`Date: November 5, 2019
`
`Trials@uspto.gov
`571-272-7822
`
`
`
`UNITED STATES PATENT AND TRADEMARK OFFICE
`
`BEFORE THE PATENT TRIAL AND APPEAL BOARD
`
`FACEBOOK, INC., INSTAGRAM, LLC, and WHATSAPP INC.,
`Petitioner,
`v.
`BLACKBERRY LIMITED,
`Patent Owner.
`
`IPR2019-00923
`Patent 7,372,961 B2
`
`
`
`
`
`
`
`
`
`Before GARTH D. BAER, JACQUELINE T. HARLOW, and
`AARON W. MOORE Administrative Patent Judges.
`HARLOW, Administrative Patent Judge.
`
`DECISION
`Denying Institution of Inter Partes Review
`35 U.S.C. § 314
`
`
`
`
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`Patent 7,372,961 B2
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`INTRODUCTION
`Facebook, Inc., Instagram, LLC, and WhatsApp Inc. (collectively,
`“Petitioner”), filed a Petition (Paper 2, “Pet.”), requesting inter partes
`review of claims 1, 2, 5, 15, 16, 19, 23, 24, and 27 of U.S. Patent
`No. 7,372,961 B2 (Ex. 1001, “the ’961 patent”). Blackberry Limited
`(“Patent Owner”) timely filed a Preliminary Response (Paper 10, “Prelim.
`Resp.”). Pursuant to our authorization, Petitioner additionally filed a Reply
`(Paper 11), and Patent Owner filed a Sur-Reply (Paper 13).
`Under 35 U.S.C. § 314(a), an inter partes review may not be instituted
`unless the information presented in the petition “shows that there is a
`reasonable likelihood that the petitioner would prevail with respect to at least
`1 of the claims challenged in the petition.” Having considered the evidence
`and arguments of record, for reasons discussed below, we deny the petition
`and do not institute inter partes review.
`A. Related Matter
`The ’961 patent is the subject of a district court proceeding in the
`Central District of California, captioned BlackBerry Ltd. v. Facebook, Inc.,
`No. 2:18-cv-01844-GW-KS (C.D. Cal.). Pet. 1; Paper 4, 1–2.
`B. The ’961 Patent
`The ’961 patent, titled “Method of Public Key Generation” (Ex. 1001,
`code (54)), describes methods for key generation in public key
`cryptosystems (id. at 1:5–6). The ’961 patent explains that public key
`cryptosystems use private keys and corresponding public keys to ensure data
`security. Id. at 1:10–14. The patent points out that the security of public
`key cryptosystems “depend[s] on the private key remaining secret” (id. at
`1:37–38), and explains that such systems employ pairs of private and public
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`keys, known as long term and short term (or ephemeral) key pairs, to shield
`the long term private key from disclosure (id. at 1:38–42).
`According to the ’961 patent, the Digital Signature Algorithm
`(“DSA”), one “of the more popular protocols for signature” (Ex. 1001, 1:52–
`54), suffers from a vulnerability in that
`the implementation of the DSA may be done in such a way as to
`inadvertently introduce a bias in to the selection of [ephemeral
`private key] k. This small bias may be exploited to extract a
`value of the [long term] private key d and thereafter render the
`security of the system vulnerable. One such implementation is
`the DSS mandated by the National Institute of Standards and
`Technology (NIST) FIPS 186-2 Standard.
`Id. at 2:32–38. With particular regard to DSS, the ’961 patent explains that
`DSS stipulates the manner in which an integer is to be selected
`for use as a private key. A seed value, SV, is generated from a
`random number generator which is then hashed by a SHA-1 hash
`function to yield a bit string of predetermined length, typically
`160 bits. The bit string represents an integer between 0 and
`2160 – 1. However this integer could be greater than the prime q
`and so the DSS requires the reduction of the integer mod q,
`i.e. k=SHA-1 (seed) mod q.
`Id. at 2:38–46. The ’961 patent goes on to observe that the “modular
`reduction [(“mod”)] to obtain k introduces sufficient bias in to the selection
`of k that an examination of 222 signatures could yield the private key d in 264
`steps using 240 memory units. This suggests that there is a need for the
`careful selection of the ephemeral key k.” Id. at 2:56–61.
