Mathematics
Bernstein has published a number of papers in mathematics and computation. Many of his papers deal with algorithms or implementations. He also wrote a survey titled "Multidigit multiplication for mathematicians".
In 2001 Bernstein circulated "Circuits for integer factorization: a proposal," which caused a stir as it potentially suggested that if physical hardware implementations could be close to their theoretical efficiency, then perhaps current views about how large numbers have to be before they are impractical to factor might be off by a factor of three. Thus as 512-bit RSA was then breakable, then perhaps 1536-bit RSA would be too. Bernstein was careful not to make any actual predictions, and emphasized the importance of correctly interpreting asymptotic expressions. However, several other important names in the field, Arjen Lenstra, Adi Shamir, Jim Tomlinson, and Eran Tromer disagreed strongly with Bernstein's conclusions. Bernstein has received funding to investigate whether this potential can be realized.
He is also the author of the mathematical libraries DJBFFT, a fast portable FFT library, and of primegen, an asymptotically fast small prime sieve with low memory footprint based on the sieve of Atkin rather than the more usual sieve of Eratosthenes. Both have been used effectively to aid the search for large prime numbers.
Read more about this topic: Daniel J. Bernstein
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