Storage-free message authenticators for error-correcting-codes
Techniques for storage-free message authentication for error-correcting-codes are disclosed. A storage controller of a storage device receives a request to encode a message in a format having an error-correcting code schema that generates a parity code. A key generator generates a pseudorandom transposition of the message and the parity code as a first part of a secret key. A pseudorandom character string is determined as a second part of the secret key. The output of the pseudorandom transposition and the pseudorandom character string are combined to generate the encoded message which is returned in response to the request. The secret key associated with the message is stored in non-volatile memory.
1. A system comprising:
one or more processors; and
a memory storing instructions that, when executed, cause the one or more processors to:
receive, at a storage controller of a storage device, a request to encode a message using an error-correcting code schema that generates a parity code;
generate the parity code based on the error-correcting code schema;
generate, at a key generating module on the storage device, a first parameter associated with the message, the first parameter comprising a pseudorandom transposition of characters of the message and the parity code;
determine a pseudorandom character string based on the error-correcting code schema, the pseudorandom character string having a same number of characters as the first parameter;
combine the first parameter and the pseudorandom character string to generate the encoded message;
return the encoded message in response to the request; and
store a secret key associated with the message in the memory, wherein the secret key comprises:
the first parameter; and
the pseudorandom character string as a second parameter.
2. The system of claim 1 , wherein the instructions further cause the one or more processors to:
receive, at the storage controller, a data retrieval request associated with a coded message stored in the memory;
process the data retrieval request by decoding the encoded message using the error-correcting code schema and the secret key;
responsive to the coded message being unsuccessfully decoded using the error-correcting code schema:
retrieve the message as originally encoded and stored in the storage device; and
decode the retrieved originally encoded message using the error-correcting code schema and the secret key; and
return the decoded message responsive to the data retrieval request.
3. The system of claim 1 , wherein:
the error-correcting code schema comprises a Bose-Chaudhuri-Hoquenghem (BCH) code;
the first parameter comprises a permutation of positions based on a pseudorandom function;
combining the first parameter and the pseudorandom character string comprises performing an exclusive-or (XOR) operation on the first parameter and the pseudorandom character string; and
the request to encode the message includes a plurality of parameters, the plurality of parameters including:
a z parameter indicating a number of zeroes to pad the message in encoding;
a k parameter indicating a number of characters in the message;
a n parameter indicating a number of characters in a constructed code comprising the message and the parity code; and
a t parameter indicating a maximum number of error corrections.
4. The system of claim 3 , wherein the instructions further cause the one or more processors to:
receive, at the storage controller, a data retrieval request including a coded message stored in the memory;
process the data retrieval request by decoding the coded message using the secret key, the decoding comprising:
performing an XOR operation on the coded message and the second parameter;
performing an inverse transposing operation, using the first parameter, on a result of the XOR operation on the coded message and the second parameter; and
performing a BCH decoding operation on a result of the inverse transposing operation;
responsive to the BCH decoding operation returning an invalid word:
retrieve the message as originally encoded and stored in the storage device; and
decode the retrieved encoded message based on the BCH code using the secret key; and
return the decoded message responsive to the data retrieval request.
5. The system of claim 1 , wherein the encoded message is stored in the storage device by the storage controller.
6. The system of claim 1 , wherein:
the error-correcting code schema comprises a Maximum Distance Separable (MDS)/Reed-Solomon (RS) code;
combining the first parameter and the pseudorandom character string comprises performing a modulo operation on each character of the first parameter and each character of the pseudorandom character string based on ordinal position; and
the request to encode the message includes a plurality of parameters, the plurality of parameters including:
a q parameter indicating an alphabet size of the MDS/RS code;
a k parameter indicating a number of characters in the message;
a n parameter indicating a number of characters in a constructed code comprising the message and the parity code; and
a t parameter indicating a maximum number of error corrections.
