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
Il existe de nombreux systèmes de cryptographie à clé publique qui nécessitent des entrées aléatoires pour chiffrer les messages et leur sécurité est toujours discutée en supposant que les objets aléatoires sont idéalement générés. Puisque les cryptosystèmes fonctionnent sur des ordinateurs, il est tout à fait naturel que ces objets aléatoires soient générés informatiquement. Une solution théorique est l'utilisation de générateurs pseudo-aléatoires au sens de Yao. De manière informelle, les générateurs pseudo-aléatoires sont des algorithmes en temps polynomial dont les sorties sont impossibles à distinguer informatiquement de la distribution uniforme. Puisque si nous utilisons les générateurs de Yao, il faut beaucoup plus de temps pour générer des objets pseudo-aléatoires que pour chiffrer des messages dans des cryptosystèmes à clé publique, nous assouplissons les conditions des générateurs pseudo-aléatoires pour les adapter aux cryptosystèmes à clé publique et donnons une exigence minimale pour les générateurs pseudo-aléatoires dans les cryptosystèmes à clé publique. . A titre d'exemple, nous discutons de la sécurité du cryptosystème ElGamal avec certains générateurs bien connus (par exemple, le générateur congruentiel linéaire). Nous proposons également un nouveau générateur de nombres pseudo-aléatoires, pour les entrées aléatoires du cryptosystème ElGamal, qui satisfait à l'exigence minimale. Le générateur nouvellement proposé est basé sur le générateur congruentiel linéaire. Nous montrons des preuves que le cryptosystème ElGamal avec le générateur proposé est sécurisé.
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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},}
Copier
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 -