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# New algorithm for security

Member Posts: 4 ■■□□□□□□□□
edited February 15
Good morning, everyone.

## 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:

• Key

• Field = 2^500

• Prime factor p = x + (>1 < 2^500) any prime within the field of 2^500

• Prime factor q = y + (>1 < 2^500) any prime within the field of 2^500

• Semiprime n = pq

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

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This is not a new method for data security. It is a mathematical algorithm that could be used to generate public/private keys that could be used in cryptosystems. It's not claiming more security, but instead that it is faster and has greater encrypting capacity than RSA--which is now several decades old (circa 1980). Every modern public key cryptosystem (DSA, ECC, etc.) is faster and more secure than RSA.
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Member Posts: 4 ■■□□□□□□□□
JDMurray said:
This is not a new method for data security. It is a mathematical algorithm that could be used to generate public/private keys that could be used in cryptosystems. It's not claiming more security, but instead that it is faster and has greater encrypting capacity than RSA--which is now several decades old (circa 1980). Every modern public key cryptosystem (DSA, ECC, etc.) is faster and more secure than RSA.

I agree. It is not a new method. I expressed myself wrongly. By new I meant a zero-time factorization system on large semiprimes.  This system could give rise to a new data encryption system based on very long and complex keys.

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Now there's something I know nothing about: the inconvenience created by the time it takes to generate very large prime factors. How must time is required to generate just one of these prime factors using a conventional key-generation algorithm? How many keys (or key-generating iterations) are required in a typical crypto-function?
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Member Posts: 4 ■■□□□□□□□□
I'm not sure if I understand it correctly.
To find two very large prime numbers, 6000 and 7000 bits, the Sympy library in Python takes about 2 minutes.
The program I presented creates a database of semiprimes the size of 13076 bits. The semiprime of 13076 bits is randomly loaded by the program and the GC57 algorithm, thanks to a specific key, factors the semiprime at zero time.
The prime factor extracted from the semiprime is used by Hash 256 to create the fingerprint to be passed to AES.
This system makes encryption very fast and always different fingerprints.
This means that if you encrypt the same text several times it will always have a different encryption

Decryption occurs with the same speed because the GC57 algorithm factors the 13076-bit half-first, contained in the message, at zero time, and kicks off the decryption of the text by fingerprinting the prime factor with SHA 256 and providing AES with the decryption key

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Member Posts: 14 ■■■□□□□□□□
Wow. This is complex. I'm surprised that there's a breakdown for something like this in this forum.
CCNA, Security+ and other certifications that haven't been worth mentioning
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Member Posts: 4 ■■□□□□□□□□
I don't know if you are referring to the algorithm or the forum but if there is anyone interested in new encryption systems based on factorization of large semiprimes I am leaving you a link where you can find information about this system. The website has no advertisements or banner ads, and it does not collect data from those who visit it, it is purely informative and free.
This new system that can factorize semiprimes of 13000 bits in zero time is very innovative and will bring a new kind of security on data encoding, faster, more secure.
There are also three already implemented encryption projects on the site that can be analyzed and are written in Python. The scrip can be downloaded from Github.
Of course, I am keen to hear your opinion, especially if you are into factoring and encryption.

Greetings

https://kyoah4fjtx.mobirisesite.com/