Abstract
In this paper, we propose two digital signature schemes based on a third order linear feedback shift register. One of them is a normal signature scheme for signing document and the other is with encryption for intended reciever. These two signature schemes are different from most of the signature schemes which are based on discrete logarithm problem, elliptic curves discrete logarithm problem, RSA or quadratic residues. The efficient computational algorithm for computing k th term of a sequence is also presented. The advantage of these two schemes is that the computation is carried out in the ground field and not in an extension field. We also show that the security of these two signature schemes is equivalent to that of Schnorr signature scheme and Signed-ElGamal encryption scheme respectively.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Blaser. A 5/2n2-lower bound for multiplicative complexity of nxn-matrix multiplication. In STACS 2001, Lecture Notes in Computer Science 2010, Springer-Verlag, (2001) 99–109.
D. Chaum. Blind signatures for untraceable payments. In Advances in Cryptology-Crypto’82, Plenum Press, New York, (1983) 199–203.
D. Chaum and E. V. Heyst. Group signatures. In Advances in Cryptology-Crypto’91, Lecture Notes in Computer Science 547, Springer-Verlag, (1991) 257–265.
Don Coppersmith. Weakness in quaternion signatures. Journal of Cryptology, 14, No. 2, (2001) 77–85.
Don Coppersmith, J. Stern and S. Vaudenay. Attacks on the birational permutation signature schemes. In Advances in Cryptology-Crypto’93, Lecture Notes in Computer Science 773, Springer-Verlag, (1993) 207–221.
W. Diffie and M. E. Hellman. New directions in cryptography. IEEE Transactions on Information Theory, 22 (1976) 644–654.
T. ElGamal. A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Transactions on Information Theory, 31 (1985) 469–472.
G. Gong and L. Harn. Public key cryptosystems based on cubic finite field extensions. IEEE Transactions on Information Theory, 45 (1999) 2601–2605.
R. Gennaro, H. Krawczyk and T. Rabin. RSA-based undeniable signatures. Journal of Cryptology, Vol 13, No. 4, (2000) 397–416.
N. Koblitz. Elliptic curve cryptosystems. Mathematics of Computation, 48, No. 177, (1987) 203–209.
R. Lidl and H. Niederreiter. Introduction to Finite Fields and Their Applications. Cambridge University Press, 1986.
U. M. Maurer and S. Wolf. The relationship between breaking the Diffie-Hellman protocol and computing discrete logarithms. SIAM J. COMPUT, Vol 28, No 5, (1999) 1689–1721.
A. J. Menezes, P. C. van Oorschot and S. A. Vanstone. Handbook of Applied Cryptography. CRC Press, 1997.
A. J. Menezes and Y. H. Wu. The discrete logarithm problem in GL(n,q). Ars Combinatoria, 47, (1998) 23–32.
R. C. Merkle and M. E. Hellman. Hiding information and signatures in trapdroor knapsacks. IEEE Transactions on Information Theory, 24 (1978) 525–530.
V. S. Miller. Use of elliptic curves in cryptography. In Advances in Cryptology-Crypto’85, Lecture Notes in Computer Science 218, Springer-Verlag, (1986) 417–426.
K. Nyberg and R. A. Rueppel. Message recovery for signature schemes based on the discrete logarithm problem. In Advances in Cryptology-Eurocrypt’94, Lecture Notes in Computer Science 547, Springer-Verlag, (1994) 175–190.
A. Odlyzko. Discrete logarithms: The past and the future. Designs, Codes and Cryptography, 19, (2000) 129–145.
H. Ong, C. P. Schnorr and A. Shamir. An efficient signature scheme based on quadratic equations. In 16th ACM Symposium Theory of Computation, (1984) 208–216.
D. Pointcheval and J. Stern. Security arguments for digital signatures and blind signatures. Journal of Cryptology, 13, No. 3, (2000) 361–396.
J. M. Pollard and C. P. Schnorr. An efficient solution of the congruence x 2 + ky 2 = m (mod n). IEEE Transactions on Information Theory, 33, (1987) 702–709.
R. L. Rivest, A. Shamir and L. Adleman. A method for obtaining digital signatures and public key cryptosystems. Communications of the ACM, 21 (1978) 120–126.
T. Satoh and K. Araki. On construction of signature scheme over a certain non-commutative ring. IEICE Transactions on Fundamentals, Vol E80-A, No. 1, (1997) 40–45.
C. P. Schnorr. Efficient signature generation for smart cards. Journal of Cryptology, 4, (1991) 161–174.
C. P. Schnorr and M. Jakobsson. Security of discrete log cryptosystems in the random oracle + generic model. In Conference on The Mathematics of Public-Key Cryptography, The Fields Institute, Toronto, Canada. 1999.
C. P. Schnorr and M. Jakobsson. Security of signed ElGamal encryption. In Advances in Cryptology-Asiacrypt’00, Lecture Notes in Computer Science 1976, Springer-Verlag, (2000) 73–89.
A. Shamir. Efficient signature schemes based on birational permutations. In Advances in Cryptology-Crypto’93, Lecture Notes in Computer Science 773, Springer-Verlag, (1993) 1–12.
V. Shoup. Lower bounds for discrete logarithms and related problems. In Advances in Cryptology-Eurocrypt’97, Lecture Notes in Computer Science 1233, Springer-Verlag, (1997) 256–266.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tan, C.H., Yi, X., Siew, C.K. (2001). Signature Schemes Based on 3rd Order Shift Registers. In: Varadharajan, V., Mu, Y. (eds) Information Security and Privacy. ACISP 2001. Lecture Notes in Computer Science, vol 2119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47719-5_35
Download citation
DOI: https://doi.org/10.1007/3-540-47719-5_35
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42300-3
Online ISBN: 978-3-540-47719-8
eBook Packages: Springer Book Archive