`The ’961 patent proposes an alternative algorithm for the generation
`of ephemeral private key k designed to avoid the above described
`vulnerability of the DSA implementation used in DSS. Id. at 3:64–4:17.
`
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`Figure 2 of the ’961 patent illustrates this algorithm and is reproduced
`below.
`
`
`Figure 2 is a flow chart depicting the method for generation of ephemeral
`private key k disclosed by the ’961 patent. Id. at 3:12–13. As shown in
`Figure 2, the method begins by obtaining a seed value from a random
`number generator, and then performs a hash function on that seed value to
`produce an output H(seed). Id. at 3:64–4:10. To eliminate the potential bias
`in the selection of k observed in DSS, the ’961 patent discloses that
`[t]he resultant output H(seed) is tested against the value of q and
`a decision made based on the relative values. If H(seed)<q then
`it is accepted for use as k. If not, the value is rejected and the
`random number generator is conditioned to generate a new value
`which is again hashed by the function 28 and tested. This loop
`continues until a satisfactory value is obtained.
`Id. at 4:11–17.
`
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`
`C. Challenged Claims
`Petitioner challenges claims 1, 2, 5, 15, 16, 19, 23, 24, and 27 of the
`’961 patent. Pet. 3–4. Claims 1, 15, and 23 are independent. Claim 1,
`reproduced below, is representative.
`1.
`A method of generating a key k for use in a
`cryptographic function performed over a group of order q, said
`method including the steps of:
`generating a seed value SV from a random number
`generator;
`performing a hash function H( ) on said seed value SV to
`provide an output H(SV);
`determining whether said output H(SV) is less than said
`order q prior to reducing mod q;
`accepting said output H(SV) for use as said key k if the
`value of said output H(SV) is less than said order q;
`rejecting said output H(SV) as said key if said value is not
`less than said order q;
`if said output H(SV) is rejected, repeating said method;
`
`and
`
`if said output H(SV) is accepted, providing said key k for
`use in performing said cryptographic function, wherein said key
`k is equal to said output H(SV).
`Ex. 1001, 5:33–51. Independent claims 15 and 23 respectively recite a
`“computer readable medium” and a “cryptographic unit” for performing the
`method of claim 1. Id. at 6:48–67, 7:24–8:9.
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`D. Asserted Evidence and Grounds of Unpatentability
`Petitioner asserts the following grounds of unpatentability (Pet. 3–4):
`Claims Challenged 35 U.S.C. §
`Basis
`1, 2, 5, 15, 16, 19
`103
`DSS,1 Schneier,2 Rose3
`1, 2, 5, 15, 16, 19
`103
`DSS, Schneier, Menezes4
`23, 24, 27
`103
`DSS, Schneier, Rose, Rao,5 Floyd6
`23, 24, 27
`103
`DSS, Schneier, Menezes, Rao, Floyd
`
`Petitioner relies on the Declaration of Dr. Jonathan Katz, Ph.D.
`(Ex. 1002) to support its patentability challenge. Patent Owner presents the
`Declaration of Dr. Markus Jakobsson, Ph.D. (Ex. 2001) in support of its
`position.
`
`ANALYSIS
`A. Level of Ordinary Skill
`Petitioner contends that a person of ordinary skill in the art at the time
`of invention of the ’961 patent “would have possessed at least a bachelor’s
`degree in electrical engineering or computer science (or equivalent degree)
`and at least two years of experience with computer-based cryptographic
`techniques.” Pet. 6 (citing Ex. 1002 ¶¶ 11–13). Patent Owner does not
`address the requisite level of skill in its Preliminary Response.
`For purposes of this Decision, we adopt Petitioner’s undisputed
`definition of the level of ordinary skill in the art, as it is consistent with the
`
`
`1 Federal Information Processing (FIPS) Publication 186, Digital Signature
`Standard (DSS) (May 19, 1994) (Ex. 1004).
`2 Schneier, Applied Cryptography (2d ed. 1996) (Ex. 1008).
`3 Rose, Re: “Card-shuffling” algorithms, USENET, sci.crypt, sci.math
`(March 10, 1993) (Ex. 1006).
`4 Menezes et al., Handbook of Applied Cryptography (1997) (Ex. 1005).
`5 Rao, Error Coding for Arithmetic Processors (1974) (Ex. 1018).
`6 Floyd, Essentials of Data Processing (1987) (Ex. 1019).
