### Table 1. Computation amount of addition and doubling

"... In PAGE 5: ... Generalizing slightly the notation used above, let us denote by t(C1 + C2 = C3) the time for addition of points in coordinates C1 and C2 giving a result in coordinates C3, and by t(2C1 = C2) the time for doubling a point in coordinates C1 giving a result in coordinates C2. Table1 gives the computation times for additions and doublings in various coordinates (not all possible combinations are given, only the most... In PAGE 6: ... On the other hand, the ratio I=M deeply depends on the eld of de nition and on the implementation: it can be estimated to be between 9M and 30M in the case of p larger than 100 bits. From Table1 , we see that for a doubling using a xed coordinate system, J m is the best choice. On the other hand, for an addition using a xed coordi- nate system, we cannot decide what is the best coordinate system independently of the relative speed of inversion: it will usually be J c, unless I=M lt; 10:6, in... In PAGE 7: ... In this case, we must also consider the computation time necessary for constructing the table of precomputed points, which requires addition routines. For those, Table1 says that t(J c + J c) lt; t(A + A) () 9M + 2S lt; I; (12) where t(J c + J c) is the fastest of all addition routines with no inversions and a xed coordinate system. From equation (12), the optimal coordinate system depends on the relative speed of inversion.... In PAGE 8: ... For C2, we search for the coordinate system such that t(2J m = C2) + t(C2 + A = J m) is as small as possible. From Table1 , we see that both J c and J are suitable choices for C2. Thus, we choose the simplest system J .... In PAGE 9: ... For C2, we search for the coordinate system such that t(2J m = C2) + t(C2 + J c = J m) is as small as possible. From Table1 , we see that both J c and J are suitable choices for C2. Thus, we choose the simplest system J .... ..."

### Table 1. Computation amount of addition and doubling

"... In PAGE 5: ... Generalizing slightly the notation used above, let us denote by t(C1 + C2 = C3) the time for addition of points in coordinates C1 and C2 giving a result in coordinates C3, and by t(2C1 = C2) the time for doubling a point in coordinates C1 giving a result in coordinates C2. Table1 gives the computation times for additions and doublings in various coordinates (not all possible combinations are given, only the most... In PAGE 6: ... On the other hand, the ratio I=M deeply depends on the eld of de nition and on the implementation: it can be estimated to be between 9M and 30M in the case of p larger than 100 bits. From Table1 , we see that for a doubling using a xed coordinate system, J m is the best choice. On the other hand, for an addition using a xed coordi- nate system, we cannot decide what is the best coordinate system independently of the relative speed of inversion: it will usually be J c, unless I=M lt; 10:6, in... In PAGE 7: ... In this case, we must also consider the computation time necessary for constructing the table of precomputed points, which requires addition routines. For those, Table1 says that t(J c + J c) lt; t(A + A) () 9M + 2S lt; I; (12) where t(J c + J c) is the fastest of all addition routines with no inversions and a xed coordinate system. From equation (12), the optimal coordinate system depends on the relative speed of inversion.... In PAGE 8: ... For C2, we search for the coordinate system such that t(2J m = C2) + t(C2 + A = J m) is as small as possible. From Table1 , we see that both J c and J are suitable choices for C2. Thus, we choose the simplest system J .... In PAGE 9: ... For C2, we search for the coordinate system such that t(2J m = C2) + t(C2 + J c = J m) is as small as possible. From Table1 , we see that both J c and J are suitable choices for C2. Thus, we choose the simplest system J .... ..."

### Table 4 PT: additional amount of penalized traffic for CUFA compared to CSFA, expressed in units of 1000 kb

### Table 5 DT: additional amount of delayed traffic for CUFA compared to CSFA, expressed as a percentage of the aggregate traffic load High Aggregate

"... In PAGE 19: ... In the experiment, the DT for a given problem instance is computed from an optimal solution to CSFA and CUFA that is returned by the optimization solver. Table5 shows that the average DT ranges from -0.... ..."

### Table 2 Amount of Elemental Operations for Point Addition in Binary Field in Different Coordinates

### Table 3 Amount of Elemental Operations for Point Addition in Prime Field in Different Coordinates Point doubling General addition Mixed coordinate

### Table 1 displays the actual memory requirements for the three models. On average, the amount of additional memory required per camera is 10.5% of the memory requirements for the static portions of the mesh.

"... In PAGE 6: ...5% of the memory requirements for the static portions of the mesh. Table1 : Memory requirements for each model Grand Canyon Three Lakes Cliff Static structures 44n +12p +32d + 2se 9,297,526 bytes 6,284,962 bytes 8,261,168 bytes Memory required per camera 4n +4p +16 1,016,184 bytes 643,064 bytes 861,088 bytes The number of active polygons and active nodes is determined at run time and varies as the user moves ... ..."

### Table 3.5 NLEQ1 for problem SST Pollution: band mode vs. full mode band mode option is obvious but not surprising. Note that the internal band mode variant for the numerical di erentiation (just 9 evaluations of F in order to generate the Jacobian) works quite e cient, as the overall computing time is just increased by 52% by switching on this option whereas, in the full mode case, the additional amount of work turns out to be 137%.

1991

Cited by 19