Factoring gains won't break strong crypto – Schneier

Serious number crunching

Concerns that improvements in factoring technology might make it easier to break large key length encryption codes are misplaced, according to noted cryptographer Bruce Schneier.

Last year mathematician Dan Bernstein circulated a paper discussing improvements in integer factorization, using specialised parallel hardware, implying that encryption keys as long as 2048 bits can now be broken.

Schneier, inventor of the Blowfish encryption algorithm and founder of Counterpane Internet Security, believes the improvements described in Bernstein's paper are unlikely to produce the claimed speed improvements in practice.

The fastest factoring algorithm currently available is the Number Field Sieve (NFS) which works in two stages. The first phase of the process is to search for equations that satisfy certain mathematical properties. This is followed by a large matrix calculation, which eventually produces the prime factors of the target number.

Bernstein attempts to improve the efficiency of both steps, but Schneier believes the improvements are marginal for practical numbers and talk of "massive parallization" in number crunching is misleading.

For very large numbers (much bigger than would be used to deliver even a 2048 bit key), Berntein's algorithms might imply a key length three times as long needs to be used to give equivalent levels of security. But, as Bernstein himself acknowledges, it is unclear if this holds true for smaller numbers, or how practical his ideas are.

"Any practical implementation of these [Bernstein's] techniques depends heavily on complicated technological assumptions and trade-offs. Parallel computing is much easier to say than it is to do, and there are always hidden complexities," Schneier will argue in a paper to be published on Friday.

"I think when all the math is said and done these other complexities will even out his enhancements," he adds.

Despite his criticisms, Schneier credits Bernstein with undertaking useful research, which "is likely to open up new research directions in the design of more efficient sorting networks and sparse matrix algorithms". ®

External links

Bernstein's home page

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