### TABLE VII NUMERICAL VALUES RELATED TO THE MINIMIZED DURATION Tn OF THE BATCH CONFLICT WITH A PRIORI KNOWN MULTIPLICITY n

2004

### Table 10. Timings (in s) of the fastest methods for point multiplications kP + lQ, P xed and Q not known a priori, in ECDSA signature veri cation.

2001

"... In PAGE 17: ... For each type of curve, two cases are distinguished|when there is no extra memory available and when memory is not heavily constrained. Table10 does the same for computing kP +lQ where P is xed and Q is not known a priori. We should note that no special e ort was expended in optimizing our eld arithmetic over the larger elds Fp384, Fp521, F2409 and F2571|the optimization techniques used for these elds were restricted to those employed in the smaller elds.... ..."

Cited by 33

### Table 11. Timings (in s) of the fastest methods for point multiplication kP, P xed, and for kP + lQ, P xed and Q not known a priori on the P-192 curve.

2001

"... In PAGE 17: ... We should note that no special e ort was expended in optimizing our eld arithmetic over the larger elds Fp384, Fp521, F2409 and F2571|the optimization techniques used for these elds were restricted to those employed in the smaller elds. Table11 presents timings for these operations for the P-192 curve when the eld arithmetic is implemented primarily in assembly, when Barrett reduction... In PAGE 19: ...8% Modular inversion (Algorithm 12) 1 0.9% 7 Conclusions Signi cant performance improvements are obtained when using Jacobian and Chudnovsky coordinates, primarily due to the high inversion to multiplication 2 Since Barrett reduction does not exploit the special nature of the NIST primes, the Barrett column of Table11 can be interpreted as rough timings for ECDSA operations over a random 192-bit prime.... ..."

Cited by 33

### Table 3. Total time, CPU time, and statistical measures for individual non-random (dual) problem instances. The size of the output, m, is known a priori. Each row corresponds to individual runs. Total Time is the number of calls of procedure add next hyperedge for the generation of all transversals.

"... In PAGE 12: ... This also serves as a test of the correctness of the algorithm as already explained. The results are summarized in Table3 . Notice that the size of the input is now de ned by the number of nodes, n, and the number of transversals, while the number of edges, m, is now the size of the output.... ..."

### Table 3. Our Results as a Percent Over Best Known Solutions.

"... In PAGE 12: ... Asterisks denote best known solution values, that is, equal to or better than the best previously published solution. Solutions reported without asterisks are greater than the best previously published solutions, as is more fully detailed in Table3 . Problems are denoted by first the number of objects, then the number of sites, and then the distance measure (rectilinear (R) or Euclidean (E)).... In PAGE 15: ... This is possible for all of our problems with the exception of the 25 object/site Euclidean problem which we devised and for which we assumed (incorrectly) the pre-formulated solution to be the optimum. Table3 shows our best found solution over the 10 runs of each problem as a percent above the best known solution. To show... In PAGE 15: ... Table 3 shows our best found solution over the 10 runs of each problem as a percent above the best known solution. To show the reliability of our approach, Table3... ..."

### Table 2. We need 16 counter over ows to cover all possible password lengths modulo 16. In this case, the average search is reduced by a factor of 220 compared to key space . If in addition the password length is known a priori, the barrel shifter is not required and the average search can be reduced by another factor of 24. Table 3 summarizes the number of DES operations and absolute timings required to break a Diskreet cipher with COPACOBANA.

