 383 TABLE 17.1 Time Comparisons of Performance on the Same Platform of Several Typical Public-Key Cryptographic Operations Public-key based cryptographic Time spent on an Intel operation description Key size Celeron 450 platform RSA signature generation 512 bits 0.4 msec/operation RSA signature verification 512 bits 0.3 msec/operation RSA signature generation 1,024 bits 27 msec/operation RSA signature verification 1,024 bits 0.7 msec/operation Digital Signature Standard (DSS) signature generation 512 bits 4 msec/operation DSS signature generation with precomputation 512 bits 2 msec/operation DSS signature verification 512 bits 5 msec/operation DSS signature generation 1,024 bits 15 msec/operation DSS signature generation with precomputation 1,024 bits 5 msec/operation DSS signature verification 1,024 bits 18 msec/operation RSA encryption 512 bits 0.2 msec/operation RSA decryption 512 bits 4 msec/operation RSA encryption 1,024 bits 1 msec/operation RSA decryption 1,024 bits 27 msec/operation The longer the key, the more computationally heavy the work. Notice the time difference (for spe- cific key lengths especially when they are getting longer) between actually generating a digital sig- nature and simply verifying one. Public-key decryption takes more time than public-key encryption. This is because in order to enhance security, the private key is usually longer than the public one. a result, the modular exponentiation operations involved with public-key decryption (the equivalent of digital signature generation) are computationally more involved. This is why security coprocessors sometimes possess extra assist units (such as the implementation of the CRT or Montgomery expo- nentiators to implement the associated arithmetic efficiently) or why they use other design tricks such as the precomputation of several powers of the modulus that accelerate calculations and keep them readily available in a lookup table. If a potential user wants to further scrutinize the internals of a security coprocessor, he or she may w