Patent ID: 7221758

Claim:
A computer-implemented method for generating a cryptographic key, comprising the steps of: choosing at least a first, second, and third exponent-number (w, x, z) as part of a private key, from a set Z q of elements modulo q, whereby q is preferably a large prime, (a.) choosing at least a first base-group-number (g 1 ) and a second base-group-number (g 2 ) from a cryptographic group (G), said second base-group-number (g 2 ) being derived from said first base-group-number (g 1 ) raised to the power of a first monotone function (ƒ 1 ) of said first exponent number (w); (b.) deriving from the chosen numbers (g 1 , g 2 , w, x, z) at least a first and a second group-number (c, h), said first group-number (c) being derivable from said first base-group-number (g 1 ) raised to the power of a second monotone function (ƒ 2 ) of said second exponent-number (x) and said second group-number (h) being derivable from said first base-group-number (g 1 ) raised to the power of a third monotone function (ƒ 3 ) of said third exponent-number (z); and (c.) making the chosen at least two base-group-numbers (g 1 , g 2 ) and said derived at least two group-numbers (c, h) part of a public key as public-key numbers (g 1 , g 2 , c, h), such that said public-key numbers (g 1 , g 2 , c, h) are usable as bases and at least a chosen single exponent-number (r) is usable as exponent together with a plaintext (m) for forming a ciphertext (t), comprising at least a first universal and second universal cipher-number (u 1 , u 2 ) and an encryption cipher-number (e) for applying the ElGamal scheme, said ciphertext (t) further comprising a verification cipher-number (v) with which said ciphertext (t) is verifiable, said ciphertext (t) being decryptable according to said ElGamal scheme, said first universal cipher-number (u 1 ) being derivable from said first base-group-number (g,) raised to the power of a fourth monotone function (ƒ 1 ) of said single exponent-number (r), and said second universal cipher-number (u 2 ) being derivable from said second base-group-number (g 2 ) raised to the power of said fourth monotone function (ƒ 4 ) of said single exponent-number (r).