US 8788827

Patent Overview — US8788827B2

Title: Accelerated verification of digital signatures and public keys

Patent number: US8788827B2 (application US13/620,206; publication US20130064367A1)

Assignee: Current assignee listed as Malikie Innovations Ltd; original assignee Certicom Corp.

Key dates: Priority date 2005-01-18; filing date 2012-09-14; granted/publication date 2014-07-22; anticipated expiration 2026-01-18. Legal status listed as "Expired - Lifetime."

Inventor(s): Marinus Struik, Daniel R. Brown, Scott A. Vanstone, Robert P. Gallant, Adrian Antipa, Robert J. Lambert.

Field/Classifications: H04L9/30, H04L9/3066, H04L9/3247, H04L9/3252, G06F7/725.

Purpose: Per the supplied text, the invention "relates to computational techniques used in cryptographic algorithms." Public key cryptography uses a key pair related by a one-way function, permitting secure communication and digital signing without transferring identical keys through independent mechanisms.

Plain-language scope: The excerpt describes accelerated verification of digital signatures and public keys in elliptic-curve settings. Verification typically involves checking a "verification equality" between values. ECDSA signatures are pairs of integers (r, s); a verifier uses the message M, public key Q, and signature (r, s). The text discusses accelerating elliptic-curve computations by pre-computing tables of multiples of the fixed generator G, and also notes that pre-computation can be applied to public key Q. Pre-computed tables save time because G is a fixed, reused system parameter; the simplest table stores multiples 2^j·G for j from 0 to t, where t is the bit-length of n. Larger tables yield better speed improvements, but memory cost must be balanced against speed. Tables of multiples of points are also generated at run-time during an initial phase of each computation.

Source: https://patents.google.com/patent/[US8788827](/patent/US8788827)/en

What the excerpt does not establish: The supplied text is excerpted ("consult the source for omitted text") and does not provide the claims, a complete description, or the precise accelerated-verification method. It does not establish validity, claim scope, or the effect of the noted litigation.

I'll research litigation involving US patent 8788827. Let me start with several targeted searches.

I found several relevant cases. Let me dig deeper into specific cases and confirm which assert the '827 patent.

Let me check for additional cases and confirm the second Foundry case and any appellate activity.

Litigation Involving US Patent No. 8,788,827 ("'827 Patent")

Summary

US 8,788,827 ("Accelerated verification of digital signatures and public keys") has been asserted in three U.S. district court patent infringement suits, all filed in 2025 by Malikie Innovations Ltd. and Key Patent Innovations Ltd. (collectively "Malikie") — the current assignee/beneficiary following the Certicom → BlackBerry → OT Patent Escrow → Malikie chain of title. All three target Bitcoin mining / cryptocurrency companies. This is consistent with the "Family has litigation" listings on the Google Patents page, which identify Texas Western District Court cases 7:25-cv-00567 and 7:25-cv-00222, and Texas Eastern District Court case 2:25-cv-00519.

I found no CAFC appeal and no earlier (pre-2025) litigation involving this specific patent; the older 2022–2024 PTAB activity found in search (Roku IPR2022-01315, Samsung IPR2022-01505, Meta IPR2023-01281) relates to a different patent, the '878 patent — not the '827 patent — and is therefore excluded.

Case 1 — Malikie Innovations Ltd. v. Core Scientific, Inc.

The complaint's theory for the '827 patent is that Bitcoin-protocol-compliant hardware/software (miners, nodes, wallets) practices claim 1 by recovering the ephemeral public key R and computing the signer's public key Q = r⁻¹(sR − eG).

Case 2 — Malikie Innovations Ltd. v. Foundry Digital LLC, et al.

The complaint targets the defendants' Bitcoin mining operations, including participation in the "Foundry USA Pool."

Case 3 — Malikie Innovations Ltd. v. MARA Holdings, Inc.

The complaint's '827 theory was again public-key recovery, e.g., computing Q = r⁻¹(sR − eG), with a related argument on the '197/'961 "indicator" for ephemeral-key recovery from r.

Related / Unconfirmed Matters (flagging for verification)

• A second Foundry Digital suit. An ex parte complaint analysis referenced a matter caption, "Malikie Innovations Ltd. v. Foundry Digital LLC," Case No. 6:26-cv-06874 (shown under a Western District of New York-style docket prefix). I could not independently confirm from a primary docket source that this case exists and asserts the '827 patent; treat as unverified.
• Malikie Innovations Ltd. v. Antpool Technologies Limited et al., W.D. Tex. Case No. 7:26-cv-00371 (filed 2026). Docket metadata confirms a Malikie patent-infringement suit naming Antpool entities, but I did not find confirmation that the '827 patent is among the patents asserted. Unconfirmed as to '827.
• Malikie Innovations Ltd. v. Hyundai Motor Company et al., E.D. Tex. Case No. 2:26-cv-00387, and Malikie Innovations Ltd. v. American Honda Motor Co., N.D. Tex. Case No. 3:26-cv-01503 — additional Malikie suits that surfaced in searches, but I found no evidence they assert the '827 patent. Do not attribute them to the '827 patent without verification.

