Quadratic residue based password authenticated key exchange method and system
AssigneeVerizon Data Services Inc.
InventorMuxiang Zhang
Life of this patent
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Abstract
A method is provided for use in secure electronic communication. The method may include obtaining a password shared with an intended key exchange entity and sending a key exchange request including a first value to the intended key exchange entity. The method may also include receiving a key exchange reply including a permutation of a first quadratic residue of the first value, and calculating a second quadratic residue of the first value based on the key exchange reply. Further, the method may also include determining a second value shared with the key exchange entity based on the first quadratic residue and the second quadratic residue.
Claims21
1-21. (canceled)
A computer-implemented method, comprising:
- receiving, from a key exchange entity, a permutation of a first quadratic residue of a public parameter;
- computing a value of the first quadratic residue, based on at least the received permutation, the computing comprising:
- identifying an inverse function associated with the received permutation;
- and
- applying the inverse function to the received permutation a plurality of times;
- determining a value of a second quadratic residue of the public parameter;
- and
- generating, using a processor, a shared value for exchange with the key exchange entity, the generating comprising:
- determining whether the first quadratic residue value corresponds to the second quadratic residue value;
- and
- establishing the second quadratic residue value as the shared value, when the first quadratic residue value corresponds to the second quadratic residue value.
A non-transitory, computer-readable medium storing a program that, when executed by a processor, causes the processor to perform a method, comprising:
- receiving, from a key exchange entity, a permutation of a first quadratic residue of a public parameter;
- computing a value of the first quadratic residue, based on at least the received permutation, the computing comprising:
- identifying an inverse function associated with the received permutation;
- and
- applying the inverse function to the received permutation a plurality of times;
- determining a value of a second quadratic residue of the public parameter;
- and
- generating, using a processor, a shared value for exchange with the key exchange entity, the generating comprising:
- determining whether the first quadratic residue value corresponds to the second quadratic residue value;
- and
- establishing the second quadratic residue value as the shared value, when the first quadratic residue value corresponds to the second quadratic residue value.
A computer-implemented method, comprising:
- obtaining a value of a first quadratic residue of a public parameter;
- computing a permutation of the first quadratic residue value, based on at least the public parameter;
- receiving a first hash value from a key exchange entity, the first hash value being based on a value of a second quadratic residue of the public parameter;
- and
- generating, using a processor, a shared value for exchange with the key exchange entity, the generating comprising:
- determining whether the first quadratic residue value corresponds to the second quadratic residue value, based on at least the first hash value;
- and
- establishing the first quadratic residue value as the shared value, when the first quadratic residue value corresponds to the second quadratic residue value.
A non-transitory, computer-readable medium storing a program that, when executed by a processor, causes the processor to perform a method for electronic communications, the method comprising:
- obtaining a value of a first quadratic residue of a public parameter;
- computing a permutation of the first quadratic residue value, based on at least the public parameter;
- receiving a first hash value from a key exchange entity, the first hash value being based on a value of a second quadratic residue of the public parameter;
- and
- generating, using a processor, a shared value for exchange with the key exchange entity, the generating comprising:
- determining whether the first quadratic residue value corresponds to the second quadratic residue value, based on at least the first hash value;
- and
- establishing the first quadratic residue value as the shared value, when the first quadratic residue value corresponds to the second quadratic residue value.
Dependencies are inferred from the claim text.