ất khó để làm chủ. Cho đến nay, ít nỗ lực đã được thực hiện để sử dụng công nghệ này trong các vi điều khiển thẻ thông minh. Tuy nhiên, điều này có thể thay đổi trong một vài năm, kể từ khi FRAM công nghệ sở hữu tất cả các tính năng cần thiết để cho phép nó hoàn toàn thay thế EEPROMs, | Cryptology 193 can be used without modifying the algorithm. The RSA algorithm is thus scaleable. However computation time and amount of memory space needed must be kept in mind since even 768-bit keys are presently still considered to be secure. With current factoring algorithms a good rule of thumb is that increasing the key length by 15 bits doubles the effort of computing the Andrew Odlyzko Odlyzko 95 provides an excellent summary of the internationally available and required processing capacity for factoring integers. Although the RSA algorithm is very secure it is rarely used to encrypt data due to its long computation time. It is primarily used in the realm of digital signatures where the benefits of an asymmetric procedure can be fully realized. The greatest drawback of the RSA algorithm with regard to smart cards is the amount of memory space required for the key. The complexity of the key generation process also causes problems in certain cases. Widespread use of the RSA algorithm is restricted by patent claims that have been made in several countries and by major import and export restrictions imposed on equipment that employs this algorithm. Smart cards with RSA coprocessors fall under these restrictions which considerably hinders their use internationally. Table Sample computation times for RSA encryption and decryption as a function of key length. The indicated values are in part subject to considerable variation since they are strongly dependent on the microcomputer used the bit structure of the key and the use of the Chinese remainder algorithm which can only be used for signing Implementation Mode 512 bits 768 bits 1024 bits 2048 bits Smart card without NPU 8-bit CPU MHz clock Signing 20 min Smart card without NPU 8-bit CPU MHz clock with Chinese remainder theorem Signing 6 min Smart card with NPU MHz clock Signing 308 ms 910 ms s Smart card with NPU MHz clock with Chinese remainder theorem Signing 84 ms 259 .
