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Welcome to the Cryptographic Primitives and Hard Problems in Cryptography wiki, the only existing exhaustive repository containing all known basic primitives and hard problems used in cryptography. Everyone can contribute to this project, but only after signing up and confirming your email address.

If you are unwilling to sign up, but still would like to contribute, it is possible to send your updates directly to the wikimaster (frederik.vercauteren at

Before you begin

The Wiki is divided into two parts. In the first part we examine basic cryptographic primitives, whereas the second part is on the hard mathematical problems. For the purposes of this Wiki a cryptographic primitive is defined as an abstract mathematical object which enables some cryptographic scheme/protocol to be constructed. This is in contrast to a concrete mathematical construction (i.e. a hard problem), or a cryptographic scheme/protocol/service (such as encryption or signatures).

One of the main goals of this wiki is to present the primitives and hard problems as uniformly as possible. It is therefore absolutely necessary to adhere to the following guidelines. If you think that these guidelines are unclear or incomplete, please contact the wikimaster.

Cryptographic Primitives

Currently we only have one category of cryptographic primitives, although this may change over time:

Hard Problems

The hard problems have been categorized into the following themes:

  • Discrete Logarithms: Hard problems related to the discrete logarithm problem in cyclic groups.
  • Factoring: Hard problems related to factoring.
  • Product Groups: Hard problems related to the discrete logarithm problem in direct products of cyclic groups.
  • Pairings: Hard problems related to pairings.
  • Lattices: Hard problems related to lattices.
  • Miscellaneous: Any problem that does not fit in the above. We will create new sub-domains if necessary.

Index of Hard Problems

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