Analysis Of Homomorphic Encryption Has Been An Open Problem For Many Years

Analysis Of Homomorphic Encryption Has Been An Open Problem For Many Years

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Homomorphic encryption has been an open problem for many years and has been a target of study in the field of public key cryptosystems. We propose a somewhat asymmetric homomorphic encryption which will provide a high security and data integrity.


subsection{Encryption today: how safe is it really? (DF Hw2)}
Security and Encryption are really important subjects in today 's technologies. Every time we use our phones and smart devices we are exposing ourselves to different types of attacks. When we check our email, make a purchase online, have you ever ask yourself how is your private information kept secure.
Our information is getting secured by attackers by using cryptographic algorithms, which basically get the information typed by the user (plain text) and modify the message in a way that cant be read by anyone else but the legitimate recipient.
Security has been a main concern for years the first cryptographic methods actually go back to the time of ancient Greece. Indeed, the word “cryptography” is a combination of the Greek words for “secret” and “writing”.
For example even the Spartans used a system where they wrapped a piece of papyrus around a staff of a certain girth, they will write the message down the length of the staff. When the papyrus was unravelled, the message was jumbled until it reached its destination and was wrapped around another staff of the correct circumference to be able to see the correct message.
A lot has change since those days modern technology has made it possible and practical to use far more complex encryption techniques, using algorithms that are harder to break.

This article is a great example of an overview of Public Key Encryption, which is one of the fundamental building blocks of SSL. As...


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The old problem with fully homomorphic encryption was solved thanks to the work of Gentry based on ideals lattices. However Gentry’s FHE was not efficient in many applications, because the computational time and ciphertext size were high-degree polynomials. Optimizations were developed by Stehle and Steinfeld, reducing complexity from Big O p6 to Big O p3.5. Even though Gentry’s wasn’t as effective he gave a construction framework that allowed a FH scheme to be transformed, by applying regularly the bootstrapping theorem from a “somewhat” homomorphic scheme, which could merely evaluate “low-degree” polynomials homomorphically. In this paper a lower Big O was achieved by applying "squash 63 decryption technique and then ciphertext refresh procedure our somewhat scheme can be easily transformed into a fully homomorphic scheme that may be practical to cloud computing.”

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