### Table 1: Bias of approximations for the E-function

"... In PAGE 4: ...about 2?57. For the analysis below, we use the following estimates for the bias of the di erent approximations of the E-function (see Table1 ). These estimates represent a modi cation of Table 7 from [1], to... ..."

### Table 7: Bias of approximations for the E-function

1998

"... In PAGE 36: ... The other approximations of the E-function can be analyzed similarly to these two examples. In Table7 we list the approxi- mations of the E-function by the subset of the values fI; L; M; Rg which they include. With each... In PAGE 39: ...IBM submission to AES 38 To devise a bound, we identify with each approximation a valid set of edges, and then consider the edges incident to the E-functions in this set and use Table7 to bound the bias of this approxima- tion. In particular, we consider the edges L and M of the E-functions in the graph (these edges correspond to approximations of the combination of rotation followed by addition).... In PAGE 39: ... A search of the graph structure of the keyed transformation verifies that in this case S must contain at least three rotation edges in every super-round, and that at least one of these rotation edges must be an L edge. From Table7 we see that every occurrence of an M edge has bias at most 2?6 and every occurrence of an L edge has bias at most 2?8. Using the Piling-up lemma, the bias of approximating one super-round is at most 2?18 and the bias of approximating the keyed transformation is at most 2?69.... In PAGE 39: ... There are E-function for which S contains a single edge. From Table7 it follows that the corresponding local approximations must be of the form (6) or (5), which have bias of only 2?15 or 2?20, respectively. Moreover, a search of the graph structure of the keyed transfor- mation verifies each E-function like this only saves at most one occurrence of a rotation edge, hence the resulting bias is even smaller than 2?69.... ..."

Cited by 32

### Table 7: Bias of approximations for the E-function

1998

"... In PAGE 36: ... The other approximations of the E-function can be analyzed similarly to these two examples. In Table7 we list the approxi- mations of the E-function by the subset of the values fI; L; M; Rg which they include. With each... In PAGE 39: ...IBM submission to AES 38 To devise a bound, we identify with each approximation a valid set of edges, and then consider the edges incident to the E-functions in this set and use Table7 to bound the bias of this approxima- tion. In particular, we consider the edges L and M of the E-functions in the graph (these edges correspond to approximations of the combination of rotation followed by addition).... In PAGE 39: ... A search of the graph structure of the keyed transformation verifies that in this case S must contain at least three rotation edges in every super-round, and that at least one of these rotation edges must be an L edge. From Table7 we see that every occurrence of an M edge has bias at most 2 ,6 and every occurrence of an L edge has bias at most 2 ,8 . Using the Piling-up lemma, the bias of approximating one super-round is at most 2 ,18 and the bias of approximating the keyed transformation is at most 2 ,69 .... In PAGE 39: ... There are E-function for which S contains a single edge. From Table7 it follows that the corresponding local approximations must be of the form (6) or (5), which have bias of only 2 ,15 or 2 ,20 , respectively. Moreover, a search of the graph structure of the keyed transfor- mation verifies each E-function like this only saves at most one occurrence of a rotation edge, hence the resulting bias is even smaller than 2 ,69 .... ..."

Cited by 32

### Table 7: Bias of approximations for the E-function

1998

"... In PAGE 36: ... The other approximations of the E-function can be analyzed similarly to these two examples. In Table7 we list the approxi- mations of the E-function by the subset of the values fI; L; M; Rg which they include. With each... In PAGE 39: ...IBM submission to AES 38 To devise a bound, we identify with each approximation a valid set of edges, and then consider the edges incident to the E-functions in this set and use Table7 to bound the bias of this approxima- tion. In particular, we consider the edges L and M of the E-functions in the graph (these edges correspond to approximations of the combination of rotation followed by addition).... In PAGE 39: ... A search of the graph structure of the keyed transformation verifies that in this case S must contain at least three rotation edges in every super-round, and that at least one of these rotation edges must be an L edge. From Table7 we see that every occurrence of an M edge has bias at most 2 ,6 and every occurrence of an L edge has bias at most 2 ,8 . Using the Piling-up lemma, the bias of approximating one super-round is at most 2 ,18 and the bias of approximating the keyed transformation is at most 2 ,69 .... In PAGE 39: ... There are E-function for which S contains a single edge. From Table7 it follows that the corresponding local approximations must be of the form (6) or (5), which have bias of only 2 ,15 or 2 ,20 , respectively. Moreover, a search of the graph structure of the keyed transfor- mation verifies each E-function like this only saves at most one occurrence of a rotation edge, hence the resulting bias is even smaller than 2 ,69 .... ..."

Cited by 32

### Table 1: Bias of approximations for the E-function

"... In PAGE 5: ...,61 to about 2 ,57 . For the analysis below, we use the following estimates for the bias of the di#0Berent approximations of the E-function #28see Table1 #29. These estimates represent a modi#0Ccation of Table 7 from #5B1#5D, to... ..."

### Table I. HBSS Preliminary Results: A sampling of the results from applying HBSS with various bias functions and 100 iterations. This is a snapshot of the data that was used to choose a bias function for the HBSS algorithm for further experiments.

2005

Cited by 4

### Table II. VBSS Preliminary Results: A sampling of the results from applying VBSS with various bias functions and 100 iterations. This is a snapshot of the data that was used to choose a bias function for the VBSS algorithm for further experiments.

2005

Cited by 4

### Table 5. CPI bias achieved with functional warming and minimal detailed warming.

2003

"... In PAGE 8: ....5. Effectiveness of functional warming Even with both functional and detailed warming, some inaccuracies in microarchitectural state remain and contribute to errors in the estimates as bias. Table5 reports the residual bias in the CPI estimated by SMARTSim when functional warming is employed in conjunction with Table 4. Detailed warming requirements without functional warming.... ..."

Cited by 113

### Table 5. CPI bias achieved with functional warming and minimal detailed warming.

2003

"... In PAGE 8: ....5. Effectiveness of functional warming Even with both functional and detailed warming, some inaccuracies in microarchitectural state remain and contribute to errors in the estimates as bias. Table5 reports the residual bias in the CPI estimated by SMARTSim when functional warming is employed in conjunction with Table 4. Detailed warming requirements without functional warming.... ..."

Cited by 113

### Table 5. CPI bias achieved with functional warming and minimal detailed warming.

"... In PAGE 8: ....5. Effectiveness of functional warming Even with both functional and detailed warming, some inaccuracies in microarchitectural state remain and contribute to errors in the estimates as bias. Table5 reports the residual bias in the CPI estimated by SMARTSim when functional warming is employed in conjunction with Table 4. Detailed warming requirements without functional warming.... ..."