Method of passing a cryptographic key that allows third party access to the key

A method of passing a cryptographic key that allows recover of the key by a third party, comprising the steps of:

• a) generating a first random number “k1a” by a first user, where “k1a” is a non-zero member of a group “Zq” and where “q” is a prime number;
• b) generating “key1=m(k1a)” by the first user, where “m” is a hashing function;
• c) generating a second random number “k2a” by the first user, where “k2a” is a non-zero member of the group “Zq”;
• d) computing “y1=m(hp2(k2a))” by the first user, where “hp2” is a public function of a public-key encryption function of a second user;
• e) computing “y2=m(Hp(k1a))” by the first user, where “Hp” is a public function of a public-key encryption function of a key escrow agent;
• f) computing “r1=f(y1,k1a)” by the first user, where “f” is a secure encryption function;
• g) computing “z=f(y2, key1)” by the first user;
• h) computing a signature, by the first user, by computing “A=(1/k2a)(xaB+k1aC)mod q,”where “z”, “r1”, and “s” are substituted for “A”, “B”, and “C,” where the equation for computing a signature is solved for “s,” and where “xa” is a long-term secret of the first user;
• i) computing “G=g{circumflex over ( )}k1a mod p” by the first user;
• j) passing (G,z,r1,s) from the first user to the second user;
• k) receiving “Y=g{circumflex over ( )}xa mod p” by the second user, where “g” is a base element, and where “p” is a prime integer;
• l) verifying the computed signature, by the second user, by computing “T=(YB*GC)((1/A) mod q) mod p,” where “z”, “r1”, and “s” are substituted for “A”, “B”, and “C”;
• m) computing “y1=m(hs2(T))” by the second user, where “hs2” is a secret function of the public-key encryption function of the second user;
• n) computing “k1a=(f−1)(y1,r1)” by the second user;
• o) computing “key1=m(k1a)” by the second user;
• p) intercepting, by a third party, (G,z,r1,s) transmitted from the first user to the second user;
• q) presenting “G” and “z,” by the third party, to a key-escrow agent;
• r) computing “y2=m(Hs(G))” by the key-escrow agent, where “Hs” is a secret function of the public-key encryption function of the key-escrow agent;
• s) computing “key2=(f−1)(y2, z)” by the key-escrow agent, where key2=key1;
• t) returning “key2” from the key-escrow agent to the third party if the third party is authorized to receive “key2”;
• and
• u) using “key2,” by the authorized third party, to decrypt an encrypted message sent between the first user and the second user which was encrypted using “key1”.