7. The system of claim 6 , wherein the instructions further cause the one or more processors to:
receive, at the storage controller, a data retrieval request including a coded message stored in the memory;
process the data retrieval request by decoding the coded message using the secret key, the decoding comprising:
performing a linear combination of each character of the coded message and each character of the second parameter based on ordinal position;
performing, for each ordinal position, a modulo operation of the linear combination and the q parameter;
performing an inverse transposing operation on a character string comprising each result of the modulo operation for each ordinal position, the inverse transposing operation on the character string based on the first parameter; and
performing an MDS/RS decoding operation on a result of the inverse transposing operation;
responsive to the MDS/RS decoding operation returning an invalid word:
retrieve the message as originally encoded and stored in the storage device; and
decode the retrieved encoded message using the secret key; and
return the decoded message responsive to the data retrieval request.
8. The system of claim 1 , wherein:
the encoded message is stored in the storage device and a plurality of other storage devices by the storage controller; and
the instructions further cause the one or more processors to:
receive, at the storage controller, a data retrieval request associated with a coded message stored in the memory;
process the data retrieval request by decoding the encoded message using the error-correcting code schema and the secret key;
responsive to the coded message being unsuccessfully decoded using the error-correcting code schema:
retrieve the message as originally encoded from one of the storage device and another storage device of the plurality of other storage devices; and
decode the retrieved originally encoded message using the error-correcting code schema and the secret key; and
return the decoded message responsive to the data retrieval request.
9. The system of claim 1 , wherein the pseudorandom character string is derived from a stored index using a pseudorandom function.
10. The system of claim 1 , wherein:
the message comprises a plurality of unique messages; and
the instructions further cause the one or more processors to:
determine a unique pseudorandom character string based on the error-correcting code schema associated with each unique message of the plurality of unique messages, each unique pseudorandom character string having a same number of characters as the first parameter;
combine the first parameter and each unique pseudorandom character string to generate a plurality of encoded messages;
return the plurality of encoded message in response to the request; and
store a plurality of unique secret keys associated with the plurality of encoded messages in a memory of the storage device accessible by the storage controller, wherein each unique secret key comprises:
the first parameter; and
the each unique pseudorandom character string as a second parameter.
11. A computer-implemented method comprising:
receiving, at a storage controller of a storage device, a request to encode a message using an error-correcting code schema that generates a parity code;
generating the parity code based on the error-correcting code schema;
generating, at a key generating module on the storage device, a first parameter associated with the message, wherein the first parameter comprises a pseudorandom transposition of characters of the message and the parity code;
determining a pseudorandom character string based on the error-correcting code schema, the pseudorandom character string having a same number of characters as the first parameter;
combining the first parameter and the pseudorandom character string to generate the encoded message;
returning the encoded message in response to the request; and
storing a secret key associated with the message in a memory of the storage device accessible by the storage controller, wherein the secret key comprises:
the first parameter; and
the pseudorandom character string as a second parameter.
12. The computer implemented method of claim 11 , further comprising:
receiving, at the storage controller, a data retrieval request associated with a coded message stored in the memory;
processing the data retrieval request by decoding the coded message using the error-correcting code schema and the secret key;
responsive to the coded message being unsuccessfully decoded using the error-correcting code schema:
retrieving the message as originally encoded and stored in the storage device; and
decoding the retrieved originally encoded message using the error-correcting code schema and the secret key; and
returning the decoded message responsive to the data retrieval request.
13. The computer-implemented method of claim 11 , wherein:
the error-correcting code schema comprises a Bose-Chaudhuri-Hoquenghem (BCH) code;
the first parameter comprises a permutation of positions based on a pseudorandom function;
combining the first parameter and the pseudorandom character string comprises performing an exclusive-or (XOR) operation on the first parameter and the pseudorandom character string; and
the request to encode the message includes a plurality of parameters, the plurality of parameters including:
a z parameter indicating a number of zeroes to pad the message in encoding;
a k parameter indicating a number of characters in the message;
a n parameter indicating a number of characters in a constructed code comprising the message and the parity code; and
a t parameter indicating a maximum number of error corrections.