Caveats on Method and Confidence

• Identifier discipline: I confined the search to "8788827" / "8,788,827" / "'827." Results referencing the "'878 patent" (e.g., Roku/Samsung/Meta IPRs) and unrelated "878"-numbered patents (e.g., U.S. 8,783,882 Magna; Puri '878) were excluded as different patents.
• Primary-source limitations: PACER/Unified Patents/CourtListener snapshots returned docket-level and filing-level detail for the three core cases; I did not retrieve every order. The precise with/without-prejudice basis of the MARA dismissal (Doc. 99) is not established by the AO-120 form alone.
• Date note: Your prompt states the current date as April 26, 2026, but several docket documents I retrieved carry later 2026 dates (e.g., a June 15, 2026 dismissal order and June 2026 discovery orders). I have reported the dates exactly as they appear in the sources.
• If you need court-verified confirmation of outcomes (e.g., whether any case settled or was dismissed on the merits), those specifics should be pulled directly from each docket on PACER/Unified Patents.

I'll verify PTAB activity on US 8,788,827 with live searches before producing the report.

The initial hits conflate US 8,788,827 with an unrelated mirror patent (US 8,783,882) and a streaming patent ("the '878 patent" in Roku/Samsung/Meta IPRs). Let me search precisely.

Good leads — the '827 patent is in active Bitcoin-mining litigation, and there's mention of an ex parte reexamination. Let me pin down whether any AIA trial (IPR/PGR/CBM) was ever filed against it.

PTAB / AIA Trial Landscape — US 8,788,827

Proceedings overview

There are zero AIA trial proceedings on file for US 8,788,827 — no IPR, no PGR, no CBM, in any status (none instituted, none denied, none settled, none decided). The USPTO Open Data Portal returns no AIA trial records for this patent, and my live searches surfaced no petition number (IPR/PGR/CBM) naming the '827 patent. The bottom-line defensive posture is therefore the opposite of "hardened": the patent has never been tested at the PTAB, which means no claim has been canceled, no claim has been adjudicated patentable, and no § 315(e)(2) estoppel attaches to any defendant. Every prior-art ground a defendant can find is still on the table, in the PTAB and in district court. Two important qualifiers: (i) the patent's term has run (anticipated expiration 2026-01-18; Google Patents status "Expired - Lifetime"), so the fight is now about past damages (six-year lookback) and about post-expiration conduct; and (ii) at least one ex parte reexamination appears to be running against one of the patents Malikie is asserting in the same campaign — a proceeding outside the AIA-trial framework (see "Flagged item" below).

Count by status (AIA trials): active 0 / claims invalidated 0 / claims sustained 0 / settled 0 / institution denied 0 / total 0.

Per-proceeding detail

The requested per-proceeding sections cannot be populated because there are no proceedings to describe. I will not invent proceeding numbers, panels, grounds, or final written decisions. For completeness, here is the empty record:

Critical anti-conflation warning — do not brief someone else's IPR as this patent's

Three PTAB proceedings are easy to misattribute to US 8,788,827, and at least one of them is a different patent with a nearly identical number:

1. US 8,783,882 (the "'882 patent") — Magna Mirrors exterior mirror. Challenged in IPR2018-00533 by SMR Automotive Systems USA (a real competitor dispute over extended-field-of-view vehicle mirrors). Same first four digits, different patent, unrelated art. Petition and exhibits: ptacts.uspto.gov petition 1505995 and docketalarm IPR2018-00533. Not our patent.
2. "The '878 patent" in IPR2022-01315 (Roku), IPR2022-01505 (Samsung), IPR2023-01281 (Meta). These challenge claims 1–23 over Madhavan/Baum/Harrington/Damick/Rankin/Varghese/Sitaraman — a media/content patent family. US 8,788,827 has only 13 claims and its art would be public-key-cryptography references, so this is definitionally not our patent. (Samsung's petition also sought joinder with Roku's and was denied institution on 2023-03-22 for failure to show a reasonable likelihood of prevailing — again, on the other patent.) Source: declaration excerpt at ptacts.uspto.gov petition 1555167.
3. US 8,806,197 ("the '197 patent") is a family member of the '827 patent (both descend from Ser. No. 13/478,288) and is asserted alongside it in the Bitcoin-mining campaign. Any PTAB activity on the '197 patent is not activity on the '827 patent.

Flagged item (non-AIA, but you should know about it)

An ex parte reexamination is visible in the docket of Malikie Innovations Ltd. v. MARA Holdings, Inc., No. 7:25-cv-00222 (W.D. Tex.) — CourtListener docket 70243940, Doc. 93-2. The excerpt shows the patent owner filing (i) a "combined petition prior to examination" and (ii) a 37 C.F.R. § 1.181 petition to vacate the order granting reexamination and terminate under 35 U.S.C. § 325(d), arguing the Office lacks statutory authority to reexamine an expired patent. The Office granted a § 1.183 waiver of § 1.540 to hear the § 325(d) argument and permitted the requester to oppose.

I could not confirm from the available excerpt which asserted patent this reexamination targets. The "expired patent" argument is consistent with the '827 patent (expired 2026-01-18 per the Google Patents record), but the MARA case also asserts the '370, '960, '062, '961 and '286 patents, and the excerpt does not name the patent. Treat this as a lead to verify against the reexamination file wrapper (and the CRU's decision on the § 1.181 petition) rather than as an established fact about the '827 patent. Note that ex parte reexamination is not an AIA trial — it does not appear in the ODP AIA-trial data, and it creates no § 315(e)(2) IPR estoppel.

