### Table 6-14: The raw data of performance in composite Galois field on smartcard

in Contents

"... In PAGE 13: ...able 5-1: The best composition of each n.......................................................................... 41 Table6 -1: Timing of decryption in different optimization on PC.... In PAGE 13: ...able 6-1: Timing of decryption in different optimization on PC....................................... 43 Table6 -2: Raw Data of Performance in basic implementation on PC.... In PAGE 13: ...able 6-2: Raw Data of Performance in basic implementation on PC................................ 45 Table6 -3: Performance of each operator on PC.... In PAGE 13: ...able 6-3: Performance of each operator on PC.................................................................. 45 Table6 -4: Percentage of each operator on PC .... In PAGE 13: ...able 6-4: Percentage of each operator on PC .................................................................... 46 Table6 -5: Final Performance in single finite field on PC.... In PAGE 13: ...able 6-5: Final Performance in single finite field on PC................................................... 46 Table6 -6: Timing of each operator under different composition.... In PAGE 13: ...able 6-6: Timing of each operator under different composition........................................ 47 Table6 -7: Raw data of performance in composite Galois field.... In PAGE 13: ...able 6-7: Raw data of performance in composite Galois field.......................................... 48 Table6 -8: Timing of each operator in composite Galois field.... In PAGE 13: ...able 6-8: Timing of each operator in composite Galois field............................................ 48 Table6 -9: Compare PMI+ with RSA on PC .... In PAGE 13: ...able 6-9: Compare PMI+ with RSA on PC ....................................................................... 49 Table6 -10: The enhanced performance after group level multiplication.... In PAGE 13: ...able 6-10: The enhanced performance after group level multiplication............................ 50 Table6 -11: The raw data of performance in single Galois field on smartcard .... In PAGE 13: ...able 6-11: The raw data of performance in single Galois field on smartcard ................... 50 Table6 -12: The timing of each operator in single Galois field on smartcard .... In PAGE 13: ...able 6-12: The timing of each operator in single Galois field on smartcard ..................... 51 Table6 -13: The final performance in single Galois field on smartcard.... In PAGE 13: ...able 6-13: The final performance in single Galois field on smartcard.............................. 51 Table6 -14: The raw data of performance in composite Galois field on smartcard .... In PAGE 13: ...able 6-14: The raw data of performance in composite Galois field on smartcard ............ 52 Table6 -15: The timing of each operator in composite Galois field on smartcard .... In PAGE 13: ...able 6-15: The timing of each operator in composite Galois field on smartcard .............. 52 Table6 -16: The final performance in composite Galois field on smartcard .... In PAGE 57: ...6 16.6 Lookup table size 800B 968B 1152B 1352B 1568B 1800B Table6 -1: Timing of decryption in different optimization on PC ... In PAGE 59: ...78 / 4715446 13.36 / 288925038 0 0 0 81s Table6 -2: Raw Data of Performance in basic implementation on PC We calculated the time per operator and make addition as the standard to normalize the time. We implemented multiplication by the bit-level multiplication .... In PAGE 59: ...12.7 1 65.3 58.6 785.5 Table6 -3: Performance of each operator on PC ... In PAGE 60: ...6 46.2% 0.2% 19.3% 11% 21.1% 2.2% Table6 -4: Percentage of each operator on PC Here is the timing of each operator in each size of block. Block Size 80bit 88 bit 96 bit 104 bit 112 bit Complexity Key Generation (ms) 42 54 81 111 150 O(n4) Encryption (ms) 0.... In PAGE 60: ...3 4.8 O(n2) Public key size (KB) 33 44 57 40 45 O(n3) Table6 -5: Final Performance in single finite field on PC ... In PAGE 61: ...874 9.773 Table6 -6: Timing of each operator under different composition The experimental result is close to our inference before. Obviously, the former factoring of 96 is better than the latter.... In PAGE 62: ...3 / 7040000 1.98 / 3840000 22s Table6 -7: Raw data of performance in composite Galois field Comparing Table 6.4 and Table 6.... In PAGE 62: ...85 10.75 Table6 -8: Timing of each operator in composite Galois field 6.... In PAGE 62: ....1.5. Comparison We see first three columns in Table6 -9 are the cryptosystems with the same security strength. Though the first column and second column are PMI+ cryptosystems, the second one implemented in composite field is much faster than traditional ... In PAGE 63: ....8 2.0 20.4 11.6 2.2 86.99 Security ECC-160 ECC-160 ECC-160 ECC-224 ECC-224 ECC-224 Table6 -9: Compare PMI+ with RSA on PC 6.2.... In PAGE 63: ... Here we set g=8, the look-up table size is n bytes. In Table6 -10, we see that Group level multiplication reduce 20% time of Bit level multiplication . ... In PAGE 64: ...0.19% 22.5% 20.98% data (bytes) 79 81 84 86 89 91 xdata (bytes) 84 164 85 173 86 182 code (bytes) 2902 3173 2921 3182 2912 3183 Table6 -10: The enhanced performance after group level multiplication 6.... In PAGE 64: ...71s / 8960 5.4s / 3840 6s / 3840 Total time 1020s 1230s 1378 342s 438s 491s 54s 70s 80s Table6 -11: The raw data of performance in single Galois field on smartcard ... In PAGE 65: ...48.5 1 51.7 36.4 Table6 -12: The timing of each operator in single Galois field on smartcard Chip Intel8052AH 3.57MHZ Intel8052AH 10MHZ Dollars-DS80C32 0 33MHZ block size 80 88 96 80 88 96 80 88 96 data size (bytes) 89 99 101 89 99 101 93 99 108 xdata size (bytes) 164 173 182 164 173 182 161 178 180 code size (bytes) 3.... In PAGE 65: ...4 43 49 5.4 7.0 8.0 Table6 -13: The final performance in single Galois field on smartcard ... In PAGE 66: ...08 5.73 Table6... In PAGE 67: ...34s 0.75s Table6 -16: The final performance in composite Galois field on smartcard ... ..."