`
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`level of skill reflected in the prior art of record. See Okajima v. Bourdeau,
`261 F.3d 1350, 1355 (Fed. Cir. 2001).
`B. Claim Construction
`In this inter partes review proceeding, the claims of the patent are
`construed using the same standard used in federal district court, including
`construing the claim in accordance with the ordinary and customary
`meaning of the claim as understood by one of ordinary skill in the art and the
`prosecution history pertaining to the patent. See Changes to the Claim
`Construction Standard for Interpreting Claims in Trial Proceedings Before
`the Patent Trial and Appeal Board, 83 Fed. Reg. 51,340, 51,340, 51,358
`(Oct. 11, 2018) (amending 37 C.F.R. § 42.100(b) effective November 13,
`2018) (now codified at 37 C.F.R. § 42.100(b) (2019)).
`Neither party requests construction of any claim term for purposes of
`this proceeding. Pet. 16–17; Prelim. Resp. 14–15. The parties note,
`however, that in response to their dispute in the related district court action
`concerning the construction of the claim term “reducing mod q,” the district
`construed that term to mean “computing the remainder of dividing a value
`by q.” Prelim. Resp. 14 (citing Ex. 2002, 31–35); Pet. 16–17.
`We have considered the claim construction analysis and ruling of the
`district court, and agree that for purposes of this Decision, the district court’s
`interpretation of “reducing mod q” as meaning “computing the remainder of
`dividing a value by q” is reasonable. As such, we adopt that interpretation
`here. We note, however, that our conclusion that Petitioner has not
`established a reasonable likelihood of prevailing as to any of the challenged
`claims does not turn on any particular construction of “reducing mod q.”
`
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`C. References Relied Upon
`1. DSS
`DSS, the Digital Signature Standard, was published in 1994 and
`adopted by the U.S. Department of Commerce. Ex. 1004, 1. DSS describes
`“the Digital Signature Algorithm (DSA) for digital signature generation and
`verification.” Id. at 5. DSS explains that “[t]he DSA authenticates the
`integrity of the signed data and the identity of the signatory. The DSA may
`also be used in proving to a third party that data was actually signed by the
`generator of the signature.” Id. at 2–3.
`Figure 1 of DSS is reproduced below.
`
`
`
`Figure 1 provides an overview of the methods for digital signature
`generation and verification taught by DSS. Id. at 1–2. As shown in
`Figure 1, each signatory has a private key and a public key. Id. at 5. A
`user’s private key is used for signature generation, and the user’s public key
`is used for signature verification. Id. “An adversary, who does not know the
`private key of the signatory, cannot generate the correct signature of the
`signatory. In other words, signatures cannot be forged. However, by using
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`the signatory’s public key, anyone can verify a correctly signed message.”
`Id.
`
`DSA requires both long term and short term (i.e., ephemeral) private
`keys to generate a digital signature for a message. Ex. 1004, 10–11, 17–18.
`Of particular relevance here is the algorithm for computing ephemeral key k
`disclosed in Appendix 3.2 of DSS, which is reproduced, in part, below.
`
`
`As shown in the above excerpt of Appendix 3.2, DSS discloses a method for
`computing an ephemeral key k by selecting a secret value for the seed-key,
`KKEY, performing a hash function, G(t,KKEY), on KKEY, and then
`performing a modular reduction (“modulo” or “mod”) operation, mod q, on
`the output of the hash function. Ex. 1004, 14.
`2. Rose
`Rose is a document that was posted to the sci.crypt and sci.math
`newsgroups on USENET in 1993. Ex. 1006, 1; see also Ex. 1030 ¶¶ 4–5.
`Rose addresses a prior USENET post that suggested generating random
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`numbers from 0 to 2 by performing a mod 3 operation on the output of a
`random number generator. Id. at 1. According to Rose, such a method is
`flawed because “[w]hen the desired interval doesn’t exactly divide the
`interval you already have, the smaller numbers are more likely than the
`larger ones. What you really have to do is throw away any result from the
`original generator that is too big.” Id. at 2.
`Rose discloses source code, reproduced below, designed to avoid the
`bias towards low numbers introduced by performing a mod 3 operation on
`the output of a random number generator. Ex. 1006, 2.
`
`
`
`As shown in the above source code excerpt, Rose discloses a method that
`generates a random number within a specified range [0, n-1]. Ex. 1006, 2.
