication lines, the attacker will only get the encrypted data. Having the ability for employees (or a third party) be able to manipulate data without being able to see the unencrypted data itself (Crane, 2019). This has many potential applications, which will be discussed later in this paper. In the world of homomorphic encryption, the cryptosystems used for evaluating ciphertexts have varying levels of homomorphism. With partially homomorphic encryption
(PHE), it allows only one type of operation with an unlimited number of times. Conversely, somewhat homomorphic encryption (SWHE) allows two types of operations, but only allows them to be carried out a limited number of times (Gentry, 2009). The problem of fully homomorphic encryption was first proposed in 1978, after the publication of the RSA cryptosystem, which itself was partially homomorphic. In “Fully homomorphic encryption using ideal lattices,” Craig Gentry proposed a fully homomorphic encryption system in which all types of operations can be carried out an unlimited number of times. Gentry begins with an SWHE scheme that can be evaluated a limited number of times. However, as the ciphertext continues to be evaluated, the level of noise will increase until the ciphertext is unable to be decrypted as a result (Gentry, 2009). However, Gentry avoids this by altering his scheme by making it bootstrappable, able to evaluate its decryption circuit plus one NAND gate. This is important because NAND gates have functional completeness, meaning it’s possible to replicate any gate using a combination of only NAND gates. The result is a ciphertext that has a reduced level of noise and can be operated on an unlimited amount of times as long it goes through the

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