A theory of randomness for public key cryptosystems: The ElGamal cryptosystem case

Takeshi Koshiba*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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 languageEnglish
Pages (from-to)614-619
Number of pages6
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number4
Publication statusPublished - 2000 Jan 1
Externally publishedYes


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

ASJC Scopus subject areas

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


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