### 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 [16]. 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 [7] 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.

Original language | English |
---|---|

Pages (from-to) | 614-619 |

Number of pages | 6 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E83-A |

Issue number | 4 |

Publication status | Published - 2000 |

Externally published | Yes |

### Fingerprint

### Keywords

- Linear congruential generator
- Pseudorandom number generator
- The ElGamal cryptosystem

### ASJC Scopus subject areas

- Signal Processing
- Computer Graphics and Computer-Aided Design
- Applied Mathematics
- Electrical and Electronic Engineering

### Cite this

**A theory of randomness for public key cryptosystems : The ElGamal cryptosystem case.** / Koshiba, Takeshi.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - A theory of randomness for public key cryptosystems

T2 - The ElGamal cryptosystem case

AU - Koshiba, Takeshi

PY - 2000

Y1 - 2000

N2 - 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 [16]. 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 [7] 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.

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 [16]. 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 [7] 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.

KW - Linear congruential generator

KW - Pseudorandom number generator

KW - The ElGamal cryptosystem

UR - http://www.scopus.com/inward/record.url?scp=0033686969&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033686969&partnerID=8YFLogxK

M3 - Article

VL - E83-A

SP - 614

EP - 619

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

SN - 0916-8508

IS - 4

ER -