US 8,532,286 System and method for reducing the computation and storage requirements for a montgomery-style reduction
4 defendants · 4 suits · updated October 13, 2026
Also cited as U.S. Patent No. 8,532,286 · US8532286B2 · US 8,532,286 B2 · 8532286 · the '286 patent
Malikie Innovations Ltd. has filed 4 patent-infringement suits on US 8,532,286, "System and method for reducing the computation and storage requirements for a montgomery-style reduction" since August 28, 2026, 2 of them in the W.D. Tex., against 4 distinct defendants including Foundry Digital LLC, Antpool Technologies Limited and ViaBTC Technology Limited. The patent was granted September 10, 2013 on a priority date of July 17, 2009. Its abstract opens: "A system and method are described that provide an alternative way in which to produce a Montgomery reduction from below by storing a new precomputed value used to substantially replace the μ and n values used in Montgomery reduction with a single value." The examiner cited 18 references during prosecution.
- Assignee
- Malikie Innovations Ltd
- Priority date
- July 17, 2009
- Granted
- September 10, 2013
- Expires
- July 17, 2029
- Status
- Active
- Claims
- 25 (3 independent)
- Inventors
- Robert John Lambert
- Full text
- Google Patents
The suits
4 cases · W.D. Tex. (2) · W.D.N.Y. (1) · E.D. Tex. (1)
| Filed | Defendant | Plaintiff | Court | Docket |
|---|---|---|---|---|
| 2026-08-28 | Foundry Digital LLC | Malikie Innovations Ltd. | W.D.N.Y. | 6:26-cv-06874 |
| 2026-09-09 | Antpool Technologies Limited | Malikie Innovations Ltd. | W.D. Tex. | 7:26-cv-00371 |
| 2026-09-09 | ViaBTC Technology Limited | Malikie Innovations Ltd. | W.D. Tex. | 7:26-cv-00372 |
| 2026-09-22 | Foris DAX, Inc. d/b/a Crypto.com | Malikie Innovations Ltd. | E.D. Tex. | 2:26-cv-00864 |
Docket links open the public record on CourtListener. Filing dates are the complaint's.
Independent claims
What is actually asserted, verbatim.
1. A method for performing, on a cryptographic apparatus, a Montgomery-style reduction in a cryptographic operation, the method comprising: obtaining an operand for the cryptographic operation; computing a modified operand using a reduction value, instead of a modulus used in performing a standard Montgomery reduction, to perform a replacement of a least significant word of the operand, rather than perform a cancellation thereof, the reduction value being a function of the modulus; and outputting the modified operand.
10. A cryptographic apparatus comprising a processor configured to operate as a Montgomery engine, and computer executable instructions that when executed by the processor: obtain an operand for the cryptographic operation; compute a modified operand using a reduction value, instead of a modulus used in performing a standard Montgomery reduction, to perform a replacement of a least significant word of the operand, rather than perform a cancellation thereof, the reduction value being a function of the modulus; and output the modified operand.
18. A non-transitory computer readable medium comprising computer executable instructions that when executed by a cryptographic apparatus, cause the cryptographic apparatus to: obtain an operand for the cryptographic operation; compute a modified operand using a reduction value, instead of a modulus used in performing a standard Montgomery reduction, to perform a replacement of a least significant word of the operand, rather than perform a cancellation thereof, the reduction value being a function of the modulus; and output the modified operand.
Art before the examiner
20 references of record, 18 cited by the examiner.
Everything listed here was before the Office and is what a challenge must go beyond. Art the examiner never saw is where an invalidity search starts.
Examiner-cited
- US5261001A — Microcircuit for the implementation of RSA algorithm and ordinary and modular arithmetic, in particular exponentiation, with large operands (Fortress U&T (2000) Ltd)
- US6182104B1 — Circuit and method of modulo multiplication (Motorola, Inc.)
- US6240436B1 — High speed montgomery value calculation (Rainbow Technologies, Inc.)
