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Weak-Keys in Public Key Cryptosystems Based on Discrete Logarithms 被引量:1

Weak-Keys in Public Key Cryptosystems Based on Discrete Logarithms
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摘要 The discrete logarithm method is the foundation of many public key algorithms. However, one type of key, defined as a weak-key, reduces the security of public key cryptosystems based on the discrete logarithm method. The weak-key occurs if the public key is a factor or multiple of the primitive element, in which case the user's private key is not needed but can be obtained based on the character of the public key. An algorithm is presented that can easily test whether there is a weak-key in the cryptosystem. An example is given to show that an attack can be completed for the Elgamal digital signature if a weak-key exists, therefore validating the danger of weak-keys. Methods are given to prevent the generation of these weak-keys. The discrete logarithm method is the foundation of many public key algorithms. However, one type of key, defined as a weak-key, reduces the security of public key cryptosystems based on the discrete logarithm method. The weak-key occurs if the public key is a factor or multiple of the primitive element, in which case the user's private key is not needed but can be obtained based on the character of the public key. An algorithm is presented that can easily test whether there is a weak-key in the cryptosystem. An example is given to show that an attack can be completed for the Elgamal digital signature if a weak-key exists, therefore validating the danger of weak-keys. Methods are given to prevent the generation of these weak-keys.
出处 《Tsinghua Science and Technology》 SCIE EI CAS 2005年第5期579-581,共3页 清华大学学报(自然科学版(英文版)
基金 Supported by the National Key Basic Research and Development (973) Program (No. 2003CB314805) and the National Natural Science Foundation of China (No. 90304014)
关键词 discrete logarithm public key cryptography weak-key Elgamal digital signature discrete logarithm public key cryptography weak-key Elgamal digital signature
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同被引文献7

  • 1[1]T ElGamal.A public-key cryptosystem and a signature scheme based on discrete logarithms[J].Advanced in Cryptology CRYPTO'84 Proceedings,1985,2(4):10-18.
  • 2[3]Daniel,Bleichenbacher.Generating ElGamal signatures without knowing the secret key[EB/OL].http://citeseer.nj.nec.com/bleichenbacher96generating.html,1996-08-16.
  • 3[4]C P Schnorr.Security of Almost ALL Discrete Log Bits[EB/OL].http://citeseer.nj.nec.com/schnon98security.html,1998-03-10.
  • 4[5]Lim Chae Hoon,Lee Pil Joong.A Key Recovery Attack on Discrete Log-based Schemes Using a Prime Order Subgroup[EB/OL].http://citeseer.nj.nec.com/lim97key.html,1997-05-06.
  • 5[6]Tsiounis Yiannis,Yung Moti.On the Security of ElGamal based Encryption[EB/OL].http://citeseer.nj.nec.com/tsiounis98security.html,1998-10-11.
  • 6[7]Claus Peter,Schnorr,Markus Jakobsson.Security of Signed ElGamal IEncryption[EB/OL].http://citeseer.nj.nec.com/387410.html,2000-02-16.
  • 7冯登国 裴定一.密码学导引[M].北京:科学出版社,2001..

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