Pure math makes SoftwarePassport/Armadillo's keys secure; in order to crack the encryption template on a single certificate by brute force, a cracker would have to try every possible key combination. If the cracker's smart about it, it would only take 2, 000 years on a 100MHz Pentium-class system; if not, it could take exponentially longer. Since there is no mathematical way to attack this encryption system (like the quadratic sieve or general number sieve for RSA encryption), it would have to be done with a brute force attack, probably with a much faster system (a 200 gigahertz system would still need about a year to go through them all... at the time of this writing, Intel and AMD are just about to come out with the first 2.5 gigahertz chips).
纯数学使得SoftwarePassport/Armadillo的密匙是安全可靠的，为了暴力破解一个认证的加密模板，破解者可能不得不尝试每一个可能的密匙组合，如果破解者聪明的话，他将需要使用2000年在一个100Mhz的奔腾系统上，如果不是，使用的时间将需要指数集的增长，因为没有数学的方法来攻击这个加密系统（就像是RSA加密系统的二次方筛选或普通数字筛选），不得不使用暴力破解，或许使用一个更快的系统（一个200Ghz的系统仍然需要大约1年时间来尝试所有的密匙…，写到这里，Intel和AMD刚发布第一款2.5Ghz的芯片）。