Strategic summary

Claim-level status of US 8,788,827. Claims 1–13 (13 claims total: three independent claims — 1, 6, 10 — with dependent claims 2–5, 7–9, 11–13) are all UNTESTED at the PTAB. None canceled, none sustained, none narrowed. The only public validity attacks on the '827 patent that exist today are in district court: Core Scientific and CoreWeave moved under Rule 12(b)(6) and 35 U.S.C. § 101, and the CoreWeave joinder confirms that Core Scientific's motion addresses the '827 patent in its Sections III.B and VI (CoreWeave took no position on the '827 and '370 patents) — E.D. Tex. 2:25-cv-00519, Doc. 115. So the live invalidity pressure on claim 1 is an Alice eligibility theory on "recovering the omitted public key … by computing Q=r⁻¹(sR−eG)," plus the standard §§ 102/103 defenses that have not yet been aired anywhere.

Estoppel landscape. Because no IPR has reached a final written decision, no petitioner or privy is estopped under § 315(e)(2), and no one is estopped under § 315(e)(1) before the Office. That is a clean slate for a defendant — but it is a closing window, not an open one. The § 315(b) one-year clock runs from service of the infringement complaint: the complaint in Malikie v. MARA was filed 2025-05-12, so any IPR by MARA or its privies is time-barred as of roughly 2026-05-12; the Core Scientific case (2:25-cv-00519, E.D. Tex.) was filed in 2025 as well, so its bar has likely also run; the Foundry Digital / Fortitude / Riot / Cipher complaint was filed 2025-12-12, giving those defendants a bar date near 2026-12-12 — making them the remaining realistic IPR petitioners. For everyone else, the practical route is joining an instituted IPR under § 315(c), an ex parte reexamination, or fighting validity in court (where § 282 lets you use product/system art that IPR cannot reach).

Pattern signals. There is no serial-petitioner pattern on this patent — no petitioner has filed against it once, let alone twice. There is no defensive-aggregator IPR on the '827 patent: Unified Patents operates a Blockchain Zone with COPA aimed precisely at NPE blockchain assertions, and press coverage has flagged Malikie's Bitcoin-wide campaign as the scenario that Zone was built for (Bitcoin Magazine) — but I found no Unified IPR naming this patent. Patent owner (Malikie / Key Patent Innovations, successors via BlackBerry → OT Patent Escrow → Malikie) has not pursued PTAB appeals on the '827 patent because there is nothing to appeal on this patent; the appellate activity in the family sits on other members. The family-wide posture is a coordinated assertion campaign, not a PTAB war: three parallel district court suits — W.D. Tex. 7:25-cv-00222, W.D. Tex. 7:25-cv-00567, and E.D. Tex. 2:25-cv-00519 — all with the '827 patent as a lead "Accelerated Verification Patent."

Recommended next steps

1. Do not represent to any court or adversary that the '827 patent has PTAB history. It has none. Any assertion that "claims 1–5 have been canceled" is false; conversely, any patent-owner assertion that the claims are "PTAB-validated" is also false — nothing has been validated.
2. Preserve the § 315(b) window. If you were served in the Foundry/Digital group litigation (complaint filed 2025-12-12), a petition filed by roughly 2026-12-12 is timely; for MARA and Core Scientific, assume the bar has run and evaluate joinder under § 315(c) to any petition that gets instituted. Verify actual service dates from the dockets before relying on this.
3. Verify the ex parte reexamination. Pull the reexamination file wrapper (CRU) and the Office's decision on patent owner's § 1.181 / § 325(d) petition referenced in Doc. 93-2. If it targets the '827 patent and survives, its claim-level outcome will be the first de jure validity ruling on these claims — and, importantly, the patent owner's own "expired patent" argument is a concession you can use to confine the damages case to the six-year lookback ending 2026-01-18.
4. Lead with § 101 in the meantime. The only tested ground so far is eligibility: the Core Scientific/CoreWeave Rule 12(b)(6) motion addresses the '827 patent at Sections III.B and VI. Ask for those sections, and consider whether claim 1's "accelerated verification" functional language and the Q=r⁻¹(sR−eG) computation support a § 112 or indefiniteness theory in parallel.
5. Re-check the sources before any filing. PTAB petition data is public at USPTO PTAB E2E / PTAB Decisions, and dockets are on CourtListener. Because the campaign is active in 2026, a new petition could appear at any time; the ODP "no AIA trial proceedings" result is accurate as of the most recent ingest but is not a permanent state.

Confidence and limitations: High confidence that no AIA trial proceeding exists against US 8,788,827 as of this review (consistent structured ODP data plus negative web-search results). Medium confidence on the § 315(b) bar-date approximations (derived from complaint filing dates, not verified service dates). Explicitly unknown: the judge panel, grounds, and claim-level outcomes you asked for — because there are no proceedings, these fields do not exist, and I have not fabricated them.

I'll research the assignment record for US 8,788,827, focusing on reel/frame numbers and correspondents of record.

Good hits. Let me dig deeper into the specific reel/frame records and correspondents for the '827 patent.

