Elliptic curve cryptography with fragmented key processing and methods for use therewith
A cryptography module includes a key store having a plurality of storage locations for storing a private key as k key fragments. One or more crypto-processing segments each operate based on corresponding ones of the k key fragments to process a message in accordance with elliptic curve digital signature algorithm (ECDSA) to produce a signed message.
1. A cryptography module comprising:
a key store having a plurality of storage locations for storing a private key as k key fragments that include k−1 key segments and a remainder key fragment, where k is greater than 2, wherein the k−1 key segments are generated as random key segments, and wherein the remainder key fragment is generated based on the k−1 key segments; and
at least one crypto-processing segment, coupled to the key store, operating based on the k key fragments for processing a message in accordance with elliptic curve digital signature algorithm (ECDSA) to produce a signed message.
2. The cryptography module of claim 1 wherein the at least one crypto-processing segment generates a modular product based on corresponding ones of the k key fragments.
3. The cryptography module of claim 1 wherein the at least one crypto-processing segment sequentially processes the message based on the k key fragments to produce the signed message.
4. The cryptography module of claim 1 wherein the at least one crypto-processing segments includes a plurality of crypto-processing segments that operate in parallel to process the message into a plurality of fragmented key results and wherein the cryptography module further comprises:
a combiner, coupled to the plurality of crypto-processing segments, that combines the plurality of fragmented key results to produce the signed message.
5. The cryptography module of claim 4 wherein the combiner generates a sum of the plurality of fragmented key results.
6. The cryptography module of claim 1 wherein:
d =( m 1 +m 2 +m 3 + . . . +m k )modulo n
where m i represents the ith of the k key fragments, d represents the key and n is an integer.
7. A method comprising:
storing a private key in k key fragments that include k−1 key segments and a remainder key fragment, where k is greater than 2, wherein the k−1 key segments are generated as random key segments, and wherein the remainder key fragment is generated based on the k−1 key segments; and
processing a message in accordance with elliptic curve digital signature algorithm (ECDSA) via at least one crypto-processing segment, based on the k key fragments, to produce a signed message.
8. The method of claim 7 wherein the at least one crypto-processing segment generates a modular product based on corresponding ones of the k key fragments.
9. The method of claim 7 wherein processing the message includes sequentially processing the message to produce the signed message.
10. The method of claim 7 wherein processing the message includes:
processing the message in parallel to generate a plurality of fragmented key results; and
combining the plurality of fragmented key results to produce the signed message.
11. The method of claim 7 wherein combining the plurality of fragmented key results includes generating a sum of the plurality of fragmented key results.
12. The method of claim 7 wherein:
d =( m 1 +m 2 +m 3 + . . . +m k )modulo n
where m i represents the ith of the k key fragments, d represents the key and n is an integer.
13. A method comprising:
generating at least one random number via a random number generator;
generating k−1 key fragments via a device based on the at least one random number, where k is greater than 2; and
generating a remainder key fragment via the device, based on a modulo remainder computed from the k−1 key fragments and a key;
wherein the key includes a private key of a elliptic curve digital signature algorithm (ECDSA).