One-way functions are among the most fundamental concepts in modern cryptography and information security. These mathematical functions are characterized by the property that they are easy to compute in the forward direction but computationally infeasible to invert without additional secret information. The security of many cryptographic systems, including public-key encryption, digital signatures, authentication protocols, and hash functions, relies on the complexity of one-way functions. This article examines the theoretical foundations of one-way functions, their mathematical properties, classifications, and practical applications in cybersecurity. Furthermore, the paper discusses common examples such as modular exponentiation, integer factorization, discrete logarithm problems, and cryptographic hash functions. The importance of one-way functions in the development of post-quantum cryptography and secure communication systems is also analyzed. The study demonstrates that one-way functions remain a critical component for ensuring confidentiality, integrity, and authentication in modern digital infrastructures.
One-Way Functions and Their Role In Modern Cryptography
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References
William Stallings, Cryptography and Network Security: Principles and Practice, Pearson Education, 2017.
Oded Goldreich, Foundations of Cryptography, Cambridge University Press, 2001.
Whitfield Diffie and Martin Hellman, “New Directions in Cryptography,” IEEE Transactions on Information Theory, vol. 22, no. 6, pp. 644–654, 1976.
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.
Peter W. Shor, “Algorithms for Quantum Computation: Discrete Logarithms and Factoring,” Proceedings of the 35th Annual Symposium on Foundations of Computer Science, 1994.
Daniel J. Bernstein, Johannes Buchmann, and Erik Dahmen, Post-Quantum Cryptography, Springer, 2009.
Jonathan Katz and Yehuda Lindell, Introduction to Modern Cryptography, CRC Press, 2020.
Michael Sipser, Introduction to the Theory of Computation, Cengage Learning, 2012.
Alfred J. Menezes, Paul C. van Oorschot, and Scott A. Vanstone, Handbook of Applied Cryptography, CRC Press, 1996.
Neal Koblitz, A Course in Number Theory and Cryptography, Springer, 1994.
National Institute of Standards and Technology (NIST), Secure Hash Standard (SHS), FIPS PUB 180-4, 2015.
Alex Biryukov, Daniel Dinu, and Dmitry Khovratovich, “Argon2: The Memory-Hard Function for Password Hashing and Other Applications,” 2016.
National Institute of Standards and Technology (NIST), Post-Quantum Cryptography Standardization, 2024.
Christof Paar and Jan Pelzl, Understanding Cryptography, Springer, 2010.
Jean-Philippe Aumasson, Serious Cryptography: A Practical Introduction to Modern Encryption, No Starch Press, 2017.