I ran web-based research against USPTO assignment data (via PTAB/court exhibits that reproduce the assignment records), Google Patents legal events, and litigation/press sources. Important limitation up front: I could not directly query the authenticated USPTO Assignment Center UI in this session, so the reel/frame numbers below are drawn from a USPTO Rule 3.73(c) chain-of-title statement and from court exhibits that quote the Assignment Center records. I flag confidence per line.

Inventors

Pattern check — no distress signal. All six are Certicom Research employees, so the inventor→Certicom assignment is a routine employment assignment, not evidence of a founder/inventor exodus. I found no evidence of mass departure within 12 months of the 2006 filing. The seven-year gap between the parent filing (2006-01-18) and the recorded inventor assignment (2013-11-19) is not unusual here: US 8,788,827 is a continuation filed 2012-09-14, and the original assignment recorded against the parent was re-recorded for the continuation. I could not retrieve the execution date on the 2013 recording, so I am not treating that gap as meaningful.

Original assignee

Certicom Corp., Mississauga, Ontario, Canada — named on the face of the issued patent (73).

• Line of business: Elliptic-curve cryptography. Founded 1985 (Vanstone, Agnew, Mullin); generated the SECG/SEC 2 standards (SEC 2 identifies Certicom's Dan Brown as main contact).
• Did it ship products embodying the claims? Yes — Certicom commercially sold ECC-based security software and toolkits (e.g., Security Builder crypto toolkits and movian VPN/file-encryption products) and licensed ECC implementations. So the original assignee was an operating technology company, not a licensor-only shell.
• Current status: Acquired by Research In Motion (RIM) in 2009 (~$100M), becoming a BlackBerry subsidiary; RIM renamed BlackBerry Limited in 2013. Certicom the entity is not dissolved — it persists under BlackBerry. In 2023 BlackBerry sold ~32,000 "non-core" patents and applications to Malikie Innovations Limited (a subsidiary of Key Patent Innovations Limited), reported at up to ~$900M ($170M upfront plus royalties). That portfolio sale is what carried the '827 patent out of BlackBerry.

Assignment timeline

Confidence note: reel/frame pairs marked (A) come from the USPTO Rule 3.73(c) chain-of-title statement signed by Richard J. Botos (Reg. No. 32,016) on 2023-12-27 and match the reel numbers Google Patents cites for the '827's 2023 corrective recordings. The 2006 and 2019 reel/frames marked (B) were not retrieved for the '827 specifically — treat as unconfirmed.

• 2006 (executed, inferred) / recorded 2013-11-19 — Reel not retrieved

  • Conveyance: Assignment of Assignors' Interest
  • Assignor: Struik; Brown; Vanstone; Gallant; Antipa; Lambert (inventors)
  • Assignee: Certicom Corp.
  • Correspondent: not retrieved
  • Context: Original employment assignment (re-recorded against the continuation); routine.

• 2019-09-30 (executed) / recorded 2019-10-02 — Reel 028294/0247 (B) (reel number inferred from the sibling '039 patent's record; same-date event for '827 is confirmed by Google Patents, reel not independently confirmed for '827)

  • Conveyance: Assignment of Assignor's Interest
  • Assignor: Certicom Corp.
  • Assignee: BlackBerry Limited
  • Correspondent: not retrieved (BlackBerry/Certicom-side counsel)
  • Context: Internal corporate consolidation — Certicom (already a BlackBerry subsidiary since 2009) moved title up to the parent.

• 2023-04-27 (recorded) — Reel 063471/0474 (A)

  • Conveyance: Assignment
  • Assignor: BlackBerry Limited
  • Assignee: OT Patent Escrow, LLC
  • Correspondent: Richard J. Botos, Reg. No. 32,016 (see §NPE signal 3)
  • Context: Transfer into a deal/escrow vehicle feeding the BlackBerry→Malikie patent sale.

• 2023-06-16 (recorded) — Reel 064015/0001 (A)

  • Conveyance: Nunc Pro Tunc Assignment
  • Assignor: OT Patent Escrow, LLC
  • Assignee: Malikie Innovations Limited (The Glasshouses GH2, 92 Georges Street Lower, Dun Laoghaire, Dublin, A96 VR66, Ireland)
  • Correspondent: Richard J. Botos, Reg. No. 32,016
  • Context: Transfer to the asserting/monetization entity.

• 2023-06-19 (recorded) — Reel 064066/0001 (A)

  • Conveyance: Nunc Pro Tunc Assignment
  • Assignor: BlackBerry Limited
  • Assignee: Malikie Innovations Limited
  • Correspondent: Richard J. Botos, Reg. No. 32,016
  • Context: Parallel direct chain to the same assignee, cleaning up the title record alongside the escrow route.

• 2023-09-05 (recorded) — Reel 064806/0669 (A)

  • Conveyance: Corrective Assignment
  • Assignor: BlackBerry Limited
  • Assignee: OT Patent Escrow, LLC
  • Correspondent: Richard J. Botos, Reg. No. 32,016
  • Context: Record correction — cover sheet amended to remove application 12,817,157 previously recorded at reel 063471/0474.

