Design of Optimized Modular Multiplier Using Montgomery Algorithm for RSA Cryptosystem
Modular multiplication plays a vital role in RSA Cryptography and Elliptical Curve Cryptography. We have implemented a 256-bit Modular multiplier using Montgomery Reduction Algorithm in VHDL. The output of the Montgomery multiplier is Z = X*Y R−1 mod M. O
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Design of Optimized Modular Multiplier Using Montgomery Algorithm for RSA Cryptosystem Sandip Kakde, Pravin Zode and Pradnya Zode
Abstract Modular multiplication plays a vital role in RSA Cryptography and Elliptical Curve Cryptography. We have implemented a 256-bit Modular multiplier using Montgomery Reduction Algorithm in VHDL. The output of the Montgomery multiplier is Z = X*Y R-1 mod M. Our main aim is to calculate the area required for the modular multiplier using Montgomery reduction algorithm. It is a full-featured circuit including Carry save Adders, shift registers, multiplexers, parallel registers component and are too big to fit into a single Altera Stratix Device on the Field Programmable platform, so that we are unable to test them in real hardware. However, each sub-component was simulated in Model-Sim SE 6.0 and Altera Quartus II 8.0 and proved functionally correct. Keywords Montgomery algorithm
RSA Cryptography Modular arithmetic
40.1 Introduction Since long era, network security is a very big issue and number of systems and algorithms are developed in order to secure the data. Advanced Encryption System (AES), Data Encryption System (DES), RSA, Elliptical Curve Cryptography, S. Kakde (&) P. Zode P. Zode Yeshwantrao Chavan College of Engineering, Nagpur, India e-mail: [email protected] P. Zode e-mail: [email protected] P. Zode e-mail: [email protected]
V. V. Das (ed.), Proceedings of the Third International Conference on Trends in Information, Telecommunication and Computing, Lecture Notes in Electrical Engineering 150, DOI: 10.1007/978-1-4614-3363-7_40, Ó Springer Science+Business Media New York 2013
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Digital Signature, Diffie Hellman Key exchange are the main algorithms for the data security. However RSA (public key encryption algorithm by Rivest, Shamir, Adelman), Digital Signature, Diffie Hellman key exchange are some examples of algorithms that use a series of modular multiplications to compute modular multiplication and exponentiation. In this age of universal electronic connectivity, it is of utmost importance to store information securely. This led to a heightened awareness to protect the data from disclosure, to guarantee the authenticity of data and messages, and to protect systems from network-based attacks. Cryptography plays a major role in mobile phone communications, sending private emails, transmitting financial information, security, computer passwords and electronic commerce digital signature and so on. Modular exponentiation ab mod m, and implicitly modular multiplication a*c mod m are the operations intensively used, underlying many cryptographic schemes. Nowadays, more and more reconfigurable hardware devices are used in network applications due to their low cost, high performance and flexibility. Such applications include extensible network routers, firewalls and Internet enable sensors, etc. These reconfigurable hardware devices are usually distributed in a large geographic area and operated over public networks, making o
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