Abstract
We present a brief introduction to post-quantum cryptography. This note introduces the concept of post-quantum cryptography, discusses its importance and provides a short overview of the mathematical techniques that are currently used to develop this field.
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References
Goldreich O (2000) Foundations of cryptography: basic tools. Cambridge University Press, New York
Shor PW (1994) Algorithms for quantum computation: discrete logarithms and factoring. In: 35th annual symposium on foundations of computer science, Santa Fe, New Mexico, USA, 20–22 Nov 1994, pp 124–134
Chen L, Jordan S, Liu YK, Moody D, Peralta R, Perlner R, Smith-Tone D. Report on post-quantum cryptography. https://nvlpubs.nist.gov/nistpubs/ir/2016/nist.ir.8105.pdf
Ajtai M (1996) Generating hard instances of lattice problems (extended abstract). In: Proceedings of the twenty-eighth annual ACM symposium on theory of computing, STOC ’96
Matsumoto T, Imai H (1988) Public quadratic polynomial-tuples for efficient signature-verification and message-encryption. In: Advances in cryptology — EUROCRYPT ’88. Springer, Berlin, Heidelberg, pp 419–453
Bardet M, Faugere JC, Salvy B, Spaenlehauer PJ (2013) On the complexity of solving quadratic boolean systems. J Complex 29(1):53–75. https://doi.org/10.1016/j.jco.2012.07.001. http://www.sciencedirect.com/science/article/pii/S0885064X12000611
Wolf C (2005) Multivariate quadratic polynomials in public key cryptography. PhD thesis, Katholieke Universiteit Leuven
Ding J, Yang BY (2009) Multivariate public key cryptography. Springer, Berlin, pp 193–241
Patarin J (1996) Hidden fields equations (hfe) and isomorphisms of polynomials (ip): two new families of asymmetric algorithms. In: Maurer U (ed) Advances in cryptology — EUROCRYPT ’96
Kipnis A, Patarin J, Goubin L (1999) Unbalanced oil and vinegar signature schemes. In: Stern J (ed) Advances in cryptology — EUROCRYPT ’99
Hashimoto Y (2018) Multivariate public key cryptosystems. In: Mathematical modelling for next-generation cryptography. Springer, pp 17–42
McEliece RJ (1978) A Public-key cryptosystem based on algebraic coding theory. Deep space network progress report, vol 44, pp 114–116
Overbeck R, Sendrier N (2009) Code-based cryptography
Merkle R (1979) Secrecy, authentication and public key systems/a certified digital signature. PhD thesis, Stanford University
Peikert C (2016) A decade of lattice cryptography 10:283–424
Ajtai M, Dwork C (1997) A public-key cryptosystem with worst-case/average-case equivalence. In: Proceedings of the twenty-ninth annual ACM symposium on theory of computing. ACM, pp 284–293
Goldreich O, Goldwasser S, Halevi S (1997) Public-key cryptosystems from lattice reduction problems. In: Annual international cryptology conference. Springer, pp 112–131
Regev O (2004) New lattice-based cryptographic constructions. J ACM (JACM) 51(6):899–942
Micciancio D, Regev O (2004) Worst-case to average-case reductions based on gaussian measures. SIAM J Comput (SICOMP) 37(1):267–302. Extended abstract in FOCS 2004
Gentry C, Peikert C, Vaikuntanathan V (2008) Trapdoors for hard lattices and new cryptographic constructions. In: STOC, pp 197–206
Micciancio D, Peikert C (2013) Hardness of sis and lwe with small parameters. In: Crypto
Regev O (2009) On lattices, learning with errors, random linear codes, and cryptography. J ACM 56(6). Extended abstract in STOC’05
Lyubashevsky V, Peikert C, Regev O (2010) On ideal lattices and learning with errors over rings. In: EUROCRYPT, vol 6110
Peikert C (2009) Public-key cryptosystems from the worst-case shortest vector problem. In: STOC, pp 333–342
Brakerski Z, Langlois A, Peikert C, Regev O, Stehlé D (2013) Classical hardness of learning with errors. In: Proceedings of the forty-fifth annual ACM symposium on theory of computing, STOC ’13. ACM
Hoffstein J, Pipher J, Silverman JH (1998) Ntru: a ring-based public key cryptosystem. In: Buhler JP (ed) Algorithmic number theory: third international symposium, ANTS-III Portland, Oregon, USA, 21–25 June 998, Proceedings
Stehlé D, Steinfeld R (2011) Making ntru as secure as worst-case problems over ideal lattices. In: Proceedings of the 30th annual international conference on theory and applications of cryptographic techniques: advances in cryptology, EUROCRYPT’11
López-Alt A, Tromer E, Vaikuntanathan V (2012) On-the-fly multiparty computation on the cloud via multikey fully homomorphic encryption. In: Proceedings of the forty-fourth annual ACM symposium on theory of computing, STOC ’12
Barak B, Dodis Y, Krawczyk H, Pereira O, Pietrzak K, Standaert FX, Yu Y (2011) Leftover hash lemma, revisited. In: Annual cryptology conference. Springer, pp 1–20
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Agrawal, S. (2020). Post-quantum Cryptography: An Introduction. In: Shukla, S., Agrawal, M. (eds) Cyber Security in India. IITK Directions, vol 4. Springer, Singapore. https://doi.org/10.1007/978-981-15-1675-7_10
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DOI: https://doi.org/10.1007/978-981-15-1675-7_10
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