• 2023-09-05 (recorded) — Reel 064807/0001 (A)

  • Conveyance: Corrective Assignment
  • Assignor: OT Patent Escrow, LLC
  • Assignee: Malikie Innovations Limited
  • Correspondent: Richard J. Botos, Reg. No. 32,016
  • Context: Record correction — "corrective assignment to correct 12817157 application number previously recorded at reel 064015, frame 0001."

Google Patents' legal-events ledger shows the same set (2013-11-19; 2019-10-02; 2023-04-27; 2023-06-16; 2023-06-19; two 2023-09-05 corrections). The current assignee of record is Malikie Innovations Limited.

Timeline diagram

timeline
    title Ownership of US 8788827
    2005 : Provisional filed by Certicom
    2006 : Parent application filed
    2013 : Inventors assign to Certicom Corp
    2014 : Patent issued to Certicom
    2019 : Certicom assigns to BlackBerry Limited
    2023 : BlackBerry assigns to OT Patent Escrow
         : OT Patent Escrow assigns to Malikie
         : BlackBerry assigns directly to Malikie
         : Corrective recordings filed
    2025 : Malikie sues Bitcoin miners

NPE / troll-pattern signals

Verdict

NPE — high confidence (2+ strong signals).

The chain moves from an operating company (Certicom → BlackBerry) into a monetization structure: BlackBerry Limited assigned the patent to OT Patent Escrow, LLC at reel 063471/0474, which assigned it to Malikie Innovations Limited at reel 064015/0001, with a parallel nunc-pro-tunc link BlackBerry → Malikie at reel 064066/0001 (all 2023, all share attorney-of-record Richard J. Botos, Reg. No. 32,016), followed by corrective recordings at reels 064806/0669 and 064807/0001. Malikie is a KPI-formed licensing entity with no product business that is now asserting this patent against Bitcoin miners — giving at least two strong NPE signals (shell/licensing-entity transfer + known asserter), reinforced by cascading 2023 transfers and a recurring correspondent.

Verify at: https://assignmentcenter.uspto.gov/ (search by patent number 8788827; mirror at https://assignment.uspto.gov/patent/index.html). Search Google Patents legal events at https://patents.google.com/patent/US8788827/en for the same ledger.

Caveats (not findings): I could not authenticate into Assignment Center directly, so confirm the reel/frame assignments for reels 063471/0474, 064015/0001, 064066/0001, 064806/0669, and 064807/0001 against the cover sheets. The 2006 and 2019 reel numbers are unconfirmed for the '827 specifically. The Botos firm name is not verified from a primary source. I found no recorded assignment beyond the seven events above; if Assignment Center shows additional entries, my "no further records" statement should be corrected.

I'll research the prior-art citations for US 8,788,827 directly. Let me run several targeted searches.

Let me pull the cited references list more directly.

Let me locate the full "References Cited" list from the patent's own PDF and sibling family members.

Prior-Art Analysis — US 8,788,827 B2 ("Accelerated Verification of Digital Signatures and Public Keys")

0. Method and a material scope limitation (please read first)

I was asked to "search the USPTO database" for US 8,788,827 and enumerate each patent citation on its face, with citation, date, description, and a § 102 anticipation analysis. I ran multiple live searches (Google Patents' mirror of the USPTO front page, patentimages.storage.googleapis.com PDFs of the printed patent, Unified Patents, CourtListener, and Espacenet/EPO search-report data).

Honest limitation: I could not retrieve the full "References Cited" list for the '827 patent. Third-party databases show the patent carries ~81–85 patent-art citations and ~68 non-patent-literature items (Unified Patents: "Patent Art (85) / Non-Patent Literature (68)"; Google Patents: "Citations (81)"). The authoritative full text supplied to me is truncated mid-list — it stops at the fourth cited patent (US 4,748,668). I therefore cannot claim to have reviewed all 81 patent citations, and I am explicitly not going to invent entries to fill the gap.

What follows is: (a) the citations I can verify, (b) a verified proxy list from the same-family patent US 8,467,535, and (c) the § 102 analysis. I flag confidence for every item.

Cross-reference note / discrepancy: The task prompt states the current date as April 26, 2026, while the working environment header states 2026-09-28. The previously generated "Patent summary" section already flagged a similar date inconsistency (it noted a June 15, 2026 dismissal order surfacing). I am not reconciling these; I report the discrepancy. This matters because the '827 patent expired 2026-01-18, so it is now only assertable for past damages in the co-pending 2025 suits.

1. What is actually on the face of US 8,788,827 (CONFIRMED, authoritative text)

These four references appear verbatim in the "Citations (81)" table of the patent text I was given. Their listed dates are the Google/INPADOC priority-and-publication dates.

(Item 4 is truncated in my source text as "US4748668A … 1986-07-09" with the description cut off; I cross-identified it via the sibling patent list below, which reads "4,748,668 A — 5/1988 — Shamir et al.")

2. Verified proxy list — the U.S. references on the sibling Certicom patent US 8,467,535 B2

US 8,467,535 B2 (Certicom, "Accelerated Verification of Digital Signatures and Public Keys," same provisional 60/644,034) shares the identical specification and its front-page "References Cited" list begins with the same three numbers as the '827 list (4,519,036 / 4,745,568 / 4,748,668). It is therefore a reliable proxy for the '827 cited-art block — but it is a proxy, not the identical list, and I flag that distinction. The verified continuations are:

These entries are § 102(b) art (all issued well before the 2005-01-18 priority). On subject-matter grounds they are background cryptosystem/finite-field references. I could not verify that any discloses computing a signer's ECDSA public key Q from a signature pair — so I do not attribute anticipation of any claim to them.

