Okamoto-Uchiyama 확률 공개키 암호 방식의 효율성 개선

Improvement of Okamoto-Uchiyama Probabilistic Public Key Cryptosystem

  • 최덕환 (성균관대학교 전기전자 및 컴퓨터공학과) ;
  • 김현주 (성균관대학교 전기전자 및 컴퓨터공학과) ;
  • 최승복 ((주)퓨쳐시스템 암호체계센터) ;
  • 원동호 (성균관대학교 전기전자 및 컴퓨터공학과)
  • Choi, Duk-Hwan (Dept.of Electric Electronics Computer Engineering, Sungkyunkwan University) ;
  • Kim, Hyun-Jue (Dept.of Electric Electronics Computer Engineering, Sungkyunkwan University) ;
  • Choi, Seung-Bok (Password System Center, Future System) ;
  • Won, Dong-Ho (Dept.of Electric Electronics Computer Engineering, Sungkyunkwan University)
  • 발행 : 2002.08.01

초록

본 논문은 Okamoto와 Uchiyama가 이산대수 함수만으로 일방향함수를 정의하여 제안한 새로운 확률 공개키 암호 방식을 개선하였다. 평문은 이들 두 이산대수 함수의 모듈라 곱으로부터 구할 수 있는데 두 함수 값 중에서 하나는 주어진 공개키에 종속된 고정된 값을 가진다. 고정된 함수 값이 단위원 1을 갖는 정선된 공개키에 의해 개선이 이루어진다. 왜냐하면 복호화 할 때 계산량을 줄일 수 있기 때문이다. 또한 이러한 성질을 충족하는 공개키를 얻을 수 있는 구체적 방법도 제시한다.

We improve a new probabilistic public key cryptosystem, in which the one wav function was defined only on the discrete logarithmic functions, proposed by Okamoto and Uchiyama. The plaintexts are calculated from the modular product of two these functions, one of which has a fixed value depending on a given public key. The improvement is achieved by a well-chosen public key assuming an unit element 1 as the fixed function value. Because it is possible to reduce the number of operations at the decryption. Also the concrete method for a public key of our improved scheme is suggested.

키워드

참고문헌

  1. W. Diffe and M. Hellman, New Direction in Cryptography IEEE Tranctions on Information Theory, Vol. IT-22(6), pp. 644-654, 1976 https://doi.org/10.1109/TIT.1976.1055638
  2. M. Rabin, Digitalized Signatures and Public Key Functions as Intractable as Factorization MIT Laboratory for Computer Science TR-212, 1979
  3. S. Goldwasser and S. Micali, Probabilistic Encryption JCSS, 28, 2, pp. 270-299. 1984 https://doi.org/10.1016/0022-0000(84)90070-9
  4. D. Dolve, C. Dwork, and M. Naor, Non-malleable Cryptography Proc. of the 23rd STOC. ACM Press, New York, 1991 https://doi.org/10.1145/103418.103474
  5. M. Bellare, A. Desai, D. Pointcheval and P. Rogaway, Relations Among Notions of Security for Public-Key Encryption Schemes Advances in cryptology-Proc. of CRYPTO'98, Lecture Notes in Computer Science, Vol. 1462, pp. 26-35, Springer-Verlag. 1998 https://doi.org/10.1007/BFb0055718
  6. T. Okamoto and S. Uchiyama, A New Public-Key Cryptosystem as secure as Factoring Proc. of EUROCRYPTO'98, pp. 309-318. 1998
  7. T. Okamoto and D. Pointcheval, Efficient Public-Key Encryption (ver. 3) Submission to P1363a, available on http://grouper.ieee.org/groups/1363/submission.html. 2000
  8. P. Paillier, Public-Key Cryptosystems Based on Composite Degree Rediduosity Classes Proc. of EUROCRYPTO'99, LNCS 1592, pp. 223-238. 1999
  9. P. Paillier and D. Pointcheval, Efficient Public-Key Cryptosystems Provably Secure Against Active Adversaries Proc. of ASIACRYPT'99, LNCS 1716, pp. 165-179. 1999