Generalized powering functions and their application to digital signatures

Hisayoshi Sato, Tsuyoshi Takagi, Satoru Tezuka, Kazuo Takaragi

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


This paper investigates some modular powering functions suitable for cryptography. It is well known that the Rabin encryption function is a 4-to-1 mapping and breaking its one-wayness is secure under the factoring assumption. The previously reported encryption schemes using a powering function are variants of either the 4-to-1 mapping or higher n-to-1 mapping, where n > 4. In this paper, we propose an optimized powering function that is a 3-to-1 mapping using a p2q-type modulus. The one-wayness of the proposed powering function is as hard as the infeasibility of the factoring problem. We present an efficient algorithm for computing the decryption for a p 2q-type modulus, which requires neither modular inversion nor division. Moreover, we construct new provably secure digital signatures as an application of the optimized functions. In order to achieve provable security in the random oracle model, we usually randomize a message using random hashing or padding. However, we have to compute the randomization again if the randomized message is a non-cubic residue element - it is inefficient for long messages. We propose an algorithm that can deterministically find the unique cubic residue element for a randomly chosen element.

Original languageEnglish
Pages (from-to)81-89
Number of pages9
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number1
Publication statusPublished - 2006 Jan
Externally publishedYes


  • Digital signature
  • Factoring
  • Modular powering function
  • RSA

ASJC Scopus subject areas

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


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