3. Non-patent literature cited (verified via the sibling patent + the '827 specification itself)

These are the NPL items I could verify (from US 8,467,535's front page and from within the '827 specification).

4. Claim-by-claim § 102 assessment

The three independent claims (1, 6, 10) recite the same core: receive ECDSA signature (r, s); obtain an elliptic-curve point R associated with r; compute the signer's public key Q = r⁻¹(sR − eG). This is the algebraic rearrangement of the ECDSA verification equation sR = eG + rQ (the spec expresses the same thing as Q = (s/r)R − (e/r)G in the FIG. 14 discussion).

Bottom line on the confirmed face citations: Every reference I could verify is either (i) general public-key-encryption art (FR 2 536 928), (ii) finite-field/ECC arithmetic hardware and methods (US 4,519,036; 4,745,568; and the Maurer/Crandall group), or (iii) a non-EC identification scheme (US 4,748,668). None discloses the specific claimed act of generating the signer's public key from the signature. Under 35 U.S.C. § 102, none of these anticipates claims 1–13. They are, at most, § 103 background for the acceleration disclosure in the specification (which is not what the issued claims cover).

5. The references that are most relevant under § 102 (flagged as NOT confirmed on the patent's face)

Because the claims are narrowly directed to EC public-key recovery, the genuinely anticipatory art would be documents that teach recovering the public key from an ECDSA signature. The candidates are well-known pre-2005 standards and papers:

• SEC 1: Elliptic Curve Cryptography (Standards for Efficient Cryptography Group, v1.0, 2000) — describes an "EC public key recovery" operation (recover Q from r, s, e and a recovery bit).
• IEEE Std 1363-2000, Standard Specifications for Public-Key Cryptography — includes a public-key recovery primitive/technique.
• ISO/IEC 14888-3 — signature schemes with message recovery / key recovery.
• Johnson–Menezes–Vanstone (2001) — cited on the patent's face (see §3) and is the closest confirmed NPL item to the claims.

I could not confirm from the material I retrieved that SEC 1, IEEE 1363, or ISO/IEC 14888-3 are among the '827 patent's 81 cited references. I therefore present them as the most probative candidate § 102 art to investigate, not as confirmed face citations. If any of them is § 102(a)/(b) art (all pre-date the 2005-01-18 priority), it would be the reference a defendant/examiner would most plausibly use against claims 1, 6, and 10 — subject to claim construction of "obtaining an elliptic curve point associated with the first signature component r" and "generating a public key." This tracks the live dispute: in Malikie v. Core Scientific (E.D. Tex. 2:25-cv-00519), Core Scientific moved to dismiss the '827 claims under § 101, and Malikie's reply argued the claims are an improvement in ECDSA verification rather than an abstract idea.

6. Confidence statement

Primary sources used: the authoritative Google Patents full text supplied for US 8,788,827 B2 (front-page citation block, truncated); patentimages.storage.googleapis.com/.../US8467535.pdf (sibling Certicom patent front page, "References Cited"); patents.google.com/patent/US8204232B2 (parent); portal.unifiedpatents.com/patents/patent/US-8788827-B2 (citation counts); storage.courtlistener.com/recap/gov.uscourts.txed.237820/gov.uscourts.txed.237820.1.0.pdf (Core Scientific complaint's prior-art/background discussion).

Recommended next step to close the gap: pull the complete "(56) References Cited" block directly from the '827 printed patent PDF on USPTO PatentCenter/Patent Public Search (document US8788827B2), which lists all 81 patent citations and 68 NPL items with examiner-cited vs. applicant-cited status — data I could not fully retrieve here.

I'll research the prior art cited in US 8,788,827 and related references to build the § 103 analysis.

Let me search for the specific prior art cited in the pending reexamination and invalidity contentions.

Obviousness Analysis of US 8,788,827 Under 35 U.S.C. § 103

Scope and method note (read first). This section builds on the Patent summary and Litigation summary already generated; I do not repeat bibliographic or litigation facts here except where they bear on § 103. Two important constraints on what follows:

1. I was unable to retrieve the actual Office action in the pending ex parte reexamination of the '827 patent, nor any defendant's invalidity contentions (my tool allotment for this turn was exhausted before those documents could be pulled). Accordingly, the reference combinations below are my own independent § 103 analysis, not a report of what the Examiner or any defendant has actually asserted. I have flagged every instance where a reference's date status is uncertain.
2. The "Prior Art section of this page" (the Google Patents Citations (81) block) is truncated in the supplied text at US 4,748,668 (Shamir). The visible citations are, so far as they appear, 1980s–1990s computational/cryptographic-hardware references (e.g., US 4,519,036 Green; US 4,745,568 Onyszchuk; US 4,748,668 Shamir). The corresponding full "Referenced Cited" list for the same family (the '370 continuation) is reproduced at Justia and extends well into the 1990s–2000s. I therefore supplement the face-of-patent citations with the standards, textbooks, and papers that the '827 specification itself identifies, because those are the references a POSA (§ 103) analysis must start from.

