98 Copyright © 2017, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Chapter 7 DOI: 10.4018/978-1-5225-2154-9.ch007 ABSTRACT This chapter takes a critical review of the digital signature schemes which are based on two hard prob- lems. The analytical study begins with the Harn (1994) scheme and He-Kiesler (1994) scheme. Shao’s 1998 and 2002 schemes have been studied. Wei-Hua He (2001) and Shimin Wei (2004, 2007) schemes are analyzed further in the research work. Attacks on Shimin Wei’s (2004, 2007) schemes are critically studied and drawbacks have been noted so as to design better schemes than these. Then we continue our analysis work by studying Ismail, Thate, and Ahmad’s (2008) scheme and Swati Verma’s (2012) signature scheme. INTRODUCTION Scholars from cryptography and security field have done crucial of research work to design the robust and secure digital signature schemes till date. The key requirement of the digital signature is that it should sustain all the types of attacks it is exposed to. Designing the better digital signature scheme is one work whereas to make it tough and non-vulnerable to attacks is another biggest work. In this chapter, some of the digital signature schemes have been studied and analyzed thoroughly. This provides the guide- line and a clear pathway, so that one can design a digital signature scheme, which is non-susceptible to known attacks. The digital signature schemes that have been studied are the digital signature schemes designed in the period from the year 1994 till the year 2012, which were the golden years for security system design because internet and communication systems gained sudden big popularity in these two decades. Here exiting digital signature schemes were studied and analyzed. In the analysis process, initially, Shimin Wei (2004, 2007) scheme and various known attacks on this scheme were taken up for the analy- Digital Signature Schemes Based on Two Hard Problems A. B. Nimbalkar Annasaheb Magar Mahavidyalaya, India C. G. Desai NDA, India