# US 9,438,425 B2 · Robust MAC aggregation with short MAC tags > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 9,438,425 B2 - Document ID: US9438425B2 - Status: Granted - Kind: B2 - Application number: 14/460,791 - Filed: 2014-08-15 - Published: 2016-02-18 - Granted: 2016-09-06 - Earliest claimed: 2014-08-15 - Assignees: Alcatel Lucent - Applicants: Alcatel-Lucent USA Inc. - Inventors: Vladimir Kolesnikov - Web page: https://patentgrep.com/patent/US9438425B2 ## CPC - H04L 9/3242: {involving keyed hash functions, e.g. message authentication codes [MACs], CBC-MAC or HMAC} - H04L 9/0643: {Hash functions, e.g. MD5, SHA, HMAC or f9 MAC} - H04L: TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION (arrangements common to telegraphic and telephonic communication H04M) ## Abstract Method of producing an aggregated message authentication code (MAC). The method comprises generating or receiving, in a computer processor, a first message and its first MAC tag (m1, t1) and computing, in the computer processor, a first hashed message-tag pair H(m1, t1), where H is a cryptographic hash function. The method comprises generating or receiving, in the computer processor, a second message and its second MAC tag (m2, t2) and computing, in the computer processor, a second hashed message-tag pair H(m2, t2). The method comprises computing, in the computer processor, an aggregated MAC (At1) by an addition operation, as follows: At1=(H(m1, t1)+H(m2, t2)) modulo N, where N is a natural number equal to two or greater. ## Claims ### Claim 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 (m1, t1); computing, in the computer processor, a first hashed message-tag pair H(m1, t1), where H is a cryptographic hash function; generating or receiving, in the computer processor, a second message and its second MAC tag (m2, t2); computing, in the computer processor, a second hashed message-tag pair H(m2, t2); computing, in the computer processor, an aggregated MAC (At1) by an addition operation, as follows: At1=(H(m1,t1)+H(m2,t2))modulo N, where N is selected to equal a natural number equal to two or greater. ### Claim 2 (depends on 1) 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(m3, t3); and the computer processor computes, a further aggregated MAC (At2) by the addition operation, as follows: At2=(H(m3,t3)+At1)modulo N. ### Claim 3 (depends on 2) The method of claim 2, including aggregating the further aggregated MAC with a plurality of m additional hashed message-tag pairs H(mm, tm), 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 (Atn) is computed, by the computer processor, using the addition operation, as follows: Atn=(H(mm,tm)+Atn-1)modulo N, where Atn-1 equals a so-far aggregated MAC. ### Claim 4 (depends on 1) The method of claim 1, further including aggregating the aggregated MAC (At1) with another aggregated MAC (Atx) to form a combined aggregated MAC (At′), computed by the computer processor, using the addition operation, as follows: At′=(At1+Atx)modulo N. ### Claim 5 (depends on 1) 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. ### Claim 6 (depends on 1) The method of claim 1, wherein H, the cryptographic hash function, is a secure hash algorithm (SHA) function. ### Claim 7 (depends on 1) 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. ### Claim 8 (depends on 7) The method of claim 7, wherein regenerating the candidate aggregated MAC includes computing the first hashed message-tag pair H(m1, t1), the second hashed message-tag pair H(m2, t2) and the addition operation, where (m1) and (m2) are messages included in the list of constituent messages and tags associated with the candidate aggregated MAC. ### Claim 9 (depends on 1) The method of claim 1, wherein the computer processor is located in a communication sensor node of a communication network. ### Claim 10 (depends on 1) 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. ### Claim 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 (m1, t1), and a second message and its second MAC tag (m2, t2), wherein: the computer processor is programmed to compute a first hashed message-tag pair H(m1, t1), and a second hashed message-tag pair H(m2, t2) where H is a cryptographic hash function; and the computer processor is programmed to compute a first aggregated MAC (At1) by an addition operation, as follows: At1=(H(m1,t1)+H(m2,t2))modulo N, where N is a natural number selected to equal to two or greater. ### Claim 12 (depends on 11) 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(m3, t3); the computer processor is programmed to compute, a further aggregated MAC (At2) by the addition operation, as follows: At2=(H(m3,t3)+At1)modulo N. ### Claim 13 (depends on 11) The apparatus of claim 11, wherein the computer processor is programmed to further aggregate the aggregated MAC (At1) to another aggregated MAC (Atx) to form a combined aggregated MAC (At′), computed by the computer processor, using the addition operation, as follows: At′=(At1+Atx)modulo N. ### Claim 14 (depends on 11) 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. ### Claim 15 (depends on 14) 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. ### Claim 16 (depends on 14) 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. ### Claim 17 (depends on 11) 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. ### Claim 18 (depends on 17) 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. ### Claim 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 (m1, t1) computing, in the computer processor, a first hashed message-tag pair H(m1, t1), where H is a cryptographic hash function; generating or receiving, in the computer processor, a second message and its second MAC tag (m2 t2); computing, in the computer processor, a second hashed message-tag pair H(m2, t2); computing, in the computer processor, an aggregated MAC (At1) by an addition operation, as follows: At1=(H(m1,t1)+H(m2,t2))modulo N, where N is selected to equal a natural number equal to two or greater. ### Claim 20 (depends on 19) 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, (At2) including computing the addition operation, as follows: At2=(H(m3,t3)+At1)modulo N where H(m3, t3) is a third hashed message-tag pair generated or received by the computer processor.