ATE472769T1 - Verbesserte natürliche montgomery- exponentenmaskierung - Google Patents

Verbesserte natürliche montgomery- exponentenmaskierung

Info

Publication number
ATE472769T1
ATE472769T1 AT04806656T AT04806656T ATE472769T1 AT E472769 T1 ATE472769 T1 AT E472769T1 AT 04806656 T AT04806656 T AT 04806656T AT 04806656 T AT04806656 T AT 04806656T AT E472769 T1 ATE472769 T1 AT E472769T1
Authority
AT
Austria
Prior art keywords
masking
montgomery
montgomery arithmetic
cryptographic device
improved natural
Prior art date
Application number
AT04806656T
Other languages
English (en)
Inventor
Carmi Gressel
Boris Dolgunov
Odile Derouet
Original Assignee
Sandisk Il Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Sandisk Il Ltd filed Critical Sandisk Il Ltd
Application granted granted Critical
Publication of ATE472769T1 publication Critical patent/ATE472769T1/de

Links

Classifications

    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
    • G06F7/60—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
    • G06F7/72—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
    • 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
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/002—Countermeasures against attacks on cryptographic mechanisms
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/06—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/30—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
    • H04L9/3006—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy underlying computational problems or public-key parameters
    • H04L9/3013—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy underlying computational problems or public-key parameters involving the discrete logarithm problem, e.g. ElGamal or Diffie-Hellman systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/30—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
    • H04L9/3006—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy underlying computational problems or public-key parameters
    • H04L9/302—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy underlying computational problems or public-key parameters involving the integer factorization problem, e.g. RSA or quadratic sieve [QS] schemes
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2207/00—Indexing scheme relating to methods or arrangements for processing data by operating upon the order or content of the data handled
    • G06F2207/72—Indexing scheme relating to groups G06F7/72 - G06F7/729
    • G06F2207/7219—Countermeasures against side channel or fault attacks
    • G06F2207/7223—Randomisation as countermeasure against side channel attacks
    • G06F2207/7233—Masking, e.g. (A**e)+r mod n
    • G06F2207/7238—Operand masking, i.e. message blinding, e.g. (A+r)**e mod n; k.(P+R)
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
    • H04L2209/04—Masking or blinding

Landscapes

  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Computing Systems (AREA)
  • Computer Security & Cryptography (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • General Physics & Mathematics (AREA)
  • Physics & Mathematics (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Mathematical Physics (AREA)
  • General Engineering & Computer Science (AREA)
  • Storage Device Security (AREA)
  • Dental Preparations (AREA)
  • Lubricants (AREA)
  • Electroplating And Plating Baths Therefor (AREA)
AT04806656T 2003-11-16 2004-11-16 Verbesserte natürliche montgomery- exponentenmaskierung ATE472769T1 (de)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
US52377303P 2003-11-16 2003-11-16
PCT/IL2004/001053 WO2005048008A2 (en) 2003-11-16 2004-11-16 Enhanced natural montgomery exponent masking

Publications (1)

Publication Number Publication Date
ATE472769T1 true ATE472769T1 (de) 2010-07-15

Family

ID=34590484

Family Applications (1)

Application Number Title Priority Date Filing Date
AT04806656T ATE472769T1 (de) 2003-11-16 2004-11-16 Verbesserte natürliche montgomery- exponentenmaskierung

Country Status (5)

Country Link
EP (1) EP1692800B1 (de)
CN (1) CN1985458B (de)
AT (1) ATE472769T1 (de)
DE (1) DE602004027943D1 (de)
WO (1) WO2005048008A2 (de)

