Advantage in computational cost Sample Clauses

Advantage in computational cost. With RSA, it is a common practice to employ a relatively small public exponent e for encryption or signature veri cation, although cautions should be taken in light of recent progress in cryptanalysis against RSA with an small exponent (see for example [17, 16]). Therefore the main computational cost is in decryption or signature generation which gen- erally involves a modular exponentiation with a full size exponent d, which takes on average 1:5` modular multiplications using the \square-and-multiply" method, where ` indicates the size of the RSA composite involved. With the help of the Chinese Remainder Theorem, the computational expense for RSA decryption can be reduced, theoretically, to a quarter of the expense with a full size exponent, although in practice it is more realistic to expect the factor to be between 1/4 and 1/3. To simplify our discussion, we assume that the max- imum speedup is achievable, namely the average computational cost for RSA decryption is 1:5 ` = 0:375` modular multiplications. For the signature-then-encryption based on RSA, four (4) modular exponentiations are required (two with public exponents and the other two with private exponents). Assuming small public exponents are employed, the computational cost will be dominated by the two modular exponentiations with full size private exponents. When the Chinese Remainder Theorem is used, this cost is on average 0:375(jnaj + jnbj) modular multiplications, where na and nb are the RSA composites generated by Xxxxx and Xxx respectively. As discussed earlier, the two signcryption schemes SCS1 and SCS2 both involve, on average, 2.17 modular exponentiations, or equivalently 3:25jqj modular multiplications, as- suming the \square-and-multiply" method and Xxxxxx's technique for fast computation of the product of exponentials are used. This shows that the signcryption schemes represent an advantage of 0:375(jnaj + jnbj) 3:25jqj 0:375(jnaj + jnbj) in average computational cost over the RSA based signature-then-encryption. For small security parameters, the advantage is less signi cant. This situation, however, changes dramatically for large security parameters: consider jnaj = jnbj = jpj = 1536 and jqj = 176 which are recommended to be used for long term (say more than 20 years) security, the signcryption schemes show a 50:3% saving in computation, when compared with the signature-then-encryption based on RSA. The advantage of the signcryption schemes in computational cost will be more visi...
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