`Rose’s method first computes the largest multiple of n that is less than or
`equal to “BIG,” i.e., “the biggest value returned by random (),” and assigns
`this value to the variable “biggest.” Ex. 1006, 2. The method then enters a
`do-while loop that repeatedly determines a random number using the
`random() function until the output of the random() function is less than the
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`value of “biggest.” Id. The method assigns final output of the random()
`function to “rval,” and then computes rval mod n. Id.
`3. Menezes
`Menezes is a cryptography textbook published in 1997. Ex. 1005, ii.
`Of particular relevance to Petitioner’s patentability challenge is Menezes’s
`discussion of random bit generators. Menezes defines a “random bit
`generator” as “a device or algorithm which outputs a sequence of
`statistically independent and unbiased binary digits.” Ex. 1005, 170.
`Menezes goes on to explain that
`[a] random bit generator can be used to generate (uniformly
`distributed) random numbers. For example, a random integer in
`the interval [0, n] can be obtained by generating a random bit
`sequence of length [lg n] + 1, and converting it to an integer; if
`the resulting integer exceeds n, one option is to discard it and
`generate a new random bit sequence.
`
`Id.
`
`4. Schneier
`Schneier is a cryptography textbook published in 1996. Ex. 1008, iv.
`Schneier describes techniques for generating random and pseudorandom
`numbers. Id. at 421–428. According to Schneier,
`[s]ometimes cryptographically secure pseudo-random numbers
`are not good enough. Many times in cryptography, you want real
`random numbers. Key generation is a prime example. It’s fine
`to generate random cryptographic keys based on a pseudo-
`random sequence generator, but if an adversary gets a copy of
`that generator and the master key, the adversary can create the
`same keys and break your cryptosystem, no matter how secure
`your algorithms are. A random-sequence generator’s sequences
`cannot be reproduced. No one, not even you, can reproduce the
`bit sequence out of those generators.
`Id. at 421–422.
`
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`
`5. Rao
`Rao is an arithmetic coding textbook published in 1974. Ex. 1018, iv.
`Rao teaches that computers are divided into functional units or subsystems,
`including an “arithmetic processor.” Id. at 39. Rao also discloses that “[a]n
`arithmetic processor is the part of a computer that provides the logic circuits
`required to perform arithmetic operations such as ADD, SUBTRACT,
`MULTIPLY, DIVIDE, SQUARE-ROOT, etc.” Id. at 41.
`6. Floyd
`Floyd is a data processing textbook published by 1987. Ex. 1019, iv.
`Floyd teaches that in computers having a microprocessor, arithmetic
`processing is performed by a portion of a computer’s central processing unit
`(CPU) known as an arithmetic/logic unit (ALU). Id. at 45–46.
`D. Obviousness Grounds Based on Rose
`Petitioner asserts that claims 1, 2, 5, 15, 16, and 19 of the ’961 patent
`are rendered obvious by the combination of DSS, Schneier, and Rose.
`Pet. 19–47. Petitioner additionally asserts that claims 23, 24, and 27 are
`rendered obvious by the combination of DSS, Schneier, Rose, Rao, and
`Floyd. Id. at 57–63. To support its contentions, Petitioner cites to
`Dr. Katz’s declaration testimony (Ex. 1002).
`Patent Owner responds that Petitioner’s proposed modification of
`DSS in view of Rose, which is essential to each of the asserted grounds of
`unpatentability based on Rose, is flawed and rooted in hindsight. Prelim.
`Resp. 16–39, 55–56. Patent Owner further asserts that the proffered
`combination of DSS and Rose would not have been obvious to try. Id. at
`31–39, 55–56. Patent Owner refers to the declaration testimony of
`Dr. Jakobsson (Ex. 2001) to support its position.
`
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`In view of the record before us, we are not persuaded by Petitioner’s
`arguments and evidence attempting to show that there is a reasonable
`likelihood that it would prevail in establishing that at least one of claims 1,
`2, 5, 16, 16, 19, 23, 24, or 27 of the ’961 patent is unpatentable over the
`combinations based on Rose.
