Term Paper: Digital Signature Scheme

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[. . .] A common method for dealing with this issue is to make a requirement that the message space be sparse meaning that very few strong are representative of messages. (Goldwasser, Micali, and Rivest, 1988, paraphrased)

(2) Rivest-Shamir-Adleman -- This scheme is selectively able to be forged through sue of a "directed chosen-message attack. (Goldwasser, Micali, and Rivest, 1988, paraphrased)

(3) Merkle-Hellman - it was shown that this scheme was able to be forged universally with a key only attack. (Goldwasser, Micali, and Rivest, 1988, paraphrased)

(4) Rabin -- This signature scheme is reported as "totally breakable if the enemy uses a directed chosen-message attack. Selective forgery is as difficult as factoring if the attacker is restricted to a known-message attack. (Goldwasser, Micali, and Rivest, 1988, paraphrased)

(5) Williams -- This is a similar scheme to Rabin's and selective forgery is reported as being hard as factoring is slightly stronger. (Goldwasser, Micali, and Rivest, 1988, paraphrased)

(6) Lieberherr -- It is reported that this scheme is "…similar to Rabin's and Williams', and is totally breakable with a directed chosen-message attack.

(7) Shamir -- This is a knapsack type signature scheme which Tulpan recently demonstrated to be universally forgeable. (Goldwasser, Micali, and Rivest, 1988, paraphrased)

(8) Goldwasser-Micali-Yao -- The researchers present a the first time signature schemes that are not the trap-door type and which have the security characteristics hold for any message space. It is reported specifically that the first signature scheme "…presented in [GMY83] was proven not to be even existentially forgeable against a generic chosen-message attack unless factoring is easy. However, it is not known to what extent directed chosen-message attacks or adaptive chosen message attacks might aid an enemy in "breaking" the scheme. (Goldwasser, Micali and Rivest, 1988)

The work of Westhoff, Lamparter, Paar and Weimerskirch (2004) reports on the use of Digital signature in Ad Hoc Networks and states that digital signatures, while tending to have weak performance and to be restricted, are becoming more conceivable for use. It is reported as well that there is a specific interest in the integration into protocols "aiming at secure routing, a technical support for accounting and charging, security aspects for peer-to-peer services, or giving incentives for cooperation." (Westhoff, Lamparter, Paar and Weimerskirch, 2004) Protocols from these classes are reported to be classified as follows:

(1) These protocols make the requirement of involvement of in excess of two entities;

(2) Relaxed security level and durability requirements;

(3) Entities involved in differing roles at different times. (Westhoff, Lamparter, Paar, and Weimerskirch, 2004)

The work of Ismail, Tahat, and Ahmad (2008) entitled " A New Digital Signature Scheme Based on Factoring and Discrete Logarithms" reports that the majority of designated signature schemes are based on a single hard problem. Although these schemes are secure it is likely that in the near future, if an adversary managed to solve this problem, he then can recover all secret information including secret keys and parameters of the scheme. Ismail, Tahat, and Ahmad report a signature scheme that prevents this issue since the scheme is "designed on two hard problems namely factoring and discreet logarithm problems. To break the scheme, the enemy has to solve the two problems simultaneously, which is impossible." (2008) The scheme is reported to be protected from five attacks and it is reported that these attacks "are the most common considering attacks for signature schemes." (Ismail, Tahat, and Ahmad, 2008) According to Ismail, Tahat, and Ahmad the performance analysis of the scheme reveals "that the signature process needs time complexity whereas the verification process requires 1202 Tmul+Th. The higher time complexity is contributed by the use of two hard problems but yet the scheme provides longer security than schemes on a single problem." (Ismail, Tahat, and Ahmad, 2008)

Summary and Conclusion

Cryptography in the form of digital signatures are varied in form and have been continuously modified and changed since they were first conceived. public key Cryptography is used for digital signatures using two keys including one that takes a plain text message and then applies one of the keys to it in an encryption process and the other key is applied to a scrambled message in the decryption process rendering the original text message. The previous forms of digital signatures have been reviewed as well as have new forms and types of digital signatures. This is a field still under development with ongoing research seeking better and more secure methods of digital signature implementation.


Abdalla, M. And Reyzin, L. (2000) A New Forward-Secure Digital Signature Scheme. Advances in Cryptology -- Asiacrypt 2000. Retrieved from: http://www.cs.bu.edu/~reyzin/papers/forwardsig.pdf

Al-Saidi, N. (2011) Signature Identification Scheme Based on Iterated Function Systems. World Academy of Science, Engineering and Technology 80, 2011. Retrieved from: http://www.waset.org/journals/waset/v80/v80-81.pdf

Diaz, RD, Encinas, H. And Jasque JM (nd) A Group Signature Scheme Based on the Integer Factorization and the Subgroup Discrete Logarithm Problems. Retrieved from: http://digital.csic.es/bitstream/10261/39204/1/CISIS11-GT-1888_GroupSignature.pdf

Goldwasser, S. et al. (2011) A Digital Signature Scheme Against Adaptive chosen-Message Attacks. Siam J. Comput. V. 17 No.2, April 1998. Online available at: http://people.csail.mit.edu/silvio/Selected%20Scientific%20Papers/Digital%20Signatures/A_Digital_Signature_Scheme_Secure_Against_Adaptive_Chosen-Message_Attack.pdf

Grabbe, I. (nd) Digital Signatures Illustrated. Retrieved from: http://orlingrabbe.com/digsig.htm

Ismail, ES, Tahat, MF and Ahmad, RR (2008) A New Digital Signature Scheme Based on Factoring and Discrete Logarithms. Journal of Mathematics and Statistics 4 (4):223-226. Retrieved from: http://www.akademik.unsri.ac.id/download/journal/files/scipub/jms244223-226.pdf

L. Harn, (1994) Public-key cryptosystems design based on factoring and discrete logarithms, IEE Proceedings of Computer Digital Techniques, Vol. 141, 1994, pp. 193-195.

Lin, HF, Gun, CY and Chen, CY (2009) Comments on Wei's Digital Signature Scheme Based on Two Hard Problems. IJCSNS International Journal of Computer Science and Network Security. Vol.9, No. 2 February 2009. Retrieved from: http://paper.ijcsns.org/07_book/200902/20090201.pdf

N. Lin and T. Hwang (1996) "Modified Harn signature scheme based on factorizing and discrete logarithms, in IEE Proceedings of Computer Digital Techniques, Vol. 143, 1996, pp. 196-198.

Westhoff, D. et al. (2004) On Digital… [END OF PREVIEW]

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