A public key cryptosystem and a signature scheme based on discrete logarithms

@article{Gamal1985APK,
  title={A public key cryptosystem and a signature scheme based on discrete logarithms},
  author={Taher El Gamal},
  journal={IEEE Trans. Inf. Theory},
  year={1985},
  volume={31},
  pages={469-472}
}
A new signature scheme is proposed, together with an implementation of the Diffie-Hellman key distribution scheme that achieves a public key cryptosystem. The security of both systems relies on the difficulty of computing discrete logarithms over finite fields. 
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References

SHOWING 1-10 OF 11 REFERENCES
A method for obtaining digital signatures and public-key cryptosystems
An encryption method is presented with the novel property that publicly revealing an encryption key does not thereby reveal the corresponding decryption key. This has two importantExpand
An efficient signature scheme based on quadratic equations
TLDR
A novel property of the new signature scheme is that legitimate users can choose k in such a way that they can sign messages even without knowing the factorization of n, and thus everyone can use the same modulus if no one knows its factorization. Expand
An improved algorithm for computing logarithms over GF(p) and its cryptographic significance (Corresp.)
TLDR
An improved algorithm is derived which requires O =(\log^{2} p) complexity if p - 1 has only small prime factors and such values of p must be avoided in the cryptosystem. Expand
New directions in cryptography
TLDR
This paper suggests ways to solve currently open problems in cryptography, and discusses how the theories of communication and computation are beginning to provide the tools to solve cryptographic problems of long standing. Expand
Discrete Logarithms in Finite Fields and Their Cryptographic Significance
  • A. Odlyzko
  • Mathematics, Computer Science
  • EUROCRYPT
  • 1984
TLDR
This paper surveys and analyzes known algorithms in this area, with special attention devoted to algorithms for the fields GF(2n), finding that in order to be safe from attacks using these algorithms, the value of n for which GF( 2n) is used in a cryptosystem has to be very large and carefully chosen. Expand
A subexponential-time algorithm for computing discrete logarithms over GF(p^2)
An algorithm for computing discrete logarithms over GF (p^{2}) , where p is a prime, in subexponential time is described. The algorithm is similar to the Merkle-Adleman algorithm for computingExpand
A subexponential-time algorithm for computing discrete logarithms over GF(p2)
TLDR
An algorithm for computing discrete logarithms over GF(p*), where p is a prime, in subexponential time is described, which uses quadratic fields as the appropriate algebraic structure. Expand
Signatures through Approximate Representation by Quadratic Forms
TLDR
A signature scheme where the private key is a random (n, n)-matrix T with coefficients in ℤm/mℤ, m a product of two large primes, which is faster than the RSA-scheme and knowledge of this prime decomposition enables forging signatures. Expand
A subexponential algorithm for the discrete logarithm problem with applications to cryptography
  • L. Adleman
  • Computer Science
  • 20th Annual Symposium on Foundations of Computer Science (sfcs 1979)
  • 1979
TLDR
A new algorithm is presented for the Discrete Logarithm Problem which runs in RTIME better than O(qE) for all E > O and the most efficient incarnation of this algorithm runs inRTIME O(2(O(/10g(q)loglog(q))). Expand
Fast evaluation of logarithms in fields of characteristic two
  • D. Coppersmith
  • Mathematics, Computer Science
  • IEEE Trans. Inf. Theory
  • 1984
TLDR
The ideas give a dramatic improvement even for moderate-sized fields such as GF (2^{127}) , and make (barely) possible computations in fields of size around 2^{400} . Expand
...
1
2
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