"... In PAGE 12: ...niquely determines which byte of a key matches which pattern, i.e., for a particular password length mod 16, there is exactly one key pattern. Table2 shows the 16 possible key patterns. Since the least signi cant bit of each key byte is a parity bit, contains in total 16 232 = 236 DES-keys.... In PAGE 13: ...DES key pattern (64 = 8 8 bit) mod 16 0 000xxxxx 000xxxxx 000xxxxx 000xxxxx 000xxxxx 000xxxxx 000xxxxx 000xxxxx 1 010xxxxx 000xxxxx 000xxxxx 000xxxxx 000xxxxx 000xxxxx 000xxxxx 000xxxxx 2 010xxxxx 010xxxxx 000xxxxx 000xxxxx 000xxxxx 000xxxxx 000xxxxx 000xxxxx 3 010xxxxx 010xxxxx 010xxxxx 000xxxxx 000xxxxx 000xxxxx 000xxxxx 000xxxxx 4 010xxxxx 010xxxxx 010xxxxx 010xxxxx 000xxxxx 000xxxxx 000xxxxx 000xxxxx 5 010xxxxx 010xxxxx 010xxxxx 010xxxxx 010xxxxx 000xxxxx 000xxxxx 000xxxxx 6 010xxxxx 010xxxxx 010xxxxx 010xxxxx 010xxxxx 010xxxxx 000xxxxx 000xxxxx 7 010xxxxx 010xxxxx 010xxxxx 010xxxxx 010xxxxx 010xxxxx 010xxxxx 000xxxxx 8 010xxxxx 010xxxxx 010xxxxx 010xxxxx 010xxxxx 010xxxxx 010xxxxx 010xxxxx 9 000xxxxx 010xxxxx 010xxxxx 010xxxxx 010xxxxx 010xxxxx 010xxxxx 010xxxxx 10 000xxxxx 000xxxxx 010xxxxx 010xxxxx 010xxxxx 010xxxxx 010xxxxx 010xxxxx 11 000xxxxx 000xxxxx 000xxxxx 010xxxxx 010xxxxx 010xxxxx 010xxxxx 010xxxxx 12 000xxxxx 000xxxxx 000xxxxx 000xxxxx 010xxxxx 010xxxxx 010xxxxx 010xxxxx 13 000xxxxx 000xxxxx 000xxxxx 000xxxxx 000xxxxx 010xxxxx 010xxxxx 010xxxxx 14 000xxxxx 000xxxxx 000xxxxx 000xxxxx 000xxxxx 000xxxxx 010xxxxx 010xxxxx 15 000xxxxx 000xxxxx 000xxxxx 000xxxxx 000xxxxx 000xxxxx 000xxxxx 010xxxxx Table2 : DES key patterns depending on password length modulo 16 for key space Key space : If we consider passwords consisting of arbitrary 8-bit ASCII characters then we obtain the whole DES-key space which contains 256 di erent keys. We denote this key space by .... In PAGE 14: ... For the key space , the xed part of the key can be hard-wired and the counter can be reduced to 30 bit. In order to cover all possible key patterns (see Table2 ) we can, e.g.... ..."

Cited by 1

### Table 2 describes several general model composition constraints. Not all domains need every constraint available in the library. For example, a simple process control modeling language may not require hierarchical behavior. For this reason, when creating domain-specific modeling languages, concepts specific to the domain must be known a priori and must be used to guide the selection of constraints from the library.

1999

"... In PAGE 11: ... Used to indicate object refinement. Table2 : General Model Composition Constraints Because of the general nature of the constraints listed in Table 2, they are family-specific (e.... In PAGE 11: ... Used to indicate object refinement. Table 2: General Model Composition Constraints Because of the general nature of the constraints listed in Table2 , they are family-specific (e.... ..."

Cited by 21

### Table 2: The a-priori probabilities for the node S of the network in Figure 1

### TABLE 6. A PRIORI STATISTICS ON ESTIMATED PARAMETERS

"... In PAGE 14: ...9 TABLE6 . A PRIORI STATISTICS ON ESTIMATED PARAMETERS (CONTINUED) Station Coordinates* a priori sigmas east north vertical 1.... ..."

### Table 1 An a priori fuzzy rule base

"... In PAGE 15: ...2 Fuzzy control using an a priori fuzzy model Because the rocket velocity will increase as the velocity of the exhaust gases increases, a rule base can be constructed a priori based only on logical consid- erations. Table1 shows this three-dimensional rule base as a sequence of two- dimensional tables, and for each of them variable C takes a different value. This rule base can be used as a starting point in the control/identification process, so that the modifications required in the learning process are applied over it.... ..."