Families Citing this family (15)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR2895609A1 (fr) 2005-12-26 2007-06-29 Gemplus Sa Procede cryptographique comprenant une exponentiation modulaire securisee contre les attaques a canaux caches, cryptoprocesseur pour la mise en oeuvre du procede et carte a puce associee
EP2015171A1 (de) * 2007-06-29 2009-01-14 Gemplus Kryptographieverfahren, das eine gesicherte modulare Potenzierung gegen Angriffe mit verborgenen Kanälen ohne Kenntnis des öffentlichen Exponenten umfasst, Kryptoprozessor zur Umsetzung des Verfahrens und dazugehörige Chipkarte
JP5390844B2 (ja) 2008-12-05 2014-01-15 パナソニック株式会社 鍵配布システム、鍵配布方法
ITMI20111992A1 (it) * 2011-11-03 2013-05-04 St Microelectronics Srl Metodo per crittografare un messaggio mediante calcolo di funzioni matematiche comprendenti moltiplicazioni modulari
DE102011088502B3 (de) * 2011-12-14 2013-05-08 Siemens Aktiengesellschaft Verfahren und Vorrichtung zur Absicherung von Blockchiffren gegen Template-Attacken
DE102012005427A1 (de) * 2012-03-16 2013-09-19 Giesecke & Devrient Gmbh Verfahren und System zur gesicherten Kommunikation zwischen einen RFID-Tag und einem Lesegerät
CN104291369A (zh) * 2014-09-28 2015-01-21 青岛康合伟业商贸有限公司 一种低温合成镁铝尖晶石的方法
EP3202079B1 (de) * 2014-10-03 2020-07-08 Cryptography Research, Inc. Exponentenspaltung für kryptografische operationen
US11522669B2 (en) 2018-03-28 2022-12-06 Cryptography Research, Inc. Using cryptographic blinding for efficient use of Montgomery multiplication
US11508263B2 (en) 2020-06-24 2022-11-22 Western Digital Technologies, Inc. Low complexity conversion to Montgomery domain
US11468797B2 (en) 2020-06-24 2022-10-11 Western Digital Technologies, Inc. Low complexity conversion to Montgomery domain
IT202100032048A1 (it) 2021-12-21 2023-06-21 Nextage S R L Sistema di gestione di dati criptati e metodo di ricerca di dati criptati
CN116830076A (zh) 2022-01-28 2023-09-29 辉达公司 用于高效模除法和模求逆的技术、设备和指令集架构
WO2023141935A1 (en) 2022-01-28 2023-08-03 Nvidia Corporation Techniques, devices, and instruction set architecture for balanced and secure ladder computations
WO2023141934A1 (en) * 2022-01-28 2023-08-03 Nvidia Corporation Efficient masking of secure data in ladder-type cryptographic computations

Family Cites Families (12)

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Publication number Priority date Publication date Assignee Title
US5003596A (en) * 1989-08-17 1991-03-26 Cryptech, Inc. Method of cryptographically transforming electronic digital data from one form to another
FR2726667B1 (fr) * 1994-11-08 1997-01-17 Sgs Thomson Microelectronics Procede de mise en oeuvre de multiplication modulaire selon la methode montgomery
JP2001527673A (ja) * 1997-05-04 2001-12-25 フォートレス ユー アンド ティー リミティド モントゴメリー乗算に基づくモジュラ乗算及び累乗の改善された装置と方法
US6748410B1 (en) * 1997-05-04 2004-06-08 M-Systems Flash Disk Pioneers, Ltd. Apparatus and method for modular multiplication and exponentiation based on montgomery multiplication
US5991415A (en) 1997-05-12 1999-11-23 Yeda Research And Development Co. Ltd. At The Weizmann Institute Of Science Method and apparatus for protecting public key schemes from timing and fault attacks
CA2253009C (en) * 1997-11-04 2002-06-25 Nippon Telegraph And Telephone Corporation Method and apparatus for modular inversion for information security and recording medium with a program for implementing the method
US6085210A (en) * 1998-01-22 2000-07-04 Philips Semiconductor, Inc. High-speed modular exponentiator and multiplier
AU6381799A (en) 1998-06-03 2000-01-10 Cryptography Research, Inc. Secure modular exponentiation with leak minimization for smartcards and other cryptosystems
FI107487B (fi) * 1999-03-08 2001-08-15 Nokia Mobile Phones Ltd Datalähetyksen salausmenetelmä radiojärjestelmässä
FR2828608B1 (fr) 2001-08-10 2004-03-05 Gemplus Card Int Procede securise de realisation d'une operation d'exponentiation modulaire
JP4360792B2 (ja) * 2002-09-30 2009-11-11 株式会社ルネサステクノロジ べき乗剰余演算器
US7532720B2 (en) * 2003-10-15 2009-05-12 Microsoft Corporation Utilizing SIMD instructions within montgomery multiplication

Also Published As

Publication number Publication date
CN1985458A (zh) 2007-06-20
CN1985458B (zh) 2013-05-08
EP1692800A2 (de) 2006-08-23
EP1692800B1 (de) 2010-06-30
EP1692800A4 (de) 2009-04-29
WO2005048008A3 (en) 2005-11-24
DE602004027943D1 (de) 2010-08-12
WO2005048008A2 (en) 2005-05-26

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