Keywords
How to Cite
Abstract
This thesis investigates the mathematical foundations, computational properties, and applied significance of one-way functions within the domains of modern cryptography and information security. Defined by their asymmetric computational behavior, one-way functions permit efficient forward computation while rendering inverse computation computationally intractable in the absence of auxiliary secret knowledge. The security of numerous cryptographic constructs—including public-key encryption algorithms, digital signature schemes, authentication protocols, and cryptographic hash functions—is intrinsically dependent on the complexity assumptions underlying these functions. A comprehensive evaluation of prominent one-way paradigms, including modular exponentiation, integer factorization, discrete logarithm problems, and hash-based constructions, is presented. Furthermore, the study assesses the relevance of one-way functions in post-quantum cryptographic frameworks and the development of resilient secure communication systems. The results demonstrate that one-way functions remain indispensable theoretical and practical components for maintaining confidentiality, integrity, authentication, and trust in modern digital infrastructures.
References
[1] William Stallings, Cryptography and Network Security: Principles and Practice, Pearson Education, 2017.
[2] Oded Goldreich, Foundations of Cryptography, Cambridge University Press, 2001.
[3] Whitfield Diffie and Martin Hellman, “New Directions in Cryptography,” IEEE Transactions on Information Theory, vol. 22, no. 6, pp. 644–654, 1976.
[4] Ronald L. Rivest, Adi Shamir, and Leonard Adleman, “A Method for Obtaining Digital Signatures and Public-Key Cryptosystems,” Communications of the ACM, vol. 21, no. 2, pp. 120–126, 1978.
[5] Peter W. Shor, “Algorithms for Quantum Computation: Discrete Logarithms and Factoring,” Proceedings of the 35th Annual Symposium on Foundations of Computer Science, 1994.
[6] Daniel J. Bernstein, Johannes Buchmann, and Erik Dahmen, Post-Quantum Cryptography, Springer, 2009.
[7] Jonathan Katz and Yehuda Lindell, Introduction to Modern Cryptography, CRC Press, 2020.
[8] Michael Sipser, Introduction to the Theory of Computation, Cengage Learning, 2012.
[9] Alfred J. Menezes, Paul C. van Oorschot, and Scott A. Vanstone, Handbook of Applied Cryptography, CRC Press, 1996.
[10] Neal Koblitz, A Course in Number Theory and Cryptography, Springer, 1994.
[11] National Institute of Standards and Technology (NIST), Secure Hash Standard (SHS), FIPS PUB 180-4, 2015.
[12] Alex Biryukov, Daniel Dinu, and Dmitry Khovratovich, “Argon2: The Memory-Hard Function for Password Hashing and Other Applications,” 2016.
[13] National Institute of Standards and Technology (NIST), Post-Quantum Cryptography Standardization, 2024.
[14] Christof Paar and Jan Pelzl, Understanding Cryptography, Springer, 2010.
[15] Jean-Philippe Aumasson, Serious Cryptography: A Practical Introduction to Modern Encryption, No Starch Press, 2017.