Nathan: What is RSA, how does it work, what are its vulnerabilities?
So what exactly is RSA encryption? RSA, or Rivest-Shamir-Adleman, its creators, is "a public-key cryptosystem that allows us to encrypt messages between two communicating parties so that an eavesdropper who overhears the encrypted messages will not be able to decode them" (Cormen). A public-key cryptosystem also allows for a party to send a digital signature along with their message. This signature loses its validity if any bit of the message is changed which provides authentication of both the message and the sender. This makes RSA encryption the perfect tool for authenticating any electronic communications.
Each party in a public-key cryptosystem has both a public key and a secret key.
Keshav:
Victor:
- Introduction
// TODO
David:
Here are APA citations for several possible sources. We don't need to use all of them but any of them could be useful, especially for comparing the quantum situation with classical and post-quantum. Manin & Zilber includes discussion of both quantum logic as a broader topic, and the character of Shor's quantum algorithm for prime factorization and how it fundamentally changed the security situation for public-key systems that rely on factoring being inefficient. Aaronson has a lot of interesting and more intuitive discussions about both theory and practical problems like quantum computers and the potential dangers they pose, and separating hype from what could feasibly happen. Garey & Johnson has a long list of NP-complete problems across different areas of math and computer science that could be interesting for comparison across topics. Cormen et al, could be a good reference for parts of the classical domain, especially RSA and related public-key systems.
Aaronson, S. (2013). Quantum computing since Democritus. Cambridge University Press.
Beltrametti, E. G. & Cassinelli, G. (1981). The logic of quantum mechanics (Peter A. Carruthers, Ed.). Addison-Wesley
Publishing Company.
Bengtsson, I. & Życzkowski, K. (2017). Geometry of quantum states: An introduction to quantum entanglement (2nd ed.).
Cambridge University Press.
Cormen, T. H., Leiserson, C. E., Rivest, R. L., & Stein, C. (2009). Introduction to algorithms (3rd ed.). MIT Press.
Garey, R. G. & Johnson, D. S. (1979). Computers and intractability: A guide to the theory of NP-completeness. W. H. Freeman
and Company.
Hughes, R. I. G. (1989). The structure and interpretation of quantum mechanics. Harvard University Press.
Jordan, T. F. (1986). Quantum mechanics in simple matrix form. Dover Publications.
Kitaev, A. Y., Shen, A. H., & Vyalyi, M. N. (2002). Classical and quantum computation. American Mathematical Society.
Manin, Y. I. & Zilber, B. (2010). A course in mathematical logic for mathematicians (2nd ed.). Springer.
Peres, A. (2002). Quantum theory: Concepts and methods. Kluwer Academic Publishers.
Pierce, J. R. (1980). An introduction to information theory: Symbols, signals and noise (2nd ed.). Dover
Publications.
Sipser, M. (2013). Introduction to the theory of computation (3rd ed.). Cengage Learning.
von Neumann, J. (1955). Mathematical foundations of quantum mechanics. (R. T. Beyer, Trans.). Princeton University Press.
- Victor: sources summary
ir.inflibnet.ac.in:8080/ir/bitstream/1944/212/3/03cali_43.pdf https://www.geeksforgeeks.org/classical-cryptography-and-quantum-cryptography/amp/ https://thetechbrook.com/quantum-ethics/ https://link.springer.com/content/pdf/10.1007/s10676-017-9439-z.pdf https://onlinelibrary.wiley.com/doi/epdf/10.1002/9781119795667.ch2 https://www.quantropi.com/differences-between-classical-quantum-post-quantum-cryptography/#:~:text=Classical%20cryptography%20uses%20difficult%20mathematical,and%20can%20withstand%20quantum%20attacks. https://medium.com/edge-elections/cryptography-conventional-quantum-post-quantum-9f7f4ec84732 https://link.springer.com/chapter/10.1007/978-3-540-88702-7_1 https://arxiv.org/pdf/1804.00200.pdf
