The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Existem muitos sistemas criptográficos de chave pública que requerem entradas aleatórias para criptografar mensagens e sua segurança é sempre discutida assumindo que objetos aleatórios são idealmente gerados. Como os criptosistemas são executados em computadores, é bastante natural que esses objetos aleatórios sejam gerados computacionalmente. Uma solução teórica é o uso de geradores pseudoaleatórios no sentido de Yao. Dizendo informalmente, os geradores pseudoaleatórios são algoritmos de tempo polinomial cujas saídas são computacionalmente indistinguíveis da distribuição uniforme. Como se usarmos os geradores de Yao, levará muito mais tempo para gerar objetos pseudoaleatórios do que para criptografar mensagens em criptosistemas de chave pública, relaxamos as condições dos geradores pseudoaleatórios para caber em criptosistemas de chave pública e fornecemos um requisito mínimo para geradores pseudoaleatórios dentro de criptosistemas de chave pública. . Como exemplo, discutimos a segurança do criptossistema ElGamal com alguns geradores bem conhecidos (por exemplo, o gerador congruente linear). Propomos também um novo gerador de números pseudoaleatórios, para entradas aleatórias no criptosistema ElGamal, que satisfaça o requisito mínimo. O gerador recentemente proposto é baseado no gerador linear congruente. Mostramos algumas evidências de que o criptossistema ElGamal com o gerador proposto é seguro.
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Takeshi KOSHIBA, "A Theory of Randomness for Public Key Cryptosystems: The ElGamal Cryptosystem Case" in IEICE TRANSACTIONS on Fundamentals,
vol. E83-A, no. 4, pp. 614-619, April 2000, doi: .
Abstract: There are many public key cryptosystems that require random inputs to encrypt messages and their security is always discussed assuming that random objects are ideally generated. Since cryptosystems run on computers, it is quite natural that these random objects are computationally generated. One theoretical solution is the use of pseudorandom generators in the Yao's sense. Informally saying, the pseudorandom generators are polynomial-time algorithms whose outputs are computationally indistinguishable from the uniform distribution. Since if we use the Yao's generators then it takes much more time to generate pseudorandom objects than to encrypt messages in public key cryptosystems, we relax the conditions of pseudorandom generators to fit public key cryptosystems and give a minimal requirement for pseudorandom generators within public key cryptosystems. As an example, we discuss the security of the ElGamal cryptosystem with some well-known generators (e. g. , the linear congruential generator). We also propose a new pseudorandom number generator, for random inputs to the ElGamal cryptosystem, that satisfies the minimal requirement. The newly proposed generator is based on the linear congruential generator. We show some evidence that the ElGamal cryptosystem with the proposed generator is secure.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e83-a_4_614/_p
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@ARTICLE{e83-a_4_614,
author={Takeshi KOSHIBA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Theory of Randomness for Public Key Cryptosystems: The ElGamal Cryptosystem Case},
year={2000},
volume={E83-A},
number={4},
pages={614-619},
abstract={There are many public key cryptosystems that require random inputs to encrypt messages and their security is always discussed assuming that random objects are ideally generated. Since cryptosystems run on computers, it is quite natural that these random objects are computationally generated. One theoretical solution is the use of pseudorandom generators in the Yao's sense. Informally saying, the pseudorandom generators are polynomial-time algorithms whose outputs are computationally indistinguishable from the uniform distribution. Since if we use the Yao's generators then it takes much more time to generate pseudorandom objects than to encrypt messages in public key cryptosystems, we relax the conditions of pseudorandom generators to fit public key cryptosystems and give a minimal requirement for pseudorandom generators within public key cryptosystems. As an example, we discuss the security of the ElGamal cryptosystem with some well-known generators (e. g. , the linear congruential generator). We also propose a new pseudorandom number generator, for random inputs to the ElGamal cryptosystem, that satisfies the minimal requirement. The newly proposed generator is based on the linear congruential generator. We show some evidence that the ElGamal cryptosystem with the proposed generator is secure.},
keywords={},
doi={},
ISSN={},
month={April},}
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TY - JOUR
TI - A Theory of Randomness for Public Key Cryptosystems: The ElGamal Cryptosystem Case
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 614
EP - 619
AU - Takeshi KOSHIBA
PY - 2000
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E83-A
IS - 4
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - April 2000
AB - There are many public key cryptosystems that require random inputs to encrypt messages and their security is always discussed assuming that random objects are ideally generated. Since cryptosystems run on computers, it is quite natural that these random objects are computationally generated. One theoretical solution is the use of pseudorandom generators in the Yao's sense. Informally saying, the pseudorandom generators are polynomial-time algorithms whose outputs are computationally indistinguishable from the uniform distribution. Since if we use the Yao's generators then it takes much more time to generate pseudorandom objects than to encrypt messages in public key cryptosystems, we relax the conditions of pseudorandom generators to fit public key cryptosystems and give a minimal requirement for pseudorandom generators within public key cryptosystems. As an example, we discuss the security of the ElGamal cryptosystem with some well-known generators (e. g. , the linear congruential generator). We also propose a new pseudorandom number generator, for random inputs to the ElGamal cryptosystem, that satisfies the minimal requirement. The newly proposed generator is based on the linear congruential generator. We show some evidence that the ElGamal cryptosystem with the proposed generator is secure.
ER -