# 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.

#### Supplemental Video

#### Topics from this paper

#### 3,117 Citations

A public-key cryptosystem based on second order linear sequences

- Computer Science
- 2008

Based on Lucas functions, an improved version of the Diffie-Hellman distribution key scheme and to the ElGamal public key cryptosystem scheme are proposed, together with an implementation and… Expand

A Publicly Verifiable Authenticated Encryption Scheme Based on Factoring and Discrete Logarithms

- Computer Science
- Int. J. Netw. Secur.
- 2017

It is pointed out that even if either factoring or discrete logarithms is broken, this scheme still could keep the authentication, integration, and confidentiality of the message. Expand

Improved digital signature scheme based on factoring and discrete logarithms

- Mathematics
- 2002

Abstract Recently, He proposed a new digital signature scheme based on factoring and discrete logarithms. In this article, we propose an improvement of He’s digital signature scheme. Our scheme is… Expand

Public-Key Cryptosystems from Lattice Reduction Problems

- Computer Science, Mathematics
- CRYPTO
- 1996

A new proposal for a trapdoor one-way function, from which the security of the new construction is based on the conjectured computational difficulty of lattice-reduction problems, providing a possible alternative to existing public-key encryption algorithms and digital signatures such as RSA and DSS. Expand

A Practical Public Key Cryptosystem Provably Secure Against Adaptive Chosen Ciphertext Attack

- Computer Science
- CRYPTO
- 1998

A new public key cryptosystem is proposed and analyzed. The scheme is quite practical, and is provably secure against adaptive chosen ciphertext attack under standard intractability assumptions.… Expand

A Public Key Cryptosystem Based on Block Upper Triangular Matrices

- Mathematics
- 2005

We propose a public key cryptosystem based on block upper triangular matrices. This system is a variant of the Discrete Logarithm Problem with elements in a finite group, capable of increasing the… Expand

A General Construction of IND-CCA2 Secure Public Key Encryption

- Computer Science
- IMACC
- 2003

A general construction for public key encryption schemes that are IND-CCA2 secure in the random oracle model and it is shown that the scheme proposed in [1,2] fits the general framework and that the method of analysis leads to a more efficient security reduction. Expand

A new public key cryptosystem based on polynomials over finite fields GF ( 2 )

- 2014

In this paper a new public key system based on polynomials over fields GF (2) is developed. The security of the system is based on the difficulty of finding discrete logarithms over GF (2) with… Expand

Improved Public Key Cryptosystems Secure against Chosen Ciphertext Attacks

- Computer Science
- 1994

This short note describes an improvement to the rst two of the three public key cryptosystems proposed by Zheng and Seberry which are provably secure against chosen ciphertext attacks The improvement… Expand

A new digital signature scheme based on factoring and discrete logarithms

- Mathematics, Computer Science
- Int. J. Comput. Math.
- 2004

A new digital signature scheme based on the difficulty of simultaneously factoring a composite number and computing discrete logarithms is proposed, which each user uses common arithmetic moduli and only owns one private key and one public key. Expand

#### References

SHOWING 1-10 OF 11 REFERENCES

A method for obtaining digital signatures and public-key cryptosystems

- Computer Science
- CACM
- 1983

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 important… Expand

An efficient signature scheme based on quadratic equations

- Mathematics, Computer Science
- STOC '84
- 1984

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.)

- Mathematics, Computer Science
- IEEE Trans. Inf. Theory
- 1978

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

- Computer Science
- IEEE Trans. Inf. Theory
- 1976

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

- Mathematics, Computer Science
- EUROCRYPT
- 1984

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)

- Mathematics
- 1985

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 computing… Expand

A subexponential-time algorithm for computing discrete logarithms over GF(p2)

- Computer Science
- IEEE Trans. Inf. Theory
- 1985

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

- Mathematics, Computer Science
- CRYPTO
- 1983

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

- Computer Science
- 20th Annual Symposium on Foundations of Computer Science (sfcs 1979)
- 1979

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

- Mathematics, Computer Science
- IEEE Trans. Inf. Theory
- 1984

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