- US6356636B1 — Circuit and method for fast modular multiplication (Motorola, Inc.)
- US6397241B1 — Multiplier cell and method of computing (Motorola, Inc.)
- US6424987B1 — Method for the implementation of a specific modular multiplication operation relating to the montgomery method (Stmicroelectronics S.A.)
- US20040096057A1 — Modular multiplication of multi-precision numbers (Moore Stephen F.)
- US6748410B1 — Apparatus and method for modular multiplication and exponentiation based on montgomery multiplication (M-Systems Flash Disk Pioneers, Ltd.)
- US6782100B1 — Accelerated finite field operations on an elliptic curve (Certicom Corp.)
- US20080147768A1 — Configurable Exponent Fifo (Intel Corporation)
- US20080144811A1 — Method for Simultaneous Modular Exponentiations (Intel Corporation)
- US20080148024A1 — Hardware Accelerator (Intel Corporation)
- US20090003594A1 — Modulus scaling for elliptic-curve cryptography (Erdinc Ozturk)
- US7552377B1 — Method of and circuit for interleaving data in a data coder (Xilinx, Inc.)
- US20090268900A1 — Signed montgomery arithmetic (Lambert Robert J)
- US20100146028A1 — Method and apparatus for modulus reduction (Certicom Corp.)
- US20100332578A1 — Method and apparatus for performing efficient side-channel attack resistant reduction (Vinodh Gopal)
- US20110270906A1 — Method and apparatus for providing flexible bit-length moduli on a block montgomery machine (Certicom Corp.)
Applicant-cited and other (2)
- US20060126830A1 — Montgomery transform device, arithmetic device, IC card, encryption device, decryption device and program
- EP1818809A1 — Apparatus for performing multiprecision integer arithmetic
Classification
- H04L9/30primary — Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
- G06F7/728 — Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers using residue arithmetic using Montgomery reduction
- H04L2209/122 — Hardware reduction or efficient architectures
Family
- US8532286B2 — B2 (2013)
- US20110013768A1 — A1 (2011)
- 4 foreign family members: CA2710064A1, CA2710064C, EP2276194A1, EP2276194B1
Abstract
A system and method are described that provide an alternative way in which to produce a Montgomery reduction from below by storing a new precomputed value used to substantially replace the μ and n values used in Montgomery reduction with a single value. By modifying the Montgomery reduction mechanism in this way, the number of multiplications and registers required to effect the Montgomery reduction can be reduced. To avoid having to store both μ and n, a modified reduction value or a logical shift or signed version of such a value can be used in place of μ and n for the bulk of the low-order reduction.
Also asserted by Malikie Innovations Ltd.
- US 7,453,856 — Method, apparatus, and communications interface for sending and receiving data blocks associated with different multiple access techniques (3 defendants)
- US 7,747,934 — Method for selecting low density parity check (LDPC) code used for encoding of variable length data (3 defendants)
- US 7,917,829 — Low density parity check (LDPC) code (3 defendants)
- US 8,291,289 — Low density parity check (LDPC) code (3 defendants)
- US 8,712,039 — Efficient implementation of hash algorithm on a processor (3 defendants)
- US 8,788,827 — Accelerated verification of digital signatures and public keys (3 defendants)
- US 8,806,197 — Accelerated verification of digital signatures and public keys (3 defendants)
Named in one of these suits? A prior-art search is commissioned once and serves every defendant who shares it. The examiner's own search record is free on the tools page, and your first preliminary search is free — one claim, back within 24 hours — so you know whether there is art the Office never saw before anyone pays for more. Flat fees: $2,500$899 for the independent claims, $5,000$1,500 for every asserted claim.
This page is assembled from public records — federal court dockets and the patent's own file — and is updated as the case list changes. It states what the record shows and is not an opinion on the validity or infringement of any claim. Patent data via Google Patents; docket data via CourtListener.