## Homomorphic encryption against SST ©, Secure System of Transmission

We are all well aware that the data we have, whether they relate to our own person, in the course and result of our work, to the ones which make the value of a company or even state secrets or assimilated, must be protected in the best way, both in the state in which they are, at rest or during their communication.

Speaking only of the protection of data, apart from that of the tools that create them, preserve them or convey them, we are obliged to note, as Julius Cesar did in his days of conquest, that only the transforming the clear text into something that can only be read by the person to whom it is intended, helps to preserve its confidentiality.

This modification of the original information is called encryption.

Kaspery gives us the following definition of encryption in modern times:

“* Encryption is the basic building block of data security and the simplest and most important way to ensure that information on a computer system cannot be stolen and read by someone who wishes to use it for malicious purposes*“

“* The principles of encryption are based on the notion of encryption algorithms and “keys”. When information is sent, it is encrypted using an algorithm and can only be decoded using the appropriate key. A key can be stored on the receiving system, or can be transmitted with the encrypted data*“.

** **

He adds, what we all know, that there are several encryption methods of which the main ones are “Symmetric Encryption Key: also known as Secret Key Algorithm” and “Asymmetric Cryptography: this method uses two different keys (public and private) mathematically related” (1).

It follows that the encryption is done using keys (mathematically linked or not), and algorithms.

For some time now a new encryption system has been in vogue, especially in the United States. This is ** Homomorphic encryption** used in particular by Eclipz and Fortanix, among others.

In cryptography, a ** Homomorphic encryption** is “an cipher which has certain algebraic characteristics which make it switch with a mathematical operation, that is to say that the decryption of the result of this operation on encrypted data gives the same result as this operation on unencrypted data; this property allows calculations to be entrusted to an external agent, without the data or the results being accessible to this agent” (2).

It was in 2009 that Craig Gentry (from Stanford University) presented the first completely homomorphic encryption scheme based on Euclidean network cryptography. It is totally new because it allows a direct calculation on encrypted data (without the need for the computing entity to decrypt it) (3) (4).

But it is immediately noticeable that this system uses at least one encryption key, mathematics and finally the intervention of an external agent.

This is its weakness.

Indeed, in addition to the fact that “the size of the keys and the cost of operations are much larger. A priori, the order of magnitude would be 1 per 1000 compared to classical encryption” (5), the quantum computer is a major challenge.

Already in 1994, the American mathematician Peter Shor invented an algorithm which, if implemented on a quantum computer, would destroy all current cryptographic systems (6).

** **

**Quantum computer breaks 2048-bit RSA encryption in 8 hours**

** **

Current security systems based on number theory (mathematics) will not last very long in the face of quantum computers (7).

One of the possibilities opened by quantum computing, mathematically proven by Shor’s algorithm (factoring a natural number N in time O and space 0) is to be able to break part of the current encryption technology (8).

However, in addition to this weakness in the face of quantum computing, homomorphic encryption is not protected against computer attacks. Whether it is used in the banking sector or in the electoral process, homomorphic encryption does not prevent the very content that is protected from being manipulated before it is decrypted:

“If one of the voting booths get infected with malware then the __votes can be manipulated__ effortlessly before the process of decryption. Such situations can be a threat to the homomorphic cryptosystem used in the banking and finance sector. Hence, vulnerability to malware could be a challenging factor over the next few years” (9).

Faced with traditional and homomorphic encryption, and in the presence of quantum computing, ** SST©**, Secure System of Transmission, created by

**holds the measure honourably (10).**

**PT SYDECO**Indeed, the ** SST**© system is not based on number theory, so it is invulnerable to quantum computing.

In addition, ** SST© does not use keys, does not use any external entities and moreover, the data is sealed at the time of its translation into alien language so that it cannot be manipulated under any circumstances before it is received by the authorized recipient**.

The SST System© is therefore, at present, the safest way to protect data at rest or in movement.