product vs difference

[AntonioLao]

Cryptology as a basic science of secret codes became popularized with the advent of the computer age. Now it is applied to creating public-keys for the security of internet e-commerce or any other forms of secret communications. The RSA program (see http://en.wikipedia.org/wiki/RSA) of the late 70’s is based on the factorizations of large numbers which are the products of two large prime factors. These factors can be as large as 60 digits each giving public-key products as much as 120 digits, reading them present no difficulty for the computer eyes or hackers with powerful laptops. However, finding which two large prime factors can take some time but RSA 129 (a number with 129 digits) have taken only 8 months to crack instead of the 40 quadrillion years originally predicted. It is now necessary to increase the number of digits for each prime factor but in the long run still does not fully guarantee complete secrecy.

Fortunately, besides elliptic curve cryptography there is an alternative scheme for securing secret messages. This one uses one of Erdős conjectures: it says that every even number greater than 2 is the difference of an infinitely many pairs of prime numbers. The smallest constant prime differences of 2 have been known as the twin primes conjecture. Nonetheless, there are infinitely many pairs of primes that give the constant prime difference of 4, of 6, of 8, of 10, of 12, 0f 14, of 16, of 18, of 20, and of 22, ad infinitum. That is to say for every even number chosen at random, it is associated with an infinity pairs of primes that give the same constant even prime difference. Furthermore, with the advent of m-commerce (mobile and wireless internet) security using elliptic curve cryptography (see http://en.wikipedia.org/wiki/Elliptic_curve_cryptography) there can be a conjecture that relates both to a final convergence. The former relies on real rationality while the latter relies on imaginary ability. The battle ground would be fought within sieves of Diophantus. The outcome of this mathematical confrontation will at most finally provide a proof for the Birch and Swinnerton-Dyer conjecture (see http://en.wikipedia.org/wiki/Birch_and_Swinnerton-Dyer_conjecture and http://mathworld.wolfram.com/Swinnerton-DyerConjecture.html).

[labelwench]

Cryptology as a basic science of secret codes became popularized with the advent of the computer age. Now it is applied to creating public-keys for the security of internet e-commerce or any other forms of secret communications. The RSA program (see http://en.wikipedia.org/wiki/RSA) of the late 70’s is based on the factorizations of large numbers which are the products of two large prime factors. These factors can be as large as 60 digits each giving public-key products as much as 120 digits, reading them present no difficulty for the computer eyes or hackers with powerful laptops. However, finding which two large prime factors can take some time but RSA 129 (a number with 129 digits) have taken only 8 months to crack instead of the 40 quadrillion years originally predicted. It is now necessary to increase the number of digits for each prime factor but in the long run still does not fully guarantee complete secrecy.

Fortunately, besides elliptic curve cryptography there is an alternative scheme for securing secret messages. This one uses one of Erdős conjectures: it says that every even number greater than 2 is the difference of an infinitely many pairs of prime numbers. The smallest constant prime differences of 2 have been known as the twin primes conjecture. Nonetheless, there are infinitely many pairs of primes that give the constant prime difference of 4, of 6, of 8, of 10, of 12, 0f 14, of 16, of 18, of 20, and of 22, ad infinitum. That is to say for every even number chosen at random, it is associated with an infinity pairs of primes that give the same constant even prime difference. Furthermore, with the advent of m-commerce (mobile and wireless internet) security using elliptic curve cryptography (see http://en.wikipedia.org/wiki/Elliptic_curve_cryptography) there can be a conjecture that relates both to a final convergence. The former relies on real rationality while the latter relies on imaginary ability. The battle ground would be fought within sieves of Diophantus. The outcome of this mathematical confrontation will at most finally provide a proof for the Birch and Swinnerton-Dyer conjecture (see http://en.wikipedia.org/wiki/Birch_and_Swinnerton-Dyer_conjecture and http://mathworld.wolfram.com/Swinnerton-DyerConjecture.html).

Interesting details in your post, Antonio.

There is a considerable difference between 8 months and 40 quadrillion years, lol. Wonder how long that estimate took someone to calculate?

Secret. My old dictionary defines the word to mean kept private; not (to be) made known or exposed to view.

Once the above parameters have been breached, I would use the word 'confidential' at best.

Regards,

Labelwench

[AntonioLao]

Wonder how long that estimate took someone to calculate?

Not long, they just made the assumption that the number must be tested by dividing it by every prime number between 2 and the largest prime with 60 digits. This process takes infinitely long by hand but not by a computer using some tricky methods. One person can definitely succeed keeping a secret but two persons, very unlikely. I think only God can absolutely keep a secret. The secret implies in RSA program is someone's credit card number but it's not a secret anymore for hackers and identity thieves.