Abstract: A digital signature method based on the discrete logarithm problem is provided that allows message recovery. The message x is transformed according to the rule e=x g.sup.-r mod p, where r is a secret value generated by the signer. A value y is then calculated according to the rule y=r+s e mod q, where y is the signer's secret key. The signature of x consists of the pair (e,y). The verifier recovers the message x according to the rule x=g.sup.y k.sup.e mod p, where k is the signer's public key. The validation of x can be based on some redundancy contained in x. Alternatively, a conventional verification equation can be constructed by using the signature method together with a hash function H. In addition, a key agreement method based on the signature method is provided which establishes with a single transmission pass a shared secret key K between two parties A and B in an authenticated fashion.

Abstract: A converter or running-key for generator producing pseudo-random sequences under the supervision of a secret or confidential key or code is substantially formed by a combination device containing a memory circuit and a feedback circuit. Periodic digital sequences are summed in an adder circuit, and the thus obtained composite digital sequence is separated in a divider circuit. A part of this composite digital sequence is used as a digital feedback sequence which is fed to an input of the same adder circuit through the feedback circuit comprising an auxiliary digital memory device or storage and an auxiliary logic circuit. In this manner, the desired memory and feedback is achieved which results in more complicated or complex pseudo-random sequences. In an advantageous exemplary embodiment, a substitution block is inserted as the auxiliary digital memory device or storage. This substitution block can be implemented by a commercially available read-and-write memory (RAM).