Information and Communications Security

The objective of this paper is to give a fast square root computation method. First the Frobenius mapping is adopted. Then a lot of calculations over an extension field are reduced to that over a proper subfield by the norm computation. In addition a inverse square root algorithm and an addition chain are adopted to save the computation cost. All of the above-mentioned steps have been proven to make the proposed algorithm much faster than the conventional algorithm. From the table which compares the computation between the conventional and the proposed algorithm, it is clearly shown that the proposed algorithm accelerates the square root computation 10 times and 20 times faster than the conventional algorithm in Fp11 and Fp22 respectively. At the same time, the proposed algorithm reduces the computation cost 10 times and 20 times less than the conventional algorithm.

[1]  Radha Poovendran,et al.  Design of secure multicast key management schemes with communication budget constraint , 2002, IEEE Communications Letters.

[2]  Jerome A. Solinas An Improved Algorithm for Arithmetic on a Family of Elliptic Curves , 1997, CRYPTO.

[3]  Moni Naor,et al.  Revocation and Tracing Schemes for Stateless Receivers , 2001, CRYPTO.

[4]  Michael Randolph Garey,et al.  Johnson: "computers and intractability , 1979 .

[5]  John S. Baras,et al.  An information-theoretic approach for design and analysis of rooted-tree-based multicast key management schemes , 2001, IEEE Trans. Inf. Theory.

[6]  Avishai Wool,et al.  Key management for restricted multicast using broadcast encryption , 2000, TNET.

[7]  Giovanni Di Crescenzo,et al.  Efficient Re-keying Protocols for Multicast Encryption , 2002, SCN.

[8]  Shueng-Han Gary Chan,et al.  Distributed server networks for secure multicast , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).

[9]  Jerome A. Solinas,et al.  Efficient Arithmetic on Koblitz Curves , 2000, Des. Codes Cryptogr..

[10]  Avishai Wool,et al.  Long-Lived Broadcast Encryption , 2000, CRYPTO.

[11]  Bobby Bhattacharjee,et al.  Scalable secure group communication over IP multicast , 2001, Proceedings Ninth International Conference on Network Protocols. ICNP 2001.

[12]  Suvo Mittra,et al.  Iolus: a framework for scalable secure multicasting , 1997, SIGCOMM '97.

[13]  Dong Hoon Lee,et al.  Efficient Multicast Key Management for Stateless Receivers , 2002, ICISC.

[14]  Adi Shamir,et al.  The LSD Broadcast Encryption Scheme , 2002, CRYPTO.

[15]  Douglas R. Stinson,et al.  Fault Tolerant and DistributedBroadcast Encryption , 2003, CT-RSA.

[16]  Tsutomu Matsumoto,et al.  A Flexible Tree-Based Key Management Framework , 2003, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[17]  Ran Canetti,et al.  Efficient Communication-Storage Tradeoffs for Multicast Encryption , 1999, EUROCRYPT.