Common use of Communication Costs Clause in Contracts

Communication Costs. For the communication costs, we determine the number of bits transmitted by both the SM and the SP. In all the considered schemes, the number of communication phases equals to three, except in [14], where there are four phases required. Note that we consider the 80-bit security level. Therefore, the length of the hash function and the nonces/random numbers equals to 160 bits. For the schemes of [9–11], the sizes of the groups G1 and G2, related to the pairing operation, are 320 and 512 bits, respectively. When sending an EC point, it is sufficient to send the x-coordinate together with a sign bit. In addition, we assume that the length of identity related information equals to 32 bits. The length of the PUF responses equals to 128 bits. As can be concluded from Table 4, our scheme, together with [12], requires the smallest number of transmitted bits to be sent over the channel, compared to the other schemes. Consequently, in our scheme messages X0, X0 from SP contain 161 and 160 bits respectively, resulting in a total message size sent by the SP equal to 321. The message M1 consists of 1 hash (160 bit), 1 EC point (161 bit) and 1 ciphertext message (192 bits) containing the identity and an EC point. Therefore, the SM sends a message of size 511 to the SP. Table 4. Comparison of communication complexity. Sent by SM Sent by SP No of Bits Comm. Rounds [9] 928 480 1408 3 [10] 1248 672 1920 3 [11] 1152 480 1632 3 [12] 512 320 832 3 [14] 576 768 1344 4 Ours 511 321 832 3 Scheme No of Bits No of Bits Total No of

Communication Costs. For the communication costs, we determine the number of bits transmitted by both the SM and the SP. In all the considered schemes, the number of communication phases equals to three, except in [14], where there are four phases required. Note that we consider the 80-bit security level. Therefore, the length of the hash function and the nonces/random numbers equals to 160 bits. For the schemes of [9–11], the sizes of the groups G1 and G2, related to the pairing operation, are 320 and 512 bits, respectively. When sending an EC point, it is sufficient to send the x-coordinate together with a sign bit. In addition, we assume that the length of identity related information equals to 32 bits. The length of the PUF responses equals to 128 bits. As can be concluded from Table 4, our scheme, together with [12], requires the smallest number of transmitted bits to be sent over the channel, compared to the other schemes. Consequently, in our scheme messages X0M0, X0 M2 from SP contain 161 and 160 bits respectively, resulting in a total message size sent by the SP equal to 321. The message M1 consists of 1 hash (160 bit), 1 EC point (161 bit) and 1 ciphertext message (192 bits) containing the identity and an EC point. Therefore, the SM sends a message of size 511 to the SP. Table 4. Comparison of communication complexity. Sent by SM Sent by SP No of Bits Comm. Rounds [9] 928 480 1408 3 [10] 1248 672 1920 3 [11] 1152 480 1632 3 [12] 512 320 832 3 [14] 576 768 1344 4 Ours 511 321 832 3 Scheme No of Bits No of Bits Total No of