### Table 2: Highest block order for some non-prime Galois fields, with a 64 bits mantissa GF

"... In PAGE 6: ... Nonetheless, on a 64-bits architecture (DEC alpha for in- stance) where machine integers have 8 bytes, this can be applied to even more cases. Table2 , in appendix B, shows that about a factor of 10 can be gained for the maximum matrix size, when compared to 53-bits mantissas. Also the biggest implementable fields are now GF(29), GF(37), GF(55), GF(114), GF(473) and GF(11292).... ..."

### Table 4.1. Device utilization summary of Galois Field Arithmetic Units

1992

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### Table 5.1. The field with the minimal Galois root discriminant dG for some small groups G.

2003

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### Table 5.1. The field with the minimal Galois root discriminant dG for some small groups G.

2003

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### Table 2. There are no central rays. Any arbitrary solution of the set of multivariate polynomial equalities and inequalities can now be expressed as

"... In PAGE 15: ...2. s X inf s X n s 1 fxi 1; xi 2g fxf 1g 2 fxi 1g fxf 1; xf 3g 3 fxi 2g fxf 1; xf 3g 4 fg fxf 2; xf 4; xf 5g 5 fg fxf 2; xf 4; xf 6g 6 fg fxf 2; xf 5; xf 6g Table2... ..."

### Table 4: Some measurement hypotheses in the construction of multivariate deprivation indexes

2000

### Table 1: The throughput of GHASH using various different methods for the Galois field multipli- cation on a Motorola G4 processor.

"... In PAGE 14: ... Storage requirements can be reduced further by using a decomposition into four-bit elements, so that M0 and R consume 256 bytes and 64 bytes, respectively. The performance of these methods is outlined in Table1 , which gives the throughput for a C implementation of GHASH using the strategies discussed above on a Motorola G4 processor (a 32- bit RISC CPU). These times should be compared to that of the OpenSSL [10] optimized C version of AES, which ran at 33.... ..."

### Table 1: The throughput of GHASH using various different methods for the Galois field multipli- cation on a Motorola G4 processor.

2005

"... In PAGE 14: ... Storage requirements can be reduced further by using a decomposition into four-bit elements, so that M0 and R consume 256 bytes and 64 bytes, respectively. The performance of these methods is outlined in Table1 , which gives the throughput for a C implementation of GHASH using the strategies discussed above on a Motorola G4 processor (a 32-... ..."

### Table 2. The Number of Quadratic Coset Leaders for Construction (1) when t = 3

2001

"... In PAGE 7: ...f the polynomial, i.e. for L = 2, where is xed as the identity permutation. p(x) = x0x3 + x1x4 + x2x5 + g(x) p(x) = x0x3 + x0x5 + x1x4 + x2x5 + g(x) p(x) = x0x3 + x0x5 + x1x4 + x1x5 + x2x5 + g(x) p(x) = x0x3 + x0x4 + x0x5 + x1x4 + x2x5 + g(x) p(x) = x0x3 + x0x4 + x1x4 + x1x5 + x2x5 + g(x) p(x) = x0x3 + x0x4 + x0x5 + x1x4 + x1x5 + x2x5 + g(x) p(x) = x0x3 + x0x5 + x1x3 + x1x4 + x2x3 + x2x4 + x2x5 + g(x) where g(x) = c0x0x1 +c1x0x2 +c2x1x2 +c3x0x1x2 +c4x3x4 +c5x3x5 +c6x4x5 + c7x3x4x5 + RM(1; 6), and c0; c1; : : : ; c7 2 Z2. An upper bound to jP j can be computed from Theorem 2, (2), and the upper bound is compared to the to- tal number of quadratics in n binary variables in Table2 . As with t = 2, an Table 2.... ..."

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