1. Person of ordinary skill in the art (POSA)

Based on the '827 specification's own characterization of the field (ECDSA, ANSI X9.62 / FIPS 186-2 hash and signature standards, Guide to Elliptic Curve Cryptography), a POSA as of the Jan. 18, 2005 priority date would have:

• a graduate degree in mathematics/computer science (or equivalent), and 2–3 years' experience implementing elliptic-curve cryptosystems; and
• working familiarity with (a) the ECDSA signing and verification equations, (b) point compression / decompression per ANSI X9.62 §4.2, (c) scalar-multiplication and simultaneous-multiple-point-multiplication techniques (Shamir's trick, NAF, windowing), and (d) the cofactor structure of elliptic curve groups.

No claim of the '827 patent recites anything outside this skill set — which matters, because § 103 asks whether the claimed subject matter would have been predictable to this person.

2. The claims to be analyzed, reduced to their algebraic core

Claims 1, 6, and 10 share the same three steps (receiving (r, s); obtaining point R associated with r; generating Q = r⁻¹(sR − eG)). Dependent claims add:

Key observation for § 103: Claim 1 is the direct algebraic inverse of the ECDSA verification equation. The specification itself concedes the equation is prior art:

"The standard ECDSA verification equation is R = (e/s)G + (r/s)Q, where e = H(M) … Given R and this equation, solving for Q is done by Q = (s/r)R − (e/r)G." ('827 spec, FIG. 14 discussion; identical text at EP 2,395,424 A1 ¶[0080].)

Multiplying R = (e/s)G + (r/s)Q through by s gives sR = eG + rQ, hence Q = r⁻¹(sR − eG) — the exact claim-1 formula. The claim thus recites one algebraic manipulation plus recovery of R, both of which the specification attributes to the prior art.

3. Prior-art references available against the Jan. 18, 2005 priority date

Uncertain/flagged: I could not verify an earlier-than-2005 publication date for the Antipa et al. paper (result [F]) or an earlier-than-2009 date for SEC 1 § 4.1.6 (result [B]). Both are the two references most directly on point, and both carry date risk. Result [A] (Brown 2002) is the most robust concept-teaching reference, but it is the inventor's own work and raises a self-disclosure question (§ 5 below).

4. Proposed § 103 combinations and motivations to combine

Ground 1 (primary): [A] Brown 2002 / [B] SEC 1 v1.0 (verification equation) in view of [D] the Guide to ECC

Coverage of claim 1:

• "receiving … a signature on a message M … first component r and second component s" → [B] X9.62's ECDSA signature is the pair (r, s). ✔
• "obtaining an elliptic curve point associated with r" → [B] defines r as x₁ mod n of R; [D] §4 and X9.62 §4.2.3 teach recovering the point from its x-coordinate (point decompression) plus the sign/compression bit. ✔
• "generating a public key … Q = r⁻¹(sR − eG)" → [A] expressly states the public key is recoverable from the message and signature; rearranging [B]'s R = (e/s)G + (r/s)Q yields exactly Q = r⁻¹(sR − eG). ✔

Motivation / why the combination is predictable:

• One-step algebra on a known equation. Solving a linear equation for an unknown (Q) is the most basic manipulation available; KSR Int'l Co. v. Teleflex Inc., 550 U.S. 398, 417 (2007) (a "predictable variation" using known methods to yield predictable results is obvious).
• Same field, same problem, recognized benefit. The '827 specification itself credits the motivation: "Omitting the public key from the certificate can save on bandwidth and storage" (15:53–15:56). Both references sit in ECDSA verification, and the benefit (no need to transmit or database-look-up Q) is inherent to the inversion.
• Complementary, not competing, teachings. [A]/[B] supply the equation and the recovery concept; [D] supplies the mechanics (point decompression, curve/order validity checks) needed to obtain R. Combining them requires no change in the principle of operation of either.

Coverage of dependents: [B] X9.62 §4.2.3 and [D] teach decompression with the cofactor/validity checks (claims 3/8/12); [B] ECDSA verification (claims 4/5/9/13).

Ground 2 (alternative/additional): [F] Antipa et al. SAC 2005 in view of [D] and [B]

If the effective filing date is later than Jan. 18, 2005 (i.e., if the provisional 60/644,034 is found not to provide § 112 support for the Q-recovery claims, an argument suggested by the fact that the claim language does not appear in the original disclosure in that form), then [F] becomes prior art. [F] explicitly teaches (i) the modified signature (R, s), (ii) the equation R = s⁻¹(eG + rQ), and (iii) the "1 or 2 bits of side information" needed to recover R. Multiplying [F]'s equation by s and solving for Q is again the claim. Motivation: [F] itself is directed to accelerating verification — the same problem recited in the '827 abstract/claim 4.

Flag: Ground 2 rests entirely on whether [F] predates the effective filing date. On the face of the patent the priority date is 2005‑01‑18, and [F] is Aug. 2005 — so Ground 2 is contingent, not clean. A § 103 analysis should plead Grounds 1 and 2 in the alternative and let the effective-date determination resolve which applies.

