### Table 2. Comparison of acceleration techniques assuming that 8-bit -processor and 9600bps communication link is used. Communication overhehad is presented in bytes, and computaion time in seconds. `#MM apos; means the number of modular multiplications, and `F.A. apos; means the factor of acceleration. protocol used comp. comm. time F.A. technique #MM time F.A. byte time (sec.)

2001

"... In PAGE 9: ... We compare the accel- erations of the proposed techniques with those of the original key establishment protocols to which they are applied. The performance comparison is presented in Table2 . We let the size of modu- lus p and n be 512-bits, and assume that ElGamal algorithm and Di e-Hellman protocol use 160-bits exponents.... In PAGE 9: ... Those of splitting-based techniques are lt;h=11,m =29 gt; for the RSA and lt;b=16,m =40 gt; for the ElGamal. The proposed techniques accelerate the previous key establishment protocols by more than ve times at maximum, as we can see Table2 . The factor of acceleration is quite di erent from one another according to the used SASC protocol.... In PAGE 9: ...ap be even larger. The overall performance gain is presented in apos;F.A. apos; eld of Table2 , including the amount of communication overhead and the expected execution time. 5 Conclusion RSA signature generation and decryption require full modular exponentiations (i.... ..."

Cited by 1

### Table 1: Main notations in the paper. Consider an array X[0:::M ? 1] of size M that is distributed according to the block cyclic distribution CYCLIC(r) onto a linear grid of P processors (numbered from p = 0 to p = P ? 1). Our goal is to redistribute X into an array Y distributed according to the block-cyclic distribution CYCLIC(s) onto Q processors (numbered from q = 0 to q = Q ? 1). For simplicity, we assume that the size M of X is a multiple of L = lcm(Pr; Qs), the least common multiple of Pr and Qs: this is because the redistribution pattern repeats after each slice of L elements. Therefore, assuming an even number of slices in X will enable us (without loss of generality) to avoid discussing side e ects. Let m = M L be the number of slices. De nition 1 We let (P; r) ! (Q; s) denote the redistribution problem from an original grid of P processors with distribution CYCLIC(r) to a target grid of Q processors with distribution CYCLIC(s), and assuming a single-slice vector of length L = lcm(Pr; Qs) to be redistributed. Any indicated 2

"... In PAGE 4: ... The construction of our optimal schedules relies on graph-theoretic algorithms, and modular algebra techniques. Notations The main variables used in the next sections are listed in Table1 .... ..."

### Table 7 Plug-in based software development summary Approach/technique Plug-in based software development Pros Plug-ins provide a model for modularization and application footprint control; they imple- ment third-party extensions to software, plug-in runtime provides dynamic load and upgrade capabilities.

2005

"... In PAGE 6: ...able 6 Meta-level programming summary ................................................................................................. 38 Table7 Open implementation summary.... ..."

### Table 3: Modularity

2007

"... In PAGE 4: ... A modularity of 0 means that there is no natural way to subdivide the network into groups, and a high modularity means that one can easily subdivide the network (maximum modularity is 1). As is shown in Table3 , for all three blog networks, we find relatively high modularity, but it is highest for DFW, which is the sparsest and most easily broken up network. In contrast, Kuwait and UAE, while displaying a degree of local interaction between subgroups of blogs, have a tighter cohesion ... ..."

Cited by 5

### Table 2: Modular restrictions

2001

"... In PAGE 2: ... For example, if p = 2, then we need only check values of n which are zero or one modulo 9. Similarly, since (9) = 6 the modulo 6 character of p will tell us precisely which values of n can satisfy np n (mod 9) as in Table2 and hence possibly be pseudopowerful. Using Theorem 2 one can eliminate about 61% of the integers in the range n 2 [2; : : : ; 9r1] with the resultant cutdown in search time.... In PAGE 3: ... Do there exist in nitely many such exponents? Probably not! Since the number of possibilities increases with each p. Next, if we consider the number of modular solutions in Table2 , we ask if it is possible that minf (p) : p 1 (mod 6)g maxf (p) : p 6 1 (mod 6)g. Despite the fact that it holds for all of Table 4 it does not hold in general, since (55) = 2 while (54) = 5.... ..."

### Table 1 Modular Properties

"... In PAGE 3: ... So, the final list of quality parameters for CM tool architectural design comparison is: Flexibility, testability, portability, availability, simplicity, traceability for correctness and communication, and interoperability 10. Based on Table1 , entries for every architecture, for each of their components, an assessment of the five parameters degree of cohesion, coupling, fan-out, complexity and module size is done, and corresponding ratings, like, M1, M2, M3, MF1 and MF2 are determined with the help of Table 1. Number of components = n; For each component compute following: CMPX_n = MF1*MF2 ; SMP_n =1-CMPX_n; MOD_n = M1*M2*M3 ; COM_n = Sqrt(MOD_n*(10-CMPX_n) ; Here, M1,M2,M3, MF1 and MF2 referrers to a particular component.... In PAGE 3: ... So, the final list of quality parameters for CM tool architectural design comparison is: Flexibility, testability, portability, availability, simplicity, traceability for correctness and communication, and interoperability 10. Based on Table 1, entries for every architecture, for each of their components, an assessment of the five parameters degree of cohesion, coupling, fan-out, complexity and module size is done, and corresponding ratings, like, M1, M2, M3, MF1 and MF2 are determined with the help of Table1 . Number of components = n; For each component compute following: CMPX_n = MF1*MF2 ; SMP_n =1-CMPX_n; MOD_n = M1*M2*M3 ; COM_n = Sqrt(MOD_n*(10-CMPX_n) ; Here, M1,M2,M3, MF1 and MF2 referrers to a particular component.... ..."

### Table 28 Design dimensions for the Modular Event System Modular Event System

2005

"... In PAGE 6: ...able 27 Design dimensions for TSpaces .................................................................................................... 59 Table28 Design dimensions for the Modular Event System .... ..."

### Table 1. Modularity scores comparison

"... In PAGE 8: ... When we compared the modularity scores, we once again found the PCA-based methods outperforming MCODE and MCL. The modularity scores are given in Table1 . As we mentioned earlier, MCL produced a large number of clusters and most of the proteins in the clusters were sparsely connected.... ..."

### Table 2: The number of modular exponentiations.

"... In PAGE 11: ...that the actual numbers of modular exponentiations in the group signature-based scheme are larger than those shown in Table2 . The numbers in the proposed scheme are actual.... ..."