### Table 1: Efficiency comparison for ElGamal variants in terms of ciphertext size, where |g|, |mac|, and |M| are sizes for a group element, an authentication tag, and a plaintext, respectively. For concreteness, one can think of |mac| = 128. DBDH and square-DBDH means the decisional bilinear Diffie-Hellman assumption [14] and the decisional square bilinear Diffie-Hellman assumption [32], respectively. ciphertext size assumption security bilinear group

2006

"... In PAGE 15: ... This method does not require any additional assumption. 5 Comparison Here, we discuss comparison among ElGamal variants in terms of ciphertext size, and it is summarized in Table1 . So far, under the DDH assumption the Kurosawa-Desmedt scheme [33] is considered as the most efficient scheme, and its ciphertext overhead is two group elements and an authentication tag.... ..."

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### Table 1: Strati cation of CP2 space under the action of the image of Td ^ T groups in the representation span by bilinear combinations of coordinates and conjugated momenta for triply degenerate vibrational representations of point symmetry group Td. Only zero dimensional strata are given.

"... In PAGE 4: ... They are all listed in Tables 1-3. There are ve zero-dimensional strata ( Table1 ), ve one-dimensional (Table 2), and ve two-dimensional ones (Table 3). The simplest Morse type functions [4,5,10] can be constructed on the CP2 space with all stationary points situated on critical orbits only.... ..."

### Table 2: Strati cation of CP2 space under the action of the image of Td ^ T groups in the representation span by bilinear combinations of coordinates and conjugated momenta for triply degenerate vibrational representations of point symmetry group Td. Only one- dimensional strata are given.

### Table 3: The strati cation of CP2 space under the action of the image of Td ^ T group in the representation span by bilinear combinations of coordinates and conjugated momenta for triply degenerate vibrational representations of point symmetry group Td. Only two- dimensional invariant subspaces are given.

### TABLES TABLE I. The table lists the set of scalar multiplets that can couple to the standard model fermions, as well as their quantum numbers under the gauge groups. The fermion bilinears to which the scalars may couple are also shown with the corresponding Yukawa couplings . In the table all generation indices are suppressed. Scalars SU(3) SU(2) Y Fermion bilinears

### TABLE XIII AVERAGE BILINEAR SAMPLES AND ALU TO BILINEAR RATIO

### Table 1: Interpolation Filters: Optimal and Bilinear

"... In PAGE 4: ...Table 1: Interpolation Filters: Optimal and Bilinear and the aliasing error AE = jjH(?z)G(z)X(?z)jj2; introduced by the sampling process, where X(z) is the Z-transform of a step signal. Optimal interpolation lters G(z) can be found in this way for di erent lter lengths n, and they are given in Table1 (a) for DF=2, along with two PSNR values: PSNR1 corresponds to the PSNR obtained with a step signal, while PSNR2 corresponds to the PSNR obtained when applying steps 1 and 4 in the horizontal direction to a real image (Figure 4). Note that little PSNR improvement results from examining lters longer than n = 6.... In PAGE 4: ... Note that little PSNR improvement results from examining lters longer than n = 6. Table1 (a) also contains the PSNR performance of the bilinear interpolation lter. Its PSNR performance is about 1 dB below that of the best optimal lters.... In PAGE 5: ...the one corresponding to a PSNR improvement over no pixel averaging. As a consequence, for all values of the DF used in the following experiments, we will consider only bilinear interpolation lters, coe cients of which are given in Table1 (b). 2 3 4 5 6 7 15 20 25 30 35 Log2(Compression Ratio) Peak-Signal-to-Noise Ratio (PSNR in dB) * : H1V1 + : H2V1 + BILIN --: H2V1 + (n=6) Figure 2: MSE (PSNR) Performance Comparison between Bilinear and Optimal Interpola- tion Filters combined with Lossy JPEG 3 Image Description and Compression Assessment The lander is in the shape of a tetrahedron.... ..."

### Table 2. Comparison of several bilinear pairing algorithms

2006

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