`Each challenged independent claim of the ’961 patent requires
`evaluating the output of a hash function performed on a random number to
`determine if that output is less than a group of order q, and, if it is not,
`rejecting that value and repeating the method. More specifically, each of
`independent claims 1, 15, and 23 recites, in relevant part:
`generating a seed value SV from a random number generator;
`performing a hash function H( ) on said seed value SV to provide
`an output H(SV);
`determining whether said output H(SV) is less than said order q
`prior to reducing mod q;
`accepting said output H(SV) for use as said key k if the value of
`said output H(SV) is less than said order q;
`rejecting said output H(SV) as said key if said value is not less
`than said order q;
`if said output H(SV) is rejected, repeating said method;
`Ex. 1001, 5:33–51, 6:48–67, 7:24–8:9.
`For both asserted grounds of unpatentability based on Rose, Petitioner
`contends that the combination of DSS and Rose discloses or suggests the
`“determining,” “accepting,” “rejecting,” and “repeating” steps of the
`challenged claims. Pet. 35–44, 59–63.
`Petitioner acknowledges that “the ’961 patent employs a different
`approach” for generating ephemeral private key k than that disclosed by
`DSS. Pet. 36. Petitioner likewise concedes that DSS does not disclose the
`
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`“determining,” “accepting,” “rejecting,” or “repeating” steps of the
`challenged claims. Id. at 35. Rather, as Petitioner recognizes (Pet. 19–23),
`DSS simply performs a modulo operation on the output of the hash of a
`random value and stores that result as ephemeral private key k. Ex. 1004, 14
`(Step 3.a.). DSS does not contemplate evaluating the output of the hash
`function prior to performing the modulo operation, much less iteratively
`repeating the process of selecting a new random number and performing a
`hash function on that number until a value less than q is obtained. Id.
`Indeed, in the context of describing a method for computing a batch of
`ephemeral private keys k, rather than select a new random number for use in
`computing each key k in the batch, DSS discloses updating the value of the
`seed-key (KKEY) and using that updated value to calculate k. Id. at 14
`(Step 3.d.).
`Rose likewise fails to disclose “determining,” “accepting,”
`“rejecting,” or “repeating” steps performed on the output of a hash function
`as recited the challenged claims. Ex. 1006, 1–2. Rather, Rose describes a
`method for performing the basic task of random number generation within a
`specified range––absent any hashing step––that avoids the bias towards low
`numbers observed with other techniques. Ex. 1002, 2. More particularly,
`Rose’s method determines a random number within the range [0, n-1] by:
`(1) computing the largest multiple of n that is less than or equal to the
`biggest value returned by the function random (); (2) entering a do-while
`loop that iteratively generates random numbers using the function random ()
`until the output of that function is less than the largest multiple of n
`determined in step (1); and (3) performing a modulo n operation on the
`output of the do-while loop and returning the result of that operation as the
`result of the software routine. Id. Rose does not disclose hashing the
`
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`random number at any point in the method. Id. Nor does Rose contemplate,
`for example, how its technique might be applied to a cryptographic key
`generation algorithm, whether its technique might be useful in avoiding bias
`in the output of a hash function performed on a random number, or whether
`avoidance of modulo bias requires iteratively repeating both the selection of
`a random number and hashing that number. Id. at 1–2.
`Petitioner does not adequately explain, in view of the gaps in DSS and
`Rose, why an ordinarily skilled artisan would have sought to modify DSS by
`applying Rose’s technique for eliminating modulo bias in basic random
`number generation to accept or reject a hashed random number, or to
`iteratively generate and hash a new random number after each rejection.
`Instead, Petitioner presumes, without sufficient explanation, that because
`Rose identifies a solution for addressing the modulo bias problem in basic
`random number generation, and because it was known at the time of
`invention of the ’961 patent that performance of a modulo operation on the
`output of a hash function, as disclosed by DSS, could create a bias towards
`lower values, an ordinarily skilled artisan would “have been motivated to
`use the technique in Rose to maintain a uniform distribution of random
`numbers over the range specified by q, resulting in a cryptographically
`stronger key k, in turn increasing the strength of the resulting digital
`signature scheme.” Pet. 43–44 (emphasis omitted).
