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An Efficient and Scalable Quasi-Aggregate Signature Scheme Based on LFSR Sequences
July 2009 (vol. 20 no. 7)
pp. 1059-1072
Saikat Chakrabarti, University of Kentucky , Lexington
Santosh Chandrasekhar, University of Kentucky, Lexington
Mukesh Singhal, University of Kentucky, Lexington
Kenneth L. Calvert, University of Kentcuky, Lexington
Aggregate signatures can be a crucial building block for providing scalable authentication of a large number of users in several applications like building efficient certificate chains, authenticating distributed content management systems, and securing path vector routing protocols. Aggregate signatures aim to prevent resources (signature and storage elements, and computation) from growing linearly in the number of signers participating in a network protocol. In this paper, we present an efficient and scalable quasi-aggregate signature scheme, {\rm CLFSR}- {\rm QA}, based on third-order linear feedback shift register (cubic LFSR) sequences that can be instantiated using both XTR and GH public key cryptosystems. In the proposed {\rm CLFSR}-{\rm QA} construction, signers sign messages sequentially; however, the verfier need not know the order in which messages were signed. The proposed scheme offers constant length signatures, fast signing, aggregation, and verification operations at each node, and requires the least storage elements (public keys needed to verify the signature), compared to any other aggregate signature scheme. To the best of our knowledge, {\rm CLFSR}- {\rm QA} is the first aggregate signature scheme to be constructed using LFSR sequences. We believe that the {\rm CLFSR}- {\rm QA} signature scheme can be catalytic in improving the processing latency as well as reducing space requirements in building secure, large-scale distributed network protocols. We perform extensive theoretical analysis including correctness and security of {\rm CLFSR}- {\rm QA} and also present a performance (computation and communication costs, storage overhead) comparison of the proposed scheme with well-known traditional constructions.

[1] D. Boneh, C. Gentry, B. Lynn, and H. Shacham, “Aggregate and Verifiably Encrypted Signatures from Bilinear Maps,” Proc. EUROCRYPT: Int'l Conf. Theory and Applications of Cryptographic Techniques, E. Biham, ed., pp.416-432, 2003.
[2] A. Lysyanskaya, S. Micali, L. Reyzin, and H. Shacham, “Sequential Aggregate Signatures from Trapdoor Permutations,” Proc. EUROCRYPT: Int'l Conf. Theory and Applications of Cryptographic Techniques, C. Cachin and J. Camenisch, eds., pp.74-90, 2004.
[3] T. Suzuki, Z. Ramzan, H. Fujimoto, C. Gentry, T. Nakayama, and R. Jain, “A System for End-to-End Authentication of Adaptive Multimedia Content,” Proc. Eighth IFIP TC-6 TC-11 Conf. Comm. and Multimedia Security (CMS '04), pp.237-249, 2005.
[4] Y. Rekhter, T. Li, and S. Hares, “A Border Gateway Protocol 4 (BGP-4),” RFC 4271 (Draft Standard),, Jan. 2006.
[5] S.T. Kent, C. Lynn, J. Mikkelson, and K. Seo, “Secure Border Gateway Protocol (S-BGP)—Real World Performance and Deployment Issues,” Proc. Network and Distributed System Security Symp. (NDSS '00), The Internet Soc., 2000.
[6] M. Zhao, S.W. Smith, and D.M. Nicol, “Aggregated Path Authentication for Efficient BGP Security,” Proc. 12th ACM Conf. Computer and Comm. Security (CCS '05), V. Atluri, C. Meadows, and A. Juels, eds., pp.128-138, 2005.
[7] W. Diffie and M.E. Hellman, “New Directions in Cryptography,” IEEE Trans. Information Theory, vol. 22, no. 6, pp.644-654, Nov. 1976.
[8] FIPS, “Digital Signature Standard (DSS)” Nat'l Inst. for Standards and Tech nology, pp.ii + 74, Jan. 2000.
