Good morning, everyone.
I would like to ask the forum what they think about this new method for data security.
A New Algorithm for Zero-Time Factoring of Semiprimes
Introduction
Context: Semiprimes, which are the product of two
prime numbers, are still an important building block in cryptography
as their factorization remains one of the unsolved problems in
mathematics. Currently, algorithms such as the Elliptic Curve Method
(ECM) and the Number Field Sieve (NFS) are used. The ECM is a
probabilistic factorization algorithm devised by H.W. Lenstra Jr. in
1985, while the NFS is based on finding relations between "smooth"
numbers (with few prime factors) in a number field. Of course, even
these algorithms are helpless against large semiprimes, and their
factorization capability decreases as the semiprime becomes larger.
Objective: To create a cryptosystem using very
large prime factors to address the challenge of quantum computers.
How the Algorithm Works
I want to talk about a new factorization system that I have named
GC57, which can factor semiprimes 2, 3, and 4 times larger than the
current semiprimes that are considered secure today, namely 13000-bit
semiprimes. This factorization system exploits a particular property,
namely the property of integers, or the property of the remainder.
The integer of the number obtained through the Euclidean greatest
common divisor is always a prime factor of the semiprime. This is
true up to a certain field that can range from 2^25 to beyond 2^500.
Let me explain:
The GC57 algorithm can factor any semiprime that is the product of
p and q within this field at ZERO time.
How the Encryption
Program Works
1. Creation of the Semiprime Database
This operation is important to maintain zero-time factorization
because finding two prime factors of size 6000 bits and beyond would
keep the system busy for a few minutes, slowing down the program.
This database is stored on the computer and made available to the
program, which will load one at random from those stored.
Furthermore, this practice facilitates the diversification of the
semiprimes used, for example, by keeping multiple semiprimes of
different sizes. The program will then distinguish which key to
retrieve to factor the selected semiprime.
2. The Key
The key, or keys, if we use multiple semiprime sizes, are stored
on a USB key that must also be in the possession of the person
receiving the messages. This also has another advantage, namely, if
the sender of the messages has all the keys while the receiver has
only some of the keys, these messages can only be decrypted by the
person with the right key. Furthermore, it becomes very convenient
when using only a shared folder, or a shared cloud, because each
message is identified by how it was created, namely by what type of
semiprime it was created from.
3. Encryption
When a message is created, the program loads a semiprime, as
described above, and factors it at zero time. From the prime factor
of this semiprime, it extracts the digital fingerprint (SHA 256) and
passes it to the AES 256 encoding which will create the encryption
key to encrypt the message. The encrypted message will then be saved
in the shared folder, or on the shared cloud, with the text, the
encrypted digital fingerprint and the semiprime inside.
4. Decryption
The message is loaded by the person to whom it is addressed and,
using the same key used in the encryption phase, also stored on a USB
key, the semiprime is extracted and factored at zero time, which is
then passed to the SHA to retrieve the digital fingerprint with which
AES will decrypt the message. The message will then be printed on the
private printer, preferably connected by cable, and then deleted from
the shared folder or cloud.
Comparison with RSA
Speed: RSA is relatively slow compared to
symmetric encryption algorithms. For this reason, it is generally
only used to exchange symmetric keys and to digitally sign documents,
not for encrypting large amounts of data. GC57 is very fast both in
zero-time factoring and in encoding large data with SHA and AES
algorithms.
• Security: RSA bases its security on the difficulty of
factorizing large semiprimes.
The GC57 also relies on this difficulty
but adopts a system that allows it to factorize semiprimes much
larger than RSA.
thank you