`Petitioner’s presumption is insufficient, however, to support
`institution of inter partes review. For example, Petitioner’s inchoate
`explanation does not adequately address why an ordinarily skilled artisan
`would have understood that Rose’s method for avoiding modulo bias in
`basic random number generation––absent any hashing––would have been
`transferable to mitigate modulo bias in the selection of an output of a hash
`
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`function after the random number has been transformed. The hindsight
`driven nature of Petitioner’s proposed combination is further underscored by
`the fact that it iterates both the random number generation and the hashing
`steps without providing sufficient explanation as to why an ordinarily skilled
`artisan would have taken such an approach. Specifically, Petitioner asserts
`that the proffered combination would have resulted in the following method
`for generating ephemeral private key k:
`(1) Generate a random number for KKEY in accordance
`with DSS alone or in combination with Schneier7 (the claimed
`“seed value SV”), as explained for claim 1[a];
`(2) perform a hash of KKEY, G(t,KKEY), according to
`DSS (the claimed “output H(SV)”), as explained for claim 1[b];
`(3) determine whether G(t,KKEY) (“output H(SV)”) is
`less than order q (i.e. the value q),[] according to the teachings of
`Rose;
`
`(4) accept G(t,KKEY) (“output H(SV)”) if G(t,KKEY) is
`less than q, according to the teachings of Rose;
`(5) reject G(t,KKEY) if it is not less than q, by repeating
`the method and going back to step (1), according to the teachings
`of Rose; and
`(6) if G(t,KKEY) (“output H(SV)”) was accepted in
`step (4), perform a “mod q” operation on G(t,KKEY), pursuant
`
`
`7 Petitioner relies on Schneier solely to establish that an ordinarily skilled
`artisan would have employed a random––rather than pseudorandom––
`number generator to generate a cryptographic key. See Pet. 33–34. As
`Petitioner’s assertions regarding Schneier are neither presently disputed by
`Patent Owner (Prelim. Resp. 17 n.5), nor germane to our discussion, we, like
`the parties, focus our analysis on the combination of DSS and Rose.
`
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`to the teachings of Rose, and provide it as a key k for use in
`performing a cryptographic function, in accordance with DSS.
`Pet. 41–42 (emphasis omitted) (citing Ex. 1002 ¶ 150). But Petitioner does
`not adequately explain why an ordinarily skilled artisan would have arrived
`at this combination given that (1) Rose does not address hashing; (2) neither
`DSS nor Rose contemplates repeating both the random number generation
`step and the hashing step; and (3) in the context of batch key generation,
`DSS does not suggest generating a new random number for each key k, but
`simply updating the original random number using a deterministic function.
`See Polaris Indus., Inc. v. Arctic Cat, Inc., 882 F.3d 1056, 1069 (Fed. Cir.
`2018) (“statements regarding preferences are relevant to a finding regarding
`whether a skilled artisan would be motivated to combine that reference with
`another reference”).
`Petitioner’s contention that “Rose’s technique would also have been
`obvious to try” (Pet. 44 (citing Ex. 1002 ¶ 158)) because “rejecting values
`that fall outside a desired range was a well-known way of obtaining a
`uniform distribution of random numbers within the range” (id.) is likewise
`unpersuasive. In view of the insufficiently explained gap between DSS’s
`method for generating key k by performing a modulo operation on the hash
`of a random number and Rose’s “simple and generic technique” (Pet. 40) for
`basic random number generation––absent any hashing––Petitioner cannot be
`said to have demonstrated that the proposed combination would have been
`obvious to try. For example, Petitioner does not adequately explain why it
`would have been obvious to try iteratively generating a new random number
`and hashing that number whenever the output of the hash function is greater
`than or equal to order q, given that neither DSS nor Rose contemplates
`performing and repeating both of those operations––each of which consumes
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`computational resources––every time the output of the hash function falls
`outside of the desired range.
`[A]n invention is not obvious to try where vague prior art does
`not guide an inventor toward a particular solution. A finding of
`obviousness would not obtain where “what was ‘obvious to try’
`was to explore a new technology or general approach that seemed
`to be a promising field of experimentation, where the prior art
`gave only general guidance as to the particular form of the
`claimed invention or how to achieve it.”
`Bayer Schering Pharma AG v. Barr Labs., Inc., 575 F.3d 1341, 1347 (Fed.
`Cir. 2009) (quoting In re O’Farrell, 853 F.2d 894 (Fed. Cir. 1988)). Absent
`sufficient justification by Petitioner, and in view of the fact that Rose does
`not contemplate hashing, DSS does not contemplate iteratively generating
`and evaluating random numbers, and neither Rose nor DSS discusses
`iteratively performing random number generation and hashing steps, we
`cannot agree that Petitioner’s proposal to modify DSS by inserting iterative
`random number generation and hashing steps in the method would have
`been obvious to try.
