Robust MAC aggregation with short MAC tags

1. A method of producing an aggregated message authentication code (MAC), comprising:

generating or receiving, in a computer processor, a first message and its first MAC tag (m 1 , t 1 );

computing, in the computer processor, a first hashed message-tag pair H(m 1 , t 1 ), where H is a cryptographic hash function;

generating or receiving, in the computer processor, a second message and its second MAC tag (m 2 , t 2 );

computing, in the computer processor, a second hashed message-tag pair H(m 2 , t 2 );

computing, in the computer processor, an aggregated MAC (At 1 ) by an addition operation, as follows:

At 1 =( H ( m 1 ,t 1 )+ H ( m 2 ,t 2 ))modulo N,

where N is selected to equal a natural number equal to two or greater.

2. The method of claim 1 , further including aggregating the aggregated MAC with a third hashed message-tag pair, wherein:

the computer processor generates or receives, a third hashed message-tag pair H(m 3 , t 3 ); and

the computer processor computes, a further aggregated MAC (At 2 ) by the addition operation, as follows:

At 2 =( H ( m 3 ,t 3 )+ At 1 )modulo N.

3. The method of claim 2 , including aggregating the further aggregated MAC with a plurality of m additional hashed message-tag pairs H(m m , t m ), wherein m is a natural number of four or greater and for each of the additional hashed message-tag pairs, a further n-th aggregated MAC (At n ) is computed, by the computer processor, using the addition operation, as follows:

At n =( H ( m m ,t m )+ At n-1 )modulo N,

where At n-1 equals a so-far aggregated MAC.

4. The method of claim 1 , further including aggregating the aggregated MAC (At 1 ) with another aggregated MAC (At x ) to form a combined aggregated MAC (At′), computed by the computer processor, using the addition operation, as follows:

At ′=( At 1 +At x )modulo N.

5. The method of claim 1 , wherein each of the MAC tags is represented by a binary number have a bit length of 50 or less.

6. The method of claim 1 , wherein H, the cryptographic hash function, is a secure hash algorithm (SHA) function.

7. The method of claim 1 , further including verifying, in the computer processor or another computer processor, a candidate MAC, including:

receiving a candidate aggregated MAC and a list of constituent messages associated with the candidate aggregated MAC;

receiving a verification key;

regenerating the candidate aggregated MAC, using the list of constituent messages and the verification key, to produce a verification aggregated MAC; and

comparing the candidate aggregated MAC to the verification aggregated MAC.

8. The method of claim 7 , wherein regenerating the candidate aggregated MAC includes computing the first hashed message-tag pair H(m 1 , t 1 ), the second hashed message-tag pair H(m 2 , t 2 ) and the addition operation, where (m 1 ) and (m 2 ) are messages included in the list of constituent messages and tags associated with the candidate aggregated MAC.

9. The method of claim 1 , wherein the computer processor is located in a communication sensor node of a communication network.

10. The method of claim 1 , wherein the computer processor is part of a computer communicably coupled to a database of records stored on a non-transitory computer readable medium.

11. An apparatus for producing an aggregated message authentication code (MAC), comprising:

a computer processor that is programmed to generate or to receive a first message and its first MAC tag (m 1 , t 1 ), and a second message and its second MAC tag (m 2 , t 2 ), wherein:

the computer processor is programmed to compute a first hashed message-tag pair H(m 1 , t 1 ), and a second hashed message-tag pair H(m 2 , t 2 ) where H is a cryptographic hash function; and

the computer processor is programmed to compute a first aggregated MAC (At 1 ) by an addition operation, as follows:

At 1 =( H ( m 1 ,t 1 )+ H ( m 2 ,t 2 ))modulo N,

where N is a natural number selected to equal to two or greater.

12. The apparatus of claim 11 , wherein the computer processor is programmed to further aggregate the aggregated MAC to a third hashed message-tag pair wherein:

the computer processor is programmed to generate or receive, a third hashed message-tag pair H(m 3 , t 3 );

the computer processor is programmed to compute, a further aggregated MAC (At 2 ) by the addition operation, as follows:

At 2 =( H ( m 3 ,t 3 )+ At 1 )modulo N.

13. The apparatus of claim 11 , wherein the computer processor is programmed to further aggregate the aggregated MAC (At 1 ) to another aggregated MAC (At x ) to form a combined aggregated MAC (At′), computed by the computer processor, using the addition operation, as follows:

At ′=( At 1 +At x )modulo N.

14. The apparatus of claim 11 , wherein the computer processor is located in the apparatus configured as one of a plurality of communication nodes of a communication network.

15. The apparatus of claim 14 , wherein the first message includes measurement data collected by a sensor of the one communication node, the sensor connected to the computer processor.

16. The apparatus of claim 14 , wherein the apparatus, configured as one of the communication node, further includes:

an input interface;

an output interface; and

a non-transitory computer readable medium, wherein the computer processor is operably coupled to the input interface, the output interface and the memory.

17. The apparatus of claim 11 , wherein the computer processor is part of an apparatus configured as a computer device, the computer device communicably coupled to a database of records stored on a non-transitory computer readable medium.

18. The apparatus of claim 17 , wherein the first message includes a copy of a first database record stored on the non-transitory computer readable medium located in the apparatus configured as a computer.

19. A non-transitory computer readable medium, comprising:

computer-executable instructions stored on the computer readable medium that, when executed by a computer processor, perform a method that includes computing an aggregated message authentication code (MAC), including:

generating or receiving, in the computer processor, a first message and its first MAC tag (m 1 , t 1 )

computing, in the computer processor, a first hashed message-tag pair H(m 1 , t 1 ), where H is a cryptographic hash function;

generating or receiving, in the computer processor, a second message and its second MAC tag (m 2 t 2 );

computing, in the computer processor, a second hashed message-tag pair H(m 2 , t 2 );

computing, in the computer processor, an aggregated MAC (At 1 ) by an addition operation, as follows:

At 1 =( H ( m 1 ,t 1 )+ H ( m 2 ,t 2 ))modulo N,

where N is selected to equal a natural number equal to two or greater.

20. The computer readable medium recited in claim 19 , wherein the computer readable medium includes further computer-executable instructions that, when executed by the computer processor, compute a further aggregated MAC, (At 2 ) including computing the addition operation, as follows:

At 2 =( H ( m 3 ,t 3 )+ At 1 )modulo N

where H(m 3 , t 3 ) is a third hashed message-tag pair generated or received by the computer processor.