Asymmetric cryptography and trapdoor one-way functions
DOI:
https://doi.org/10.7494/automat.2016.20.2.39Keywords:
cryptography, RSA algorithm, one-way function, one-way trapdoor function, public-key encryption, asymmetric encryptionAbstract
The asymmetric-key (public-key) encryption scheme is considered to be the most important discovery in the history of cryptography. It is based on the use of two complementary keys generated according to a chosen trapdoor one-way function (TOWF). Since its first implementation, asymmetric encryption has revolutionized our way of communicating as well as the safety of information transfer, and it is now widely used around the world for various purposes, especially in the field of online transaction security. The safety of the asymmetric-key scheme relies on the assumption that any known cryptographic attack using an efficient problem-solving algorithm will not be able to succeed in applying the inverse (decryption) function onto the cryptogram in a polynomial time without additional knowledge (secret information). The most-challenging aspect of creating a new asymmetric cryptographic algorithm is selecting a one-way function for encryption purposes and finding a trapdoor in its inverse. In this paper, the concept of public-key cryptography will be explained using the RSA algorithm as an example. In addition, the review of the most-important functions that are considered to be trapdoor one-way functions will be conducted.References
Catalano D., Fiore D., Gennaro R., Vamvourellis K., Algebraic (Trapdoor) One-Way Functions and their Applications, in: A. Sahai (ed.) Theory of Cryptography. Lecture Notes in Computer Science, Vol. 7785, Berlin – Heidelberg 2013, pp. 680–699
Pandey O., Pass R., Vaikuntanathan V., Adaptive One-way Functions and Applications, in: D. Wagner (ed.), CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology, Santa Barbara 2008, pp. 57–74
Ostrovsky R., CS-282A / MATH-209A Foundations of Cryptography, “Draft Lecture Notes”, Winter 2010
Gardner M., “Trapdoor Ciphers” and “Trapdoor Ciphers II.” Chs. 13–14, in: Penrose Tiles and Trapdoor Ciphers and the Return of Dr. Matrix, New York 1989, pp. 183–204.
Khan Academy, Euler’s totient function, https://pl.khanacademy.org [26.02.2016]
Hurd J., Blum Integers, Trinity College, 20.01.1997, www.gilith.com/research/talks/cambridge 1997.pdf [26.02.2016]
Cathalo J., Petit Smals Ch., One-Time Trapdoor One-Way Functions, in: M. Burmester, G. Tsudik, S. Magliveras, I. Ilić (ed.), Information Security. ISC 2010. Lecture Notes in Computer Science, Vol. 6531, Berlin – Heidelberg 2010, pp. 283–298.
Vincenzo Conti S.V., Fingerprint Traits and RSA Algorithm Fusion Technique, in: Sixth International Conference on Complex, Intelligent, and Software Intensive Systems, Palermo 2012, pp. 351–356.
Ananth G., Karthikeyan U.S. [participants], Kamakoti V. [instructor], Cryptographic Algorithm Using a MultiBoard FPGA Architecture, Nios II Embedded Processor Design Contest – Outstanding Designs, 2005
Srinivasan R., Vaidehi V., Balaji J., Heema S., Single Chip Efficient FPGA implementation of RSA and DES for Digital Envelope Scheme, “WSEAS Transactions on Communication”, Iss. 2, Vol. 3, April 2004, pp. 664–669, https://www.researchgate.net/publication/242093457_A_Single_Chip_Efficient_FPGA_implementation_of_RSA_and_DES_for_Digital_Envelope_Scheme [26.02.2016]
Nikolaus L., Single-chip implementation of a cryptosystem for financial applications, in: R. Hirschfeld (ed.), Financial Cryptography. First International Conference, FC ‘97. Proceedings, Berlin – Heidelberg – New York 1997
Alkalbani A.S., Mantoro T., Md Tap A.O., Comparison between RSA Hardware and Software Implementation for WSNs Security Schemes, in: International Conference on Information and Communication Technology for the Muslim World (ICT4M), Jakarta 2010
Maxim Integrated Products © 2013 Inc., Cryptography in software or hardware – it depends on the need. Tutorial, 25.05.2012, pdfserv.maximintegrated.com/en/an/TUT5716.pdf [26.02.2016]