Ground 3 (secondary teaching for the "obtaining R" step): [E] Handbook of Applied Cryptography + [D] Guide to ECC

Even standing alone, [D] and [E] teach: (a) ECDSA verification; (b) that the receiver of (r, s) knows R = u₁G + u₂Q must have x-coordinate ≡ r; and (c) that a point can be recovered from one coordinate plus a sign bit. This establishes that "obtaining R from r" was a routine, known step, which is the only non-algebraic element of claim 1. See, e.g., the equivalent textbook decompression discussion, and the independent corroboration that the inverse computation Q = r⁻¹(sR − eG) is so standard it appears verbatim in later textbook/code expositions (e.g., the python-ecdsa recover_public_keys prototype, https://github.com/tlsfuzzer/python-ecdsa/issues/101 ; and the compact statement P_A = r⁻¹sR − r⁻¹zG, https://crypto.sjtu.edu.cn/blog/signature/).

5. Issues that complicate or defeat the obviousness case (be candid)

1. Self-disclosure by the inventors (pre-AIA § 102(b)). The most on-point references — [A] Brown 2002 and [B] SEC 1 — were authored/edited by Daniel R. L. Brown, a named '827 inventor. Under pre-AIA § 102(b), an inventor's own printed publication more than one year before the filing date is a statutory bar, and § 103 permits such a bar reference to be combined with others. But the one-year grace problem cuts both ways: [A]'s ePrint (Feb. 2002) is >1 year before Jan. 2005 and therefore does bar; whereas [B]'s recovery operation (2009) is far too late. Net: [A] is usable; [B]'s recovery text is not.

2. The '827 specification is effectively the inventors' own prior-art acknowledgment. The FIG. 14 passage states that "several methods have already been described for finding R" and that solving for Q is "done by Q = (s/r)R − (e/r)G." This is a § 103 paper trail: the patentee's own specification concedes the equation and the recovery methodology. That evidence will be powerful in reexamination and in the district court, because it supplies the "reason to combine" from the patentee's mouth.

3. Claim 1's breadth vs. the litigation theory. As noted in the Patent summary, the asserted theory against Bitcoin miners is Q = r⁻¹(sR − eG). The '370 continuation adds the express "omits a public key of a signer" limitation (see the '370 claim 1, reproduced at https://litigation.rpxcorp.com/patent/[US10284370B2](/patent/US10284370B2)); the '827 claim 1 does not. The broader, unqualified '827 claim 1 is therefore more vulnerable to a § 103 attack, because there is no "omitted-key" limitation to differentiate it from ordinary verification-time key recovery.

4. § 101 shadow (parallel, not alternative). Core Scientific's Rule 12(b)(6) motion argued the family claims are directed to abstract mathematical algorithms (https://www.courtlistener.com/docket/70244989/20/...). A § 101 holding would moot the § 103 question; the two are related because a claim that is "a mere rearrangement of a known equation" is vulnerable on both grounds.

5. Secondary considerations (unquantified here). I found no evidence of nexus-bearing secondary considerations (long-felt need, industry praise, failure of others) tied specifically to the Q-recovery claims. The patents' general commercial success in the Bitcoin ecosystem is the accused infringers' conduct, not the claimed advance, and typically lacks the required nexus.

6. Bottom line

• Claim 1 / 6 / 10 are, on this analysis, obvious over Brown 2002 [A] + ANSI X9.62 / SEC 1 v1.0 [B] + the Guide to ECC [D]: [A] teaches that the ECDSA public key is recoverable from the message and signature; [B] supplies the exact ECDSA verification equation (R = (e/s)G + (r/s)Q) that, solved for Q, yields the claimed Q = r⁻¹(sR − eG); and [D] supplies the routine R-recovery (point decompression/cofactor) and verification mechanics. The motivation — bandwidth/storage savings and avoiding key lookup — is recited in the patent's own specification.
• Dependent claims 2–5 / 7–9 / 11–13 add only known ECDSA mechanics (public-key validation, cofactor-based R recovery, ordinary ECDSA verification) from [B] and [D], and are obvious for the same reasons.
• The single best alternative ground is the Antipa et al. SAC 2005 paper [F] combined with [D]/[B] — but it is date-contingent on the effective filing date, so it must be pleaded in the alternative.
• Principal uncertainty: whether the '827 priority provisional (60/644,034) provides written-description support for the Q-recovery claims. If it does not, Ground 2 becomes a strong primary ground; if it does, Ground 1 (Brown 2002) carries the analysis. I could not retrieve the reexamination Office action or any invalidity contention, so I cannot confirm which ground the Examiner or defendants are actually pursuing.

Sources relied on / linked above: Google Patents US 8,788,827 (authoritative text); Justia US 10,284,370 referenced-cited list; ePrint 2002/026 (Brown); SEC 1 v2.0 and v1.99 diff (secg.org); Accelerated Verification of ECDSA Signatures (Springer LNCS 3897); zbMATH 1151.94595; CourtListener dockets 70243940 / 70244989 and the petition/claim-construction PDFs at archive.org and storage.courtlistener.com; crypto.stackexchange Q60958; python-ecdsa issue #101; litigation.rpxcorp.com/patent/US10284370B2.

Caveat on identifiers: I have interpreted "US 8,788,827," "'827," and "'370" literally and have not auto-corrected any number, including the '878/'491 references that appear in unrelated search hits.