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In cryptography, a cryptosystem is called a 'threshold cryptosystem', if in order to decrypt an encrypted message a number of parties exceeding a threshold is required to cooperate in the decryption protocol. The message is encrypted using a public key and the corresponding private key is shared among the participating parties. Let be the number of parties. Such a system is called (t,n)-threshold, if at least t of these parties can efficiently decrypt the ciphertext, while less than t have no useful information. Similarly it is possible to define (t,n)-threshold signature scheme, where at least t parties are required for creating a signature.

Threshold versions of encryption schemes can be built for many public encryption schemes. The natural goal of such schemes is to be as secure as the original scheme. Such threshold versions have been defined for:

  • RSA
  • Pallier cryptosystem
  • Damgård-Jurik cryptosystem [1][2]
  • El-Gamal

See also[]


  1. Ivan Damgård, Mads Jurik: A Length-Flexible Threshold Cryptosystem with Applications. ACISP 2003: 350-364
  2. Ivan Damgård, Mads Jurik: A Generalisation, a Simplification and Some Applications of Paillier's Probabilistic Public-Key System. Public Key Cryptography 2001: 119-136