14. The computer-implemented method of claim 13 , further comprising:
receiving, at the storage controller, a data retrieval request associated with a coded message stored in the memory;
processing the data retrieval request by decoding the coded message using the secret key, the decoding comprising:
performing an XOR operation on the coded message and the second parameter;
performing an inverse transposing operation, using the first parameter, on a result of the XOR operation on the coded message and the second parameter; and
performing a BCH decoding operation on a result of the inverse transposing operation;
responsive to the BCH decoding operation returning an invalid word:
retrieving the message as originally encoded and stored in the storage device; and
decoding the retrieved encoded message based on the BCH code using the secret key; and
returning the decoded message responsive to the data retrieval request.
15. The computer-implemented method of claim 11 , wherein the encoded message is stored in the storage device by the storage controller.
16. The computer-implemented method of claim 11 , wherein:
the error-correcting code schema comprises a Maximum Distance Separable (MDS)/Reed-Solomon (RS) code;
combining the first parameter and the pseudorandom character string comprises performing a modulo operation on each character of the first parameter and each character of the pseudorandom character string based on ordinal position; and
the request to encode the message includes a plurality of parameters, the plurality of parameters including:
a q parameter indicating an alphabet size of the MDS/RS code;
a k parameter indicating a number of characters in the message;
a n parameter indicating a number of characters in a constructed code comprising the message and the parity code; and
a t parameter indicating a maximum number of error corrections.
17. The computer-implemented method of claim 16 , further comprising:
receiving, at the storage controller, a data retrieval request associated with a coded message stored in the memory;
processing the data retrieval request by decoding the coded message using the secret key, the decoding comprising:
performing a linear combination of each character of the coded message and each character of the second parameter based on ordinal position;
performing, for each ordinal position, a modulo operation of the linear combination and the q parameter;
performing an inverse transposing operation on a character string comprising each result of the modulo operation for each ordinal position, the inverse transposing operation on the character string based on the first parameter; and
performing an MDS/RS decoding operation on a result of the inverse transposing operation;
responsive to the MDS/RS decoding operation returning an invalid word:
retrieving the message as originally encoded and stored in the storage device; and
decoding the retrieved originally encoded message using the secret key; and
returning the decoded message responsive to the data retrieval request.
18. The computer implemented method of claim 11 , wherein:
the encoded message is stored in the storage device and a plurality of other storage devices by the storage controller; and
the method further comprises:
receiving, at the storage controller, a data retrieval request associated with a coded message stored in the memory;
processing the data retrieval request by decoding the encoded message using the error-correcting code schema and the secret key;
responsive to the coded message being unsuccessfully decoded using the error-correcting code schema:
retrieving the message as originally encoded from one of the storage device and another storage device of the plurality of other storage devices; and
decoding the retrieved originally encoded message using the error-correcting code schema and the secret key; and
returning the decoded message responsive to the data retrieval request.
19. The computer implemented method of claim 11 , wherein:
the message comprises a plurality of unique messages; and
the method further comprises:
determining a unique pseudorandom character string based on the error-correcting code schema associated with each unique message of the plurality of unique messages, each unique pseudorandom character string having a same number of characters as the first parameter;
combining the first parameter and each unique pseudorandom character string to generate a plurality of encoded messages;
returning the plurality of encoded message in response to the request; and
storing a plurality of unique secret keys associated with the plurality of encoded messages in a memory of the storage device accessible by the storage controller, wherein each unique secret key comprises:
the first parameter; and
the each unique pseudorandom character string as a second parameter.
20. A system, comprising:
means for receiving, at a storage controller of a storage device, a request to encode a message using an error-correcting code schema that generates a parity code;
means for generating the parity code based on the error-correcting code schema;
means for generating, at a key generating module on the storage device, a first parameter associated with the message, wherein the first parameter comprises a pseudorandom transposition of characters of the message and the parity code;
means for determining a pseudorandom character string based on the error-correcting code schema, the pseudorandom character string having a same number of characters as the first parameter;
means for combining the first parameter and the pseudorandom character string to generate the encoded message;
means for returning the encoded message in response to the request; and
means for storing a secret key associated with the message in a memory of the storage device accessible by the storage controller, wherein the secret key comprises:
the first parameter; and
the pseudorandom character string as a second parameter.