Multivariate Cryptography is a family of public key cryptosystems. Multivariate cryptography is the generic term for asymmetric cryptographic primitives based on multivariate polynomials over finite fields. Multivariate polynomials could be defined over both ground field and extension field. The degree two polynomials can be called as multivariate quadratics. Multivariate cryptography thus called, Multivariate quadratics can be used to build signatures.

Features of Multivariate Cryptography

  • Multivariate quadratics involves public key and private key. Signatures are generated by the private key and verified using the public key.
  • The private key consists of transformations such as S, P’, T, where P’ maps elements from GFn –> GFm. S
  • In Multivariate Cryptography, P’ is the private transformation.
  • The transformations involved in the Multivariate Cryptography are invertible.
  • The public key results by linking the private transformation as P=S.P’.T.
  • The Multivariate polynomials can be solved by Grobner computational methods and with the help of other computer algebra softwares such as MAGMA and MAPLE.
  • Multivariate cryptography is more persistent and easy as it in involves polynomials and mathematical computation methods.

Applications of Multivariate Cryptography

  • Multivariate cryptography is used in attacking RSA variants.
  • It is used to provide security and authentication to signatures.
  • Multiple encryptions are possible with the help of multivariate cryptography.
  • Multivariate cryptography found many applications in public-key cryptography

Open Problems in Multivariate Cryptography

  • The statistical approach of designing block ciphers and hash functions by multivariate cryptography is immune to statistical attacks, which are based on probabilistic characteristics.
  • Designing of block ciphers and hash functions by Multivariate cryptography using algebraic approach involves complexity.
  • Boolean approach of solving multivariate polynomials involves decoding Reed-Muller codes.
  • The output of multivariate cryptography is in the form of key bits which is easily disposed by the attacker.