Saving in computational cost Sample Clauses

Saving in computational cost. With the signature-then-encryption based on Xxxxxxx signature and ElGamal encryption, the number of modular exponentiations is three, both for the process of signature-then- encryption and that of decryption-then-veri cation. a Among the three modular exponentiations for decryption-then-veri cation, two are used in verifying Xxxxxxx signature. More speci cally, these two exponentiations are spent in computing gs yr mod p. Using a technique for fast computation of the product of multiple exponentials with the same modulo which has been attributed to Xxxxxx (see Appendix B), a gs yr mod p can be computed, on average, in (1 + 3=4)jqj modular multiplications. Since a modular exponentiation can be completed, on average, in about 1:5jqj modular multi- plications when using the classical \square-and-multiply" method, (1 + 3=4)jqj modular multiplications is computationally equivalent to 1.17 modular exponentiations. Thus with \square-and-multiply" and Xxxxxx's technique, the number of modular exponentiations in- volved in decryption-then-veri cation can be reduced from 3 to 2.17. The same reduction techniques, however, cannot be applied to the sender's computation. Consequently, the combined computational cost of the sender and the recipient is 5.17 modular exponentia- tions. In contrast, with SCS1 and SCS2, the number of modular exponentiations is one for the process of signcryption and two for that of unsigncryption respectively. Since Xxxxxx's technique can also be used in unsigncryption, the computational cost of unsigncryption is about 1.17 modular exponentiations. The total average computational cost for signcryption security parameters jpj jqj jKH ( )j saving average comp. cost saving in comm. overhead 512 144 72 58% 70.3% 768 152 80 58% 76.8% 1024 160 80 58% 81.0% 1280 168 88 58% 83.3% 1536 176 88 58% 85.3% 1792 184 96 58% 86.5% 2048 192 96 58% 87.7% 2560 208 104 58% 89.1% 3072 224 112 58% 90.1% 4096 256 128 58% 91.0% 5120 288 144 58% 92.0% 8192 320 160 58% 94.0% 10240 320 160 58% 96.0% jhash( )j+jqj+jpj

Saving in computational cost. With the signature-then-encryption based on SECDSS1 or SECDSS2 and elliptic curve ElGamal encryption, the number of computations of multiples of points is three, both for the process of signature-then-encryption and that of decryption-then-veri cation. Shortened schemes Signature (r; s) on a message m Veri cation of signature Length of signature ECDSS r = (vG) mod q s = hash(m)+var mod qv K = s0(hash(m)G + rPa) where s0 = 1 mod q, s check whether K mod q = r 2jqj SECDSS1 r = hash(vG; m) s = v mod q r+va K = s(Pa + rG) check whether hash(K; m) = r jhash( )j + jqj SECDSS2 r = hash(vG; m) s = v mod q 1+va r K = s(G + rPa) check whether hash(K; m) = r jhash( )j + jqj =