Montgomery Reduction in Cryptographic Operations

SECURITY DEVICE AND METHOD FOR PERFORMING INTEGER MULTIPLICATION OPERATION

Methods for Determining a Gaussian Integer Congruent to a Given Gaussian Integer Modulo a Gaussian Integer Modulus and for Determining a Reduction of a Given Gaussian Integer Modulo a Gaussian Integer Modulus

PARALLEL POLYNOMIAL MODULAR MULTIPLICATION USING NTT AND INVERSE NTT

MULTI-LANE CRYPTOGRAPHIC ENGINES WITH SYSTOLIC ARCHITECTURE AND OPERATIONS THEREOF

Decoding multipath data communications system and methods

OPTIMIZATION TECHNIQUE FOR MODULAR MULTIPLICATION ALGORITHMS

Low-latency pipeline and method for use of a low latency pipeline in homomorphic encryption

System and Method for Big Number Hardware Multiplication for Cryptography

DESIGN OF HIGH-PERFORMANCE AND SCALABLE MONTGOMERY MODULAR MULTIPLIER CIRCUITS

Modular multiplication circuit and corresponding modular multiplication method

METHODS AND APPARATUS TO IMPROVE PERFORMANCE OF ENCRYPTION AND DECRYPTION TASKS

Fast precomputation for Montgomery multiplier

Efficient montgomery multiplier

Device and Method of Handling a Modular Multiplication

System and method to generate prime numbers in cryptographic applications

Efficient squaring with loop equalization in arithmetic logic units

Low complexity conversion to Montgomery domain

Low complexity conversion to Montgomery domain

INTEGRATED CIRCUIT FOR MODULAR MULTIPLICATION OF TWO INTEGERS FOR A CRYPTOGRAPHIC METHOD, AND METHOD FOR THE CRYPTOGRAPHIC PROCESSING OF DATA BASED ON MODULAR MULTIPLICATION

Reduced and pipelined hardware architecture for Montgomery Modular Multiplication

Secure transformation from a residue number system to a radix representation

COUNTERMEASURE TO SAFE-ERROR FAULT INJECTION ATTACKS ON CRYPTOGRAPHIC EXPONENTIATION ALGORITHMS

Quantum resource estimates for computing elliptic curve discrete logarithms

Dynamic channels in secure queries and analytics

Systems and methods for efficient fixed-base multi-precision exponentiation

Compression and homomorphic encryption in secure query and analytics

Secure web browsing via homomorphic encryption

Key processing method and device

Montgomery multiplication processors, methods, systems, and instructions

Apparatus and method for modular multiplication

Parallel computation techniques for accelerated cryptographic capabilities

Modular multiplication device and method

Montgomery modular multiplication device and embedded security chip with same

METHOD, DEVICE AND NON-TRANSITORY COMPUTER-READABLE MEDIUM FOR CRYPTOGRAPHIC COMPUTATION

Modular multiplier and modular multiplication method thereof

Cryptographic accelerator

Method for implementing precomputation of large number in embedded system

Montgomery modular multiplication-based data processing method

Montgomery multiplication method for performing final modular reduction without comparison operation and montgomery multiplier

Efficient prime-number check

Multiplication method and modular multiplier using redundant form recoding

Modular multiplier and modular multiplication method thereof

Modular arithmatic unit and secure system including the same

Method for encrypting a message through the computation of mathematical functions comprising modular multiplications

Modular exponentiation with partitioned and scattered storage of Montgomery Multiplication results

Montgomery multiplication method

Montgomery multiplication circuit

Montgomery inverse calculation device and method of calculating montgomery inverse using the same

MODULAR EXPONENTIATION RESISTANT AGAINST SKIPPING ATTACKS

Arithmetic device

CIRCUITS FOR MODULAR ARITHMETIC BASED ON THE COMPLEMENTATION OF CONTINUED FRACTIONS

Exponentiation method resistant against side-channel and safe-error attacks

Instruction support for performing montgomery multiplication

Method and apparatus for providing flexible bit-length moduli on a block Montgomery machine

