We first review basic concepts from elementary number theory, including the notion of primes, greatest common divisors, congruences and Euler's phi function. The number theoretic concepts and Sage ...

We first review basic concepts from elementary number theory, including the notion of primes, greatest common divisors, congruences and Euler's phi function. The number theoretic concepts and Sage ...

The RSA algorithm works because, when n is sufficiently large, deriving d from a known e and n will be an impractically long calculation — unless we know p, in which case we can use the shortcut.

Despite RSA's gesture, several competitors who have paid royalties for use of the algorithm for up to 17 years, argue that the industry could have done with the patent relaxation earlier.

RSA is currently doing an internal review of all of its products to see where the algorithm gets invoked and to change those. A company spokesman said the review is expected to be completed next week.

The team factored RSA-240, an RSA key that is 795 bits in size, with 240 decimal digits. The previous RSA record was set in 2010, with a key of 232 decimal digits and 768 bits.