Abstract
Seurin (PKC 2014) proposed the 2-Φ/4-hiding assumption which asserts the indistinguishability of Blum Numbers from pseudo Blum Numbers. In this paper, we investigate the lossiness of 2k-th power based on the 2k-Φ/4-hiding assumption, which is an extension of the 2-Φ/4-hiding assumption. And we prove that 2k-th power function is a lossy trapdoor permutation over Quadratic Residuosity group. This new lossy trapdoor function has 2k-bits lossiness for k-bits exponent, while the RSA lossy trapdoor function given by Kiltz et al. (Crypto 2010) has k-bits lossiness for k-bits exponent under Φ-hiding assumption in lossy mode. We modify the square function in Rabin-OAEP by 2k-th power and show the instantiability of this Modified Rabin-OAEP by the technique of Kiltz et al. (Crypto 2010). The Modified Rabin-OAEP is more efficient than the RSA-OAEP scheme for the same secure bits. With the secure parameter being 80 bits and the modulus being 2048 bits, Modified Rabin-OAEP can encrypt roughly 454 bits of message, while RSA-OAEP can roughly encrypt 274 bits.
Keywords
Supported by the National Basic Research Program of China (973 project)(No.2013CB338002), the National Nature Science Foundation of China (No.61070171, No.61272534).
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Xue, H., Li, B., Lu, X., Wang, K., Liu, Y. (2014). On the Lossiness of 2k-th Power and the Instantiability of Rabin-OAEP. In: Gritzalis, D., Kiayias, A., Askoxylakis, I. (eds) Cryptology and Network Security. CANS 2014. Lecture Notes in Computer Science, vol 8813. Springer, Cham. https://doi.org/10.1007/978-3-319-12280-9_3
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DOI: https://doi.org/10.1007/978-3-319-12280-9_3
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