Montgomery multiplier having efficient hardware structure

Montgomery multiplication architecture

Method and apparatus for processing arbitrary key bit length encryption operations with similar efficiencies

Modular multiplication processing apparatus

System and method for reducing the computation and storage requirements for a montgomery-style reduction

Serially connected processing elements having forward and reverse processing time intervals

Modular multiplier apparatus with reduced critical path of arithmetic operation and method of reducing the critical path of arithmetic operation in arithmetic operation apparatus

ARRANGEMENT FOR AND METHOD OF PROTECTING A DATA PROCESSING DEVICE AGAINST AN ATTACK OR ANALYSIS

Scalable Montgomery multiplication architecture

Arithmetic circuit for montgomery multiplication and encryption circuit

MONTGOMERY-BASED MODULAR EXPONENTIATION SECURED AGAINST HIDDEN CHANNEL ATTACKS

METHOD AND APPARATUS FOR MODULAR OPERATION

Method and apparatus for modulus reduction

Methods of calculating negative inverse of modulus

Arrangement for and method of protecting a data processing device against an attack or analysis

Information security device, information security method, computer program, computer-readable recording medium, and integrated circuit

Embedded device having countermeasure function against fault attack

Modular multiplication calculation apparatus used for montgomery method

Cryptographic method comprising secure modular exponentiation against hidden-channel attacks, cryptoprocessor for implementing the method and associated chip card

Signed montgomery arithmetic

Method for scalar multiplication in elliptic curve groups over prime fields for side-channel attack resistant cryptosystems

Method and apparatus for efficient modulo multiplication

Computational method, system, and apparatus

Circuit and method for performing multiple modulo mathematic operations

MODULAR REDUCTION OPERATOR

MONTGOMERY MASKED MODULAR MULTIPLICATION PROCESS AND ASSOCIATED DEVICE

Method and apparatus for processing arbitrary key bit length encryption operations with similar efficiencies

Method for implementing montgomery modular multiplication and device therefore

Calculating apparatus having a plurality of stages

Data processing method and related device

Signal processing apparatus and method for performing modular multiplication in an electronic device, and smart card using the same

Computation of a multiplication operation with an electronic circuit and method

Modular multiplication acceleration circuit and method for data encryption/decryption

Scalable, faster method and apparatus for montgomery multiplication

Ring arithmetic method, system, and apparatus

Multiplicand shifting in a linear systolic array modular multiplier

Modular multiplication processing apparatus

Extending the range of computational fields of integers

Device and method for calculating conversion parameter of montgomery modular multiplication and program therefor

Computation method, computing device and computer program

Methods and apparatus for pipeline processing of encryption data

Montgomery transform device, arithmetic device, IC card, encryption device, decryption device and program

Inverse calculation circuit, inverse calculation method, and storage medium encoded with computer-readable computer program code

Montgomery multiplier for RSA security module

Method and apparatus for performing Montgomery multiplications

Method and apparatus for performing modular exponentiations

Modular multipliers having segmentable structure and cryptography systems utilizing same

Circuit and method for performing multiple modulo mathematic operations

Circuit and method for performing multiple modulo mathematic operations

Modular-multiplication computing unit and information-processing unit

Modular-multiplication computing unit and information processing unit

Method and apparatus for calculating a modular inverse

Microprocessor apparatus and method for modular exponentiation

Apparatus and method for consistency checking public key cryptography computations

Correction parameter determination system

Montgomery modular multiplier

Multiple-word multiplication-accumulation circuit and montgomery modular multiplication-accumulation circuit

Encryption/decryption system for calculating effective lower bits of a parameter for Montgomery modular multiplication

Split radix multiplication

Utilizing SIMD instructions within montgomery multiplication

Method and apparatus for modular inversion for information security and recording medium with a program for implementing the method

Pipeline core in Montgomery multiplier

Architecture for small and efficient modular multiplication using carry-save adders

System and methods for multipath data communications

Montgomery multiplication devices

Multiple algorithm cryptography system