`Accordingly, based on the record before us, we determine that
`Petitioner has not demonstrated a reasonable likelihood of establishing that
`an ordinarily skilled artisan would have had reason to combine DSS and
`Rose in the proposed manner. As such, we conclude that Petitioner has not
`shown a reasonable likelihood in prevailing in its assertion that any of
`claims 1, 2, 5, 15, 16, 19, 23, 24, or 27 would have been obvious in view of
`the combinations based on Rose.
`E. Obviousness Grounds Based on Menezes
`Petitioner asserts that claims 1, 2, 5, 15, 16, and 19 of the ’961 patent
`are rendered obvious by the combination of DSS, Schneier, and Menezes.
`Pet. 47–57. Petitioner also asserts that claims 23, 24, and 27 are rendered
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`obvious by the combination of DSS, Schneier, Menezes, Rao, and Floyd. Id.
`at 57–63. To support its contentions, Petitioner cites to Dr. Katz’s
`declaration testimony (Ex. 1002).
`Patent Owner responds that Petitioner’s proposed modification of
`DSS in view of Menezes, which is central to each asserted ground of
`unpatentability including Menezes, is flawed and rooted in hindsight.
`Prelim. Resp. 39–52, 55–56. Patent Owner further asserts that the proffered
`combination of DSS and Menezes would not have been obvious to try. Id. at
`52–56. Patent Owner refers to the declaration testimony of Dr. Jakobsson
`(Ex. 2001) to support its position.
`In view of the record before us, we are not persuaded by Petitioner’s
`arguments and evidence attempting to show that there is a reasonable
`likelihood that it would prevail in establishing that at least one of claims 1,
`2, 5, 16, 16, 19, 23, 24, or 27 of the ’961 patent is unpatentable over the
`combinations based on Menezes.
`For each asserted ground of unpatentability based on Menezes,
`Petitioner contends that the combination of DSS and Menezes discloses or
`suggests the “determining,” “accepting,” “rejecting,” and “repeating” steps
`of the challenged claims. Pet. 50–55, 59–63.
`Petitioner’s contentions concerning the combination of DSS and
`Menezes are similar to those described above regarding the combination of
`DSS and Rose, and, thus, suffer from similar deficiencies. Like DSS and
`Rose, the portions of Menezes relied upon by Petitioner fail to disclose
`“determining,” “accepting,” “rejecting,” and “repeating” steps performed on
`the output of a hash function as required by the challenged claims. Pet. 50–
`55; Ex. 1005, 170. The primary excerpt of Menezes cited by Petitioner
`explains that “a random integer in the interval [0, n] can be obtained by
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`generating a random bit sequence of length [lg n] + 1, and converting it to an
`integer; if the resulting integer exceeds n, one option is to discard it and
`generate a new random bit sequence.” Ex. 1005, 170. It does not mention
`hashing, and does not contemplate, for example, whether its technique might
`be useful for accepting or rejecting the result of performing a hash function
`on a randomly generated seed value, or whether iterative repetition of both
`the generation of a random number and performance of a hash function on
`that number when the output of the hash function falls outside of a desired
`range would be appropriate. Id. Moreover, as Petitioner acknowledges
`(Pet. 54), the cited portions of Menezes do not address modulo bias.
`Ex. 1005, 170.
`In view of these gaps, as with the combination of DSS and Rose,
`Petitioner does not adequately explain why an ordinarily skilled artisan
`would have sought to modify DSS by applying Menezes’s technique for
`random number generation to accept or reject a hashed random number. As
`an initial matter, Petitioner acknowledges that, in contrast to Rose, “Menezes
`does not specifically describe the potential bias that can arise from
`performing a modulo reduction on a random number.” Pet. 54.
`Accordingly, Petitioner contends that such an artisan would “have been
`motivated to use the technique in Menezes to solve a particular problem in
`implementing DSS – ensuring that the resulting k value falls within the
`desired range of 0 to q-1.” Id. (citing Ex. 1002 ¶ 188). But Petitioner does
`not present evidence or argument sufficient to establish, for purposes of
`institution, that obtaining k values within the desired range was a “problem
`in implementing DSS” (id.