I think it's possible to simply brute force the 128-bit encryption key the 3DS uses.
340,282,366,920,938,463,463,374,607,431,768,211,456 possible values for a 128-bit key.
The 10 fastest supercomputers in the world combined is capable of approximately 107 * 10^15 floating point operations per second. If well optimized custom-coded OS is running with the sole purpose of cracking RSA keys, a single key guess and check can probably be done under 100 floating point operations. Therefore, it's probable to say that this computer will be able to guess 107 * 10^13 keys per second.
Now, there's 33,766,632,000,000,000,000,000 keys per year.
Therefore, it would only take an absolute maximum of 10 07747 43220 15250 years. With the average time required being approximately 5 quadrillion years.
See? It's doesn't tale long as the OP described and is perfectly reasonable.
You might even be able to cut the time down to 4 quadrillion years, if you also recruit the usage of the Storm botnet, which has the power of a top-of-the-line supercomputer all on it's own.
Now, someone go contact the world's governments and begin brute forcing the key.