Abstract
Ordinarily, RSA and Rabin ciphertexts and signatures are log N bits, where N is a composite modulus; here, we describe how to “compress” Rabin ciphertexts and signatures (among other things) down to about (2/3)log N bits, while maintaining a tight provable reduction from factoring in the random oracle model. The computational overhead of our compression algorithms is small. We also improve upon Coron’s results regarding partial-domain-hash signature schemes, reducing by over 300 bits the hash output size necessary to prove adequate security.
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References
Apostol, T.M.: Modular Functions and Dirichlet Series in Number Theory. Springer, Heidelberg (1976)
Barr, K., Asanović, K.: Energy Aware Lossless Data Compression. In: Proc. of MobiSys 2003 (2003)
Bellare, M., Rogaway, P.: The Exact Security of Digital Signatures – How to Sign with RSA and Rabin. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 399–416. Springer, Heidelberg (1996)
Bellare, M., Rogaway, P.: Optimal Asymmetric Encryption – How to Encrypt with RSA. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 92–111. Springer, Heidelberg (1995)
Bernstein, D.J.: A Secure Public-Key Signature System with Extremely Fast Verification (2000), Available at http://cr.yp.to/djb.html
Bernstein, D.J.: Proving Tight Security for Standard Rabin-Williams Signatures (2003), Available at http://cr.yp.to/djb.html
Bernstein, D.J.: Reducing Lattice Bases to Find Small-Height Values of Univariate Polynomials (2003), Available at http://cr.yp.to/djb.html
Bleichenbacher, D.: Compressed Rabin Signatures. In: Proc. of CT-RSA 2004 (2004)
Boneh, D.: Simplified OAEP for the RSA and Rabin Functions. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 275–291. Springer, Heidelberg (2001)
Boneh, D., Gentry, C., Lynn, B., Shacham, H.: Aggregate and Verifiably Encrypted Signatures from Bilinear Maps. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 416–432. Springer, Heidelberg (2003)
Boneh, D., Durfee, G., Howgrave-Graham, N.: Factoring N = prq for Large r. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 326–337. Springer, Heidelberg (1999)
Boneh, D., Venkatesan, R.: Breaking RSA May Not Be Equivalent to Factoring. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 59–71. Springer, Heidelberg (1998)
Cocks, C.: An Identity Based Encryption Scheme Based on Quadratic Residues. In: Honary, B. (ed.) Cryptography and Coding 2001. LNCS, vol. 2260, p. 360. Springer, Heidelberg (2001), http://www.cesg.gov.uk/technology/id-pkc/media/ciren.pdf
Cohen, H.: A Course in Computational Algebraic Number Theory, Graduate Texts in Mathematics, 4th edn. Springer, Heidelberg (2000)
Coron, J.S.: On the Exact Security of Full Domain Hash. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 229–235. Springer, Heidelberg (2000)
Coron, J.-S.: Security Proof for Partial-Domain Hash Signature Schemes. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 613–626. Springer, Heidelberg (2002)
Coppersmith, D.: Finding a Small Root of a Univariate Modular Equation. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 155–165. Springer, Heidelberg (1996)
Feige, U., Fiat, A., Shamir, A.: Zero-Knowledge Proofs of Identity. Jour. of Cryptology 1, 77–94 (1988)
Fiat, A., Shamir, A.: How to Prove Yourself: Practical Solutions to Identification and Signature Problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987)
Hardy, G.H., Wright, E.M.: An Introduction to the Theory of Numbers, 5th edn. Oxford Science Publications
Jonsson, J.: A OAEP Variant with a Tight Security Proof (2003), Available at http://www.math.kth.se/~jakobj/crypto.html
Lenstra, A.K., Verheul, E.R.: The XTR Public Key System. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 1–20. Springer, Heidelberg (2000)
Lysyanskaya, A., Micali, S., Reyzin, L., Shacham, H.: Sequential Aggregate Signatures from Trapdoor Homomorphic Permutations. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 74–90. Springer, Heidelberg (2004)
Malone-Lee, J., Mao, W.: Two Birds One Stone: Signcryption Using RSA (2002), Available at http://www.hpl.hp.com/techreports/2002/HPL-2002-293.html
Menezes, A., van Oorschot, P., Vanstone, S.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1996)
Micali, S., Shamir, A.: An Improvement of the Fiat-Shamir Identification and Signature Scheme. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 244–247. Springer, Heidelberg (1990)
Ong, H., Schnorr, C.P.: Fast Signature Generation with a Fiat Shamir - Like Scheme. In: Damgård, I.B. (ed.) EUROCRYPT 1990. LNCS, vol. 473, pp. 432–440. Springer, Heidelberg (1991)
Rabin, M.O.: Digitalized Signatures and Public-Key Functions as Intractable as Factorization, MIT/LCS/TR-212, MIT Laboratory for Computer Science (1979)
Rivest, R.L., Shamir, A., Tauman, Y.: How to Leak a Secret. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 552–565. Springer, Heidelberg (2001)
Rubin, K., Silverberg, A.: Torus-based Cryptography. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 349–365. Springer, Heidelberg (2003)
Shoup, V.: OAEP Reconsidered. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 239–259. Springer, Heidelberg (2001)
Lenstra, A.K., Shamir, A., Tomlinson, J., Tromer, E.: Analysis of Bernstein’s Factorization Circuit. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 1–26. Springer, Heidelberg (2002)
Vallée, B.: Provably Fast Integer Factoring with Quasi-Uniform Small Quadratic Residues. In: Proc. of STOC 1989, pp. 98–106 (1989)
Vallée, B.: Generation of Elements with Small Modular Squares and Provably Fast Integer Factoring Algorithms. Mathematics of Computation 56(194), 823–849 (1991)
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Gentry, C. (2004). How to Compress Rabin Ciphertexts and Signatures (and More). In: Franklin, M. (eds) Advances in Cryptology – CRYPTO 2004. CRYPTO 2004. Lecture Notes in Computer Science, vol 3152. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28628-8_11
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