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Trapdoor one-way functions on elliptic curves and their application to shorter signatures and asymmetric encryption

  • US 20060140400A1
  • Filed: 11/14/2005
  • Published: 06/29/2006
  • Est. Priority Date: 11/11/2004
  • Status: Active Grant
First Claim
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1. A cryptographic system operating on an elliptic curve E of order n, said cryptosystem having an endomorphism [z] corresponding to a quadratic algebraic integer z that has the form z2+uz+v=0, where u and v are secret integers, and v is relatively prime to n;

  • a public key operation to apply said endomorphism [z] to cryptographic data x to obtain modified data x′

    ; and

    a private key operation to apply [−

    w][u]+[z] to said modified data x′

    in order to obtain said data x, where w is an integer and wv=1 mod n.

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