DE102014016656A1 - MEC30.2 Factorization procedure - Google Patents

Abstract

Characterized in that the finiteness of the positions of the numbers represents a Habtisch physical property. Since these are unknown, the physical properties of the numbers in the positions and information are not used. Which are visualized as a folding rule of the MEC 30 and described for the factorization. Features of the prior art include using the chaotic distribution of non-divisible numbers to encrypt data. For example, the factorization problem for integers is a task to determine the non-trivial divisors of a composite number. To date, no factorization method is known that non-trivial divisors and thus the prime factorization of a number calculated efficiently. This means that a huge computational effort is needed to factorize a number with several hundred digits. This difficulty is exploited in cryptography. The security of encryption methods such as the RSA cryptosystem is based on the fact that factoring the RSA module to decrypt the messages is expensive. The factorization method presented here uses the tool MEC 30, DE 10 2011 101 032 A1. In which the physical property is shown that a number in the position has certain distances, which are represented in the folding rule MEC 30.

Description

The factorization procedure is based on the MEC 30. In 1 the first member of the folding rule MEC 30 is shown, which in the patent specification, scale "MEC 30", which shows the energy distribution in systems. File number 10 2011 101 032.0 , Registration 10.05.2011, Disclosure 02.07. 2014, exam place for class G01B.

The scale as a member of the folding rule is in 1 shown. Thus, the positions 1, 7, 11, 13, 17, 19, 23, 29, give the value 30 a determinable size.

Now it is shown here how the tool, the first member of the folding rule MEC 30 with the positions in the space size 30, is used as a new tool. We represent the space size 30 as space information 1, so the position 1 in the space = 0.0333∞ With this simple position determination we are able to decompose infinitely many prime products in their prime factors, see 2 the Excel spreadsheet.

With this upper block 30, the numbers ² are exactly check. And all numbers up to ∞ that factor the divider below 30 sample number 106596431. 106596431 / 0,9666666666666 = 110272170 The occurrences of the number to be examined, dividend, should be about 4 digits less than the divisor behind the comma.

110272170/30 = 3675739 × 29 = 106596431 and is in position 29. From 1 to 29 we have shown the relationship how the prime numbers behave to infinity. So we can provide the numeric keypad 1 to 29 with a counter, as in 2 and 3 , This counter runs in the given case, to the size of the number to be checked to infinity.

In the 2 In the Excel table the block of the MEC 30 is increased from C to N by 1. Thus, the limb scale of the MEC 30 is increased by 12 terms. Thus, in the space of the block elements of the MEC 30 (12 · 30) ² = 129600, all the prime positions that are important for the factorization are displayed exactly.

To check all numbers, first divide the number by 2, 3, 5, if there is no whole divisor, it is a number in prime positions, 1, 7, 11, 13, 17, 19, 23, 29. The basis is now the distances of the 8 positions in the folding rule of the MEC 30. In 2 this number N is to be entered in position C10 and is divided by the prime positions or compared in their mutual distances.

Thus, a number 8100, in the following example, should be exactly checked in the prime positions (3 × 30) ² = 8100 with initially 8 × 3 = 24 calculations.

In the next step, the 8 positions in the block of the counter are to be reduced by reduntante thus producing the primes.

Now the 24 computations are reduced to 21 computations, through the prime positions where only products of primes are located (except the primary products of 2, 3, 5,).
As

In these positions not only primes but also your products are of smaller primes. As a product they stand as a permutation in the positions and are to be excluded for the factorization.

That is, since the reduced prime positions as product of the prime numbers follow a permutation, they are systematically removed. This permutation is thus graphically represented and reduces the required storage space z. B. in the computer.

So we only use primes to factorize the number N = p × g. Since the primes decrease with increasing even numbers, the computational effort is reduced proportionally as the number increases. Ie. the computational effort is reduced in proportion as the number increases, see the following examples:
(30 × 30) ² = 810000 numbers with 151 calculations to be checked exactly
(300 × 30) ² = 81,000,000 numbers with 1113 calculations to verify exactly
(3000 × 30) ² = 8100000000 numbers with 8710 calculations to verify exactly
(30000 × 30) ² = 810000000000 numbers with 71271 calculations to verify exactly

4 shows the systemlogical permutation of the prime number products of a cycle 7 to 31, this cycle runs to infinity, each additional cycle increases by a factor of 30, identical to the numerator counter.

5 Shows the transfer of the individual permutations to the system, which seems like a chaotic system. It is shown, however, that the density of the primes decreases as the number to be checked increases, and thus also the number of calculations required for factoring.

In 6 A range of 233 numbers is shown in the 7 is transmitted, and is shown from 1 to 233 on a straight line.

8th shows a simplified representation of the permutation that always shows the same pattern. 9 shows why it has to work to infinity. 10 shows the appropriate coordinate system of the unequal distribution of the primary products in the finite 8 prime positions, so the axes (XY) are to be extended to infinity.

The algorithm presented here is now able to represent all primes without gaps. Now we are able by MEC 30 position to accelerate the factorization of N in RSA encryption. Thus, the system uses the fewer numbers of prime numbers in position in the larger number space. In RSA encryption, two very large primes p and g are used to generate N. p × g = N

Since N also has a position, N modula 30 = position, we can see in Table 11 show in which positions the divisors p and g have to be primes. So we just have to pull the root from N and calibrate that number in the positions (unless the value of the root p and g does not already exist). An example number N like 95477 is the root = 308.99 Put it in modula 30 so it is 8.99.

Now we check the number N for their position by Mudula 30 so we get the prime position 17. According to the table of 11 the possible prime positions of p × g are to be determined as follows: 17 = 1 × 17/7 × 11/29 × 13/19 × 23 Thus, the next positions of 8.99 = 7 and 11 are to be transmitted as follows.
7 ... 8.99 ... 11
307 ... 308.99 ... 311
10.23333 10.36666 ...

Through the root of N, we can calibrate the largest possible positions by the scale of the MEC 30 in which the prime numbers p and g, which are the sum of the number N, are present. This allows us to start billing at the highest possible prime and finish at the smallest possible prime. Please refer 12 from right to left to calculating.

Thus, in the numerical example p is calibrated to 307 and g is calibrated to 311. 307 x 311 = 95477, in this example we can show that without division, the number 95477 is to be factored into its prime factors. Now another prediction is possible: Since N = 95477 belongs to RSA encryption, it is a product of p and g, so 307 is a prime and 311 is also a prime.

• 1. Die geringere Dichte von Primzahlen in den großen Bereichen.
• 2. Nutzen wir die notwendige Größe der Primzahlen für eine effektive RSA Verschlüsselung, die Primpositionen von p und g sind somit in den größeren Informationsbereiche der Positionen aufzufinden.

This result is now to be transferred from the MEC 30 to the algorithm shown above. Since we start the factorization with the largest possible prime position, we use

• 1. The lower density of primes in the large areas.
• 2. If we use the necessary size of the primes for an effective RSA encryption, the prime positions of p and g can be found in the larger information areas of the positions.

In 12 with the calibration of the MEC 30 we calculated from right to left and could start with the factorization of the largest possible prime positions. Thus, we were able to factor almost 100% without division, in this probably simple example.

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• DE 102011101032 [0001]

Claims (1)

The method of decryption with the scale MEC 30 shows according to claim. Characterized. With a small amount of computation, with a small computer, a highly efficient factoring is possible. Claim. That the processor architecture can be improved by the given software so that the computing speed is increased and the storage capacity is reduced. The thus allows a further increase in the computing speed.

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