[9] H. Niederreiter, “A Public-Key Cryptosystem Based on Shift Register Sequences,” Proc. EUROCRYPT: Workshop Theory and Application of Cryptographic Techniques, F. Pichler, ed., pp.35-39, 1986.
[10] G. Gong and L. Harn, “Public-key Cryptosystems Based on Cubic Finite Field Extensions,” IEEE Trans. Information Theory, vol. 45, no. 7, pp.2601-2605, 1999.
[11] A.K. Lenstra and E.R. Verheul, “The XTR Public Key System,” Proc. 20th Ann. Int'l Cryptology Conf. (CRYPTO '00), M. Bellare, ed., pp.1-19, 2000.
[12] S. Chakrabarti, S. Chandrasekhar, M. Singhal, and K.L. Calvert, “Authenticating DSR Using a Novel Multisignature Scheme Based on Cubic LFSR Sequences,” Proc. Fourth European Workshop Security and Privacy in Ad Hoc and Sensor Networks (ESAS '07), F.Stajano, C. Meadows, and S. Capkun, eds., pp.156-171, 2007.
[13] S. Chakrabarti, S. Chandrasekhar, K.L. Calvert, and M. Singhal, “Efficient Blind Signatures for Accountability,” Proc. Third Workshop Secure Network Protocols (NPSec '07), Oct. 2007.
[14] M. Bellare and P. Rogaway, “Random Oracles are Practical: A Paradigm for Designing Efficient Protocols,” Proc. First ACM Conf. Computer and Comm. Security (CCS '93), pp.62-73, 1993.
[15] D. Boneh, B. Lynn, and H. Shacham, “Short Signatures from The Weil Pairing,” J. Cryptology, vol. 17, no. 4, pp.297-319, 2004.
[16] J. Xu, Z. Zhang, and D. Feng, “Id-Based Aggregate Signatures from Bilinear Pairings,” Proc. Fourth Int'l Conf. Cryptology and Network Security (CANS '05), Y. Desmedt, H. Wang, Y. Mu, and Y.Li, eds., pp.110-119, 2005.
[17] S. Lu, R. Ostrovsky, A. Sahai, H. Shacham, and B. Waters, “Sequential Aggregate Signatures and Multisignatures Without Random Oracles,” Proc. 25th Ann. Int'l Conf. Theory and Applications of Cryptographic Techniques (EUROCRYPT '06), S. Vaudenay, ed., pp.465-485, 2006.
[18] B. Waters, “Efficient Identity-Based Encryption without Random Oracles,” Proc. 24th Ann. Int'l Conf. Theory and Applications of Cryptographic Techniques (EUROCRYPT '05), R. Cramer, ed., pp.114-127, 2005.
[19] C. Gentry and Z. Ramzan, “Identity-Based Aggregate Signatures,” Proc. Ninth Int'l Conf. Theory and Practice of Public-Key Cryptography (PKC '06), M. Yung, Y. Dodis, A. Kiayias, and T. Malkin, eds., pp.257-273, 2006.
[20] A. Boldyreva, C. Gentry, A. O'Neill, and D.H. Yum, “Ordered Multisignatures and Identity-Based Sequential Aggregate Signatures, with Applications to Secure Routing,” Proc. 14th ACM Conf. Computer and Comm. Security (CCS '07), S.D.C. di Vimercati and P.Syverson, eds., pp.276-285, 2007.
[21] K. Itakura, H. Nakamura, and K. Nakazawa, “A Public-Key Cryptosystem Suitable for Digital Multisignatures,” NEC Research and Development, pp.1-8, Oct. 1983.
[22] L. Harn, “New Digital Signature Scheme Based on Discrete Logarithm,” Electronics Letters, vol. 30, no. 5, pp.396-398, Mar. 1994.
[23] S. Micali, K. Ohta, and L. Reyzin, “Accountable-Subgroup Multisignatures: Extended Abstract,” Proc. Eighth ACM Conf. Computer and Comm. Security (CCS '01), pp.245-254, 2001.
