Abstract
Recall that a cryptosystem consists of a 1-to-1 enciphering transformation f from a set p of all possible plaintext message units to a set C of all possible ciphertext message units. Actually, the term “cryptosystem” is more often used to refer to a whole family of such transformations, each corresponding to a choice of parameters (the sets P and C, as well as the map f, may depend upon the values of the parameters).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
References for § IV.1
M. Blum, “Coin-flipping by telephone — a protocol for solving impossible problems,” IEEE Proc., Spring Compcon., 133–137.
W. Diffie and M. E. Hellman, “New directions in cryptography,” IEEE Transactions on Information Theory IT-22 (1976), 644–654.
D. Chaum, “Achieving electronic privacy,” Scientific American, 267 (1992), 96–101.
S. Goldwasser, “The search for provably secure cryptosystems,” Cryptology and Computational Number Theory, Proc. Symp. Appl. Math. 42 (1990), 89–113.
M. E. Hellman, “The mathematics of public-key cryptography,” Scientific American, 241 (1979), 146–157.
E. Kranakis, Primality and Cryptography, John Wiley & Sons, 1986.
R. Rivest, “Cryptography,” Handbook of Theoretical Computer Science, Vol. A, Elsevier, 1990, 717–755.
G. Ruggiu, “Cryptology and complexity theories,” Advances in Cryptology, Proceedings of Eurocrypt 84, Springer-Verlag, 1985, 3–9.
References for § IV.2
L. M. Adleman, R. L. Rivest and A. Shamir,“A method for obtaining digital signatures and public-key cryptosystems,” Communications of the ACM, 21 (1978), 120–126.
R. L. Rivest, “RSA chips (past/present/future),” Advances in Cryptology, Proceedings of Eurocrypt 84, Springer, 1985, 159–165.
J. A. Gordon, “Strong primes are easy to find,” Advances in Cryptology, Proceedings of Eurocrypt 84, Springer, 1985, 216–223.
References for § IV.3
L. M. Adleman, “A subexponential algorithm for the discrete logarithm problem with applications to cryptography,” Proc. 20th Annual Symposium on the Foundations of Computer Science (1979), 55–60.
L. M. Adleman and J. DeMarrais, “A subexponential algorithm for discrete logarithms over all finite fields,” Math. comp. 61 (1993), 1–15.
D. Coppersmith, “Fast evaluation of logarithms in fields of characteristic two,” IEEE Transactions on Information Theory IT-30 (1984), 587–594.
D. Coppersmith, A. Odlyzko, and R. Schroeppel, “Discrete logarithms in GF(p),” Algorithmica 1 (1986), 1–15.
W. Diffie and M. E. Hellman, “New directions in cryptography,” IEEE Transactions on Information Theory IT-22 (1976), 644–654.
T. ElGamal, “A public key cryptosystem and a signature scheme based on discrete logarithms,” IEEE Transactions on Information Theory IT-31, (1985), 469–472.
T. ElGamal, “A subexponential-time algorithm for computing discrete logarithms over GF(p 2),” IEEE Transactions on Information Theory IT-31 (1985), 473–481.
M. Fellows and N. Koblitz, “Fixed-parameter complexity and cryptography,” Proc. Tenth Intern. Symp. Appl. Algebra, Algebraic Algorithms and Error Correcting Codes (San Juan, Puerto Rico), 1993.
D. Gordon, “Discrete logarithms in GF(p) using the number field sieve,” SIAM J. Discrete Math. 6 (1993), 124–138.
D. Gordon and K. McCurley, “Massively parallel computation of discrete logarithms,” Advances in Cryptology — Crypto ′92, Springer-Verlag, 1993.
D. E. Knuth, The Art of Computer Programming, Vol. II, Addison-Wesley, 1973.
B. LaMacchia and A. Odlyzko, “Computation of discrete logarithms in prime fields,” Designs, Codes and Cryptography 1 (1991), 47–62.
J. L. Massey, “Logarithms in finite cyclic groups — cryptographic issues,” Proc. 4th Benelux Symposium on Information Theory (1983), 17–25.
K. McCurley, “The discrete logarithm problem,” Cryptology and Computational Number Theory, Proc. Symp. Appl. Math. 42 (1990), 49–74.
