Tham khảo tài liệu 'hacker professional ebook part 183', công nghệ thông tin, kỹ thuật lập trình phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | How fast is RSA An RSA operation whether for encrypting or decrypting signing or verifying is essentially a modular exponentiation which can be performed by a series of modular multiplications. In practical applications it is common to choose a small public exponent for the public key in fact entire groups of users can use the same public exponent. This makes encryption faster than decryption and verification faster than signing. Algorithmically public-key operations take O kA2 steps private key operations take O kA3 steps and key generation takes O kA4 steps where k is the number of bits in the modulus O-notation refers to the an upper bound on the asymptotic running time of an algorithm 22 . There are many commercially available hardware implementations of RSA and there are frequent announcements of newer and faster chips. The fastest current RSA chip 76 has a throughput greater than 600 Kbits per second with a 512-bit modulus implying that it performs over 1000 RSA private-key operations per second. It is expected that RSA speeds will reach 1 Mbit second within a year or so. By comparison DES is much faster than RSA. In software DES is generally at least 100 times as fast as RSA. In hardware DES is between 1 000 and 10 000 times as fast depending on the implementations. RSA will probably narrow the gap a bit in coming years as it finds growing commercial markets but will never match the performance of DES. How much extra message length is caused by using RSA Only a very small amount of data expansion is involved when using RSA. For encryption a message may be padded to a length that is a multiple of the block length usually 64 bits since RSA is usually combined with a secret-key block cipher such as DES see Question . Encrypting the DES key takes as many additional bits as the size of the RSA modulus. For authentication an RSA digital signature is appended to a document. An RSA signature including information such as the name of the signer is .
