Decryption of encrypted data missing a private key
A method for decrypting encrypted data/message whereby a computing device derives the prime numbers that are used to make up a public key by searching the decimals of the inverse of the quasi-prime number that is the public key. The computing devices designates a search range around a jump point of the decimals of the inverse of the public key and searches within the search range for prime numbers by testing them against the quasi-prime. When the prime numbers are found, the computing device then uses them to derive the private key and decrypt the data.
1. A method of decrypting a message encrypted by a cryptographic key, comprising:
obtaining, by a computing device, an encrypted message wherein the message was encrypted by a public key;
calculating, by the computing device, an inverse of the public key, wherein the public key is a quasi-prime number;
calculating, by the computing device a jump point within the inverse of the public key, wherein the jump point is a function of a reciprocal equation and a binary expression;
determining, by the computing device, a search range around the calculated jump point;
selecting, by the computing device, a designated search length;
locating, by the computing device, at least one prime number within the search range, by:
from a starting point within the search range, sequentially identifying blocks of digits along the search range corresponding to the designated search length;
for each block of digits, dividing the public key by the block of digits; and
designating a particular block of digits from the identified blocks of digits as a prime number if the division of the public key by the respective block of digits returns an integer value for an answer;
determining, by the computing device, a second prime number based on the public key value and the designated prime number;
determining, by the computing device, a private key corresponding to the public key value based on the designated prime number and the second prime number; and
decrypting, by the computing device, the encrypted message using the private key.
2. The method of claim 1 , wherein the step of sequentially identifying blocks of digits further comprises:
for each identified block of digits, determining, by the computing device, whether the block of digits ends in 0, 2, 4, 5, 6 or 8; and
for each block of digits determined to end in 0, 2, 4, 5, 6 or 8, skipping, by the computing device, to the next block of digits in the sequence.
3. The method of claim 1 , further comprising:
from a second starting point within the second search range, sequentially identifying additional blocks of digits along the search range corresponding to the search length simultaneously with the blocks of digits;
for each block of digits, dividing the public key by the block of digits; and
designating a particular block of digits from the additional blocks of digits as a prime number if the division of the public key by the respective block of digits returns an integer value for an answer.
4. The method of claim 1 , further comprising, upon reaching an end of the search range without locating the at least one prime number:
selecting a second designated search length; and
locating the at least one prime number within the second designated search range by:
from a starting point within the second designated search range, sequentially identifying additional blocks of digits along the search range corresponding to the second search length;
for each block of digits, dividing the public key by the block of digits; and
designating a particular block of digits from the sequentially identified additional blocks of digits as a prime number if the division of the public key by the respective block of digits returns an integer value for an answer.
5. The method of claim 1 , further comprising, upon reaching an end of the search range without locating the at least one prime number:
determining, by the computing device, a second search range; and
locating, by the computing device, at least one prime number within the second search range, by:
from a starting point within the second search range, sequentially identifying additional blocks of digits along the second search range corresponding to the search length;
for each block of digits, dividing the public key by the block of digits; and
designating a particular block of digits from the sequentially identified additional blocks of digits as a prime number if the division of the public key by the respective block of digits returns an integer value for an answer.
6. The method of claim 1 , further comprising, for each of the blocks of digits:
calculating a digital root for the particular block of digits; and
in response to the digital root equaling 3, 6 or 9, proceeding to the next block of digits in the sequence.