[24] C.P. Schnorr, “Efficient Signature Generation by Smart Cards,” J.Cryptology, vol. 4, no. 3, pp.161-174, 1991.
[25] A. Boldyreva, “Threshold Signatures, Multisignatures and Blind Signatures Based on The Gap-Diffie-Hellman-Group Signature Scheme,” Proc. Sixth Int'l Workshop Theory and Practice in Public Key Cryptography (PKC '03), Y. Desmedt, ed., pp.31-46, 2003.
[26] S. Chakrabarti, S. Chandrasekhar, M. Singhal, and K.L. Calvert, “Authenticating Feedback in Multicast Applications Using a Novel Multisignature Scheme Based on Cubic LFSR sequences,” Proc. 21st Int'l Conf. Advanced Information Networking and Applications Workshops (AINAW '07), vol. 1, pp.607-613, 2007.
[27] G. Gong, L. Harn, and H. Wu, “The GH Public-Key Cryptosystem,” Proc. Eighth Ann. Int'l Workshop Selected Areas in Cryptography (SAC '01), revised papers, S. Vaudenay and A.M. Youssef, eds., pp.284-300, 2001.
[28] K.J. Giuliani and G. Gong, “New LFSR-based Cryptosystems and the Trace Discrete Log Problem (Trace-DLP),” Proc. ThirdInt'l Conf. Sequences and Their Applications (SETA '04), T. Helleseth, D.V. Sarwate, H.-Y. Song, and K. Yang, eds., pp.298-312, 2004.
[29] S.W. Golomb, Shift Register Sequences. Holden Day, 1967.
[30] E.R. Berlekamp, “Factoring Polynomials pver Large Finite Fields*,” Proc. Second ACM Symp. Symbolic and Algebraic Manipulation (SYMSAC '71), p. 223, 1971.
[31] A.K. Lenstra and E.R. Verheul, “Key Improvements to XTR,” Proc. Sixth Int'l Conf. Theory and Application of Cryptology and Information Security (ASIACRYPT '00), T. Okamoto, ed., pp.220-233, 2000.
[32] A.K. Lenstra and E.R. Verheul, “Fast Irreducibility and Subgroup Membership Testing in XTR.” Proc. Fourth Int'l Workshop Practice and Theory in Public Key Cryptography (PKC '01), K. Kim, ed., pp.73-86, 2001.
[33] E. Peeters, M. Neve, and M. Ciet, “XTR Implementation on Reconfigurable Hardware,” Proc. Sixth Int'l Workshop Cryptographic Hardware and Embedded Systems (CHES '04), M. Joye and J.-J. Quisquater, eds., pp.386-399, 2004.
[34] P. Horster, H. Petersen, and M. Michels, “Meta-Elgamal Signature Schemes.” Proc. Second ACM Conf. Computer and Comm. Security (CCS '94), pp.96-107, 1994.
[35] P.S.L.M. Barreto, B. Lynn, and M. Scott, “On the Selection of Pairing-Friendly Groups.” Proc. 10th Ann. Int'l Workshop Selected Areas in Cryptography (SAC '03), revised papers, M. Matsui and R.J.Zuccherato, eds., pp.17-25, 2003.
[36] K.J. Giuliani and G. Gong, “Efficient Key Agreement and Signature Schemes Using Compact Representations in ${GF}(p^{10})$ ,” Proc. Int'l Symp. Information Theory (ISIT '04), June 2004.

Index Terms:
Digital signature, aggregate signature, compressed certificate chain, distributed content management, secure path-vector protocols, LFSR sequences, LFSR-based public key cryptosystems.
Saikat Chakrabarti, Santosh Chandrasekhar, Mukesh Singhal, Kenneth L. Calvert, "An Efficient and Scalable Quasi-Aggregate Signature Scheme Based on LFSR Sequences," IEEE Transactions on Parallel and Distributed Systems, vol. 20, no. 7, pp. 1059-1072, July 2009, doi:10.1109/TPDS.2008.261
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