A. M. Odlyzko, “Discrete logarithms in finite fields and their cryptographic significance,” Advances in Cryptology, Proc. Eurocrypt 84, Springer, 1985, 224–314.
P. K. S. Wah and M. Z. Wang, “Realization and application of the Massey-Omura lock,” Proc. International Zürich Seminar (1984), 175–182.
References for § IV.4
E. Brickell, “Breaking iterated knapsacks,” Advances in Cryptology — Crypto ′84, Springer-Verlag, 1985, 342–358.
E. Brickell and A. Odlyzko, “Cryptanalysis: A survey of recent results,” Proc. IEEE 76 (1988), 578–593.
B. Chor and R. Rivest, “A knapsack-type public key cryptosystem based on arithmetic in finite fields,” Advances in Cryptology — Crypto ′84, Springer-Verlag, 1985, 54–65; revised version in IEEE Transactions on Information Theory IT-34 (1988), 901-909.
M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman, 1979.
R. M. F. Goodman and A. J. McAuley, “A new trapdoor knapsack public key cryptosystem,” Advances in Cryptography, Proc. Eurocrypt 84, Springer, 1985, 150–158.
M. E. Hellman, “The mathematics of public-key cryptography,” Scientific American 241 (1979), 146–157.
M. E. Hellman and R. C. Merkle, “Hiding information and signatures in trapdoor knapsacks,” IEEE Transactions on Information Theory IT-24 (1978), 525–530.
A. Odlyzko, “The rise and fall of knapsack cryptosystems,” Cryptology and Computational Number Theory, Proc. Symp. Appl. Math. 42 (1990), 75–88.
C. Schnorr, “Efficient identification and signatures for smart cards,” Advances in Cryptology — Crypto ′89, Springer-Verlag, 1990, 239–251.
A. Shamir, “A polynomial time algorithm for breaking the basic Merkle-Hellman cryptosystem,” Proc. 23rd Annual Symposium on the Foundations of Computer Science (1982), 145–152.
P. van Oorschot, “A comparison of practical public-key cryptosystems based on integer factorization and discrete logarithms,” in G. Simmons, ed., Contemporary Cryptology: The Science of Information Integrity, IEEE Press, 1992, 289–322.
References for § IV.5
M. Bellare and S. Micali, “Non-interactive oblivious transfer and applications,” Advances in Cryptology — Crypto ′89, Springer-Verlag, 547–557.
M. Ben-Or, O. Goldreich, S. Goldwasser, J. Håstad, J. Kilian, S. Micali, and P. Rogaway, “Everything provable is provable in zero-knowledge,” Advances in Cryptology — Crypto ′88, Springer-Verlag, 1990, 37–56.
M. Blum, P. Feldman, and S. Micali, “Non-interactive zero-knowledge proofs and their applications,” Proc. 20th ACM Symposium on the Theory of Computing (1988).
D. Chaum, J.-H. Evertse, J. van de Graaf, and R. Peralta, “Demonstrating possession of a discrete logarithm without revealing it,” Advances in Cryptology — Crypto ′86, Springer-Verlag, 1987, 200–212.
M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman, 1979.
S. Goldwasser, S. Micali, and C. Rackoff, “The knowledge complexity of interactive proof systems,” SIAM J. Computing 18 (1989), 186–208.
J. Kilian, “Founding cryptography on oblivious transfer,” Proc. 20th ACM Symposium on the Theory of Computing (1988), 20–31.
M. Rabin, “How to exchange secrets by oblivious transfer,” Technical Report TR-81, Aiken Computation Laboratory, Harvard University, 1981.
A. Shamir, “The search for provably secure identification schemes,” Proc. Intern. Cong. Math. (1986), 1488–1495.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media New York
About this chapter
Cite this chapter
Koblitz, N. (1994). Public Key. In: A Course in Number Theory and Cryptography. Graduate Texts in Mathematics, vol 114. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8592-7_4
Download citation
DOI: https://doi.org/10.1007/978-1-4419-8592-7_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6442-2
Online ISBN: 978-1-4419-8592-7
eBook Packages: Springer Book Archive