Abstract: A method is set forth for signing and subsequently verifying a plurality of digital messages, including the following steps implemented using at least one processor-based subsystem: selecting parameters including an integer q, a relatively smaller integer p that is coprime with q, and a Gaussian function parameter; generating random polynomial f relating to p and random polynomial g relating to q; producing a public key that includes h, where h is equal to a product that can be derived using g and the inverse of f mod q; producing a private key from which f and g can be derived; storing the private key and publishing the public key; producing a plurality of message digests by hashing each of the digital messages with the public key; for each message digest, producing a digital signature using the message digest, the private key, and a Gaussian noise polynomial related to the Gaussian function parameter; and performing a batch verification procedure utilizing the plurality of digital signatures and the public

Abstract: A method for signing and subsequently verifying a digital message, including the following steps: generating an irreducible monic polynomial f(x) of degree n in a ring Fq[x]; generating an irreducible monic polynomial F(y) of degree n in a ring Fq[y]; producing first and second finite fields as Fq[x]/(f(x)) and Fq[y]/(F(y)), respectively; producing a secret isomorphism from the first finite field to the second finite field; producing and publishing a public key that depends on F(y); producing a private key that depends on the secret isomorphism; producing a message digest by applying a hash function to the digital message and the public key; producing a digital signature using the message digest and the private key; and performing a verification procedure utilizing the digital signature and the public key.

Abstract: A method is set forth for signing and subsequently verifying a plurality of digital messages, including the following steps implemented using at least one processor-based subsystem: selecting parameters including an integer q, a relatively smaller integer p that is coprime with q, and a Gaussian function parameter; generating random polynomial f relating to p and random polynomial g relating to q; producing a public key that includes h, where h is equal to a product that can be derived using g and the inverse off mod q; producing a private key from which f and g can be derived; storing the private key and publishing the public key; producing a plurality of message digests by hashing each of the digital messages with the public key; for each message digest, producing a digital signature using the message digest, the private key, and a Gaussian noise polynomial related to the Gaussian function parameter; and performing a batch verification procedure utilizing the plurality of digital signatures and the public k

Abstract: A method for signing and subsequently verifying a digital message, including the following steps: generating an irreducible monic polynomial f(x) of degree n in a ring Fq[x]; generating an irreducible monic polynomial F(y) of degree n in a ring Fq[y]; producing first and second finite fields as Fq[x]/(f(x)) and Fq[y]/(F(y)), respectively; producing a secret isomorphism from the first finite field to the second finite field; producing and publishing a public key that depends on F(y); producing a private key that depends on the secret isomorphism; producing a message digest by applying a hash function to the digital message and the public key; producing a digital signature using the message digest and the private key; and performing a verification procedure utilizing the digital signature and the public key.

Abstract: A method for signing and subsequently verifying a digital message, including the following steps implemented using at least one processor-based subsystem: selecting parameters including an integer q and a relatively smaller integer p that is coprime with q; generating random polynomial f relating to p and random polynomial g relating to q; producing a public key that includes h, where h is equal to a product that can be derived using g and the inverse of f mod q; producing a private key from which f and g can be derived; storing the private key and publishing the public key; producing a message digest by applying a hash function to the digital message; producing a digital signature using the message digest and the private key; and performing a verification procedure utilizing the digital signature and the public key to determine whether the signature is valid.

Abstract: A method for signing and subsequently verifying a digital message, including the following steps implemented using at least one processor-based subsystem: selecting parameters including an integer q and a relatively smaller integer p that is coprime with q; generating random polynomial f relating to p and random polynomial g relating to q; producing a public key that includes h, where h is equal to a product that can be derived using g and the inverse of f mod q; producing a private key from which f and g can be derived; storing the private key and publishing the public key; producing a message digest by applying a hash function to the digital message; producing a digital signature using the message digest and the private key; and performing a verification procedure utilizing the digital signature and the public key to determine whether the signature is valid.

Abstract: Methods, systems and computer readable media for signing and verifying a digital message m are described. First, ideals p and q of a ring R are selected. Elements f and g of the ring R are generated, followed by generating an element F, which is an inverse of f, in the ring R. A public key h is produced, where h is equal to a product that can be calculated using g and F. Then, a private key that includes f is produced. A digital signature s is signed to the message m using the private key. The digital signature is verified by confirming one or more specified conditions using the message m and the public key h. A second user also can authenticate the identity of a first user. A challenge communication that includes selection of a challenge m in the ring R is generated by the second user. A response communication that includes computation of a response s in the ring R, where s is a function of m and f, is generated by the first user.

Abstract: A method of communicating information between users of a communications system includes the following steps: generating a ring R, ideals P and Q in R, a set of coset representatives CQ for the ring R modulo the ideal Q, and a set of coset representatives Cp for the ring R modulo the ideal P; generating at least one public key element h1, . . . , hk in the ring R as a function of at least two private key elements ƒ1, . . . ƒn in R and the ideal Q of the first user; and transmitting from a first user to a second user a description of the ring R, the ideal Q, the ideal P, and the elements h1, . . . , hk in R; generating an element e in R as a function of the ideals P and Q, the public key elements h1, . . . , hk, a private message element m in R, and at least one private random element ø1, . . .

Abstract: The public key encryption system of the present invention has short and easily created encryption keys and wherein the encoding and decoding processes are performed extremely rapidly, and has low memory requirements. The encoding and decoding processes use both the addition and multiplication operations in a ring modulo with two different ideals. The cryptosystem of the present invention allows encryption keys to be chosen essentially at random from a large set of binary vectors, for which key lengths are comparable to the key lengths of the most widely used prior art cryptosystems. The present invention features an appropriate security level (.about.2.sup.80), with encoding and decoding processes ranging from approximately one to two orders of magnitude faster than the prior art, particularly the exponentiation cryptosystems.