A survey of fast exponentiation methods
Journal of Algorithms
Checking Before Output May Not Be Enough Against Fault-Based Cryptanalysis
IEEE Transactions on Computers
Observability Analysis - Detecting When Improved Cryptosystems Fail
CT-RSA '02 Proceedings of the The Cryptographer's Track at the RSA Conference on Topics in Cryptology
Efficient elliptic curve exponentiation
ICICS '97 Proceedings of the First International Conference on Information and Communication Security
A Countermeasure against One Physical Cryptanalysis May Benefit Another Attack
ICISC '01 Proceedings of the 4th International Conference Seoul on Information Security and Cryptology
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other Systems
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
IFIP/Sec '93 Proceedings of the IFIP TC11, Ninth International Conference on Information Security: Computer Security
Elliptic Curves with the Montgomery-Form and Their Cryptographic Applications
PKC '00 Proceedings of the Third International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
A Fast Parallel Elliptic Curve Multiplication Resistant against Side Channel Attacks
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
Weierstraß Elliptic Curves and Side-Channel Attacks
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
Power Analysis Attacks of Modular Exponentiation in Smartcards
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Resistance against Differential Power Analysis for Elliptic Curve Cryptosystems
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Fast Multiplication on Elliptic Curves over GF(2m) without Precomputation
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
An RSA Implementation Resistant to Fault Attacks and to Simple Power Analysis
IEEE Transactions on Computers
Efficient elliptic curve scalar multiplication algorithms resistant to power analysis
Information Sciences: an International Journal
Design methods for security and trust
Proceedings of the conference on Design, automation and test in Europe
On the power of simple branch prediction analysis
ASIACCS '07 Proceedings of the 2nd ACM symposium on Information, computer and communications security
IEEE Transactions on Computers
Sequential Circuit Design for Embedded Cryptographic Applications Resilient to Adversarial Faults
IEEE Transactions on Computers
Highly Regular Right-to-Left Algorithms for Scalar Multiplication
CHES '07 Proceedings of the 9th international workshop on Cryptographic Hardware and Embedded Systems
RSA with CRT: A New Cost-Effective Solution to Thwart Fault Attacks
CHES '08 Proceeding sof the 10th international workshop on Cryptographic Hardware and Embedded Systems
CHES '08 Proceeding sof the 10th international workshop on Cryptographic Hardware and Embedded Systems
Method for Detecting Vulnerability to Doubling Attacks
ICICS '08 Proceedings of the 10th International Conference on Information and Communications Security
Twisted Edwards Curves Revisited
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Using Templates to Attack Masked Montgomery Ladder Implementations of Modular Exponentiation
Information Security Applications
Novel PUF-Based Error Detection Methods in Finite State Machines
Information Security and Cryptology --- ICISC 2008
On Second-Order Fault Analysis Resistance for CRT-RSA Implementations
WISTP '09 Proceedings of the 3rd IFIP WG 11.2 International Workshop on Information Security Theory and Practice. Smart Devices, Pervasive Systems, and Ubiquitous Networks
A new fault cryptanalysis on montgomery ladder exponentiation algorithm
Proceedings of the 2nd International Conference on Interaction Sciences: Information Technology, Culture and Human
On Cryptographic Schemes Based on Discrete Logarithms and Factoring
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
ISPEC'07 Proceedings of the 3rd international conference on Information security practice and experience
Fault attacks for CRT based RSA: new attacks, new results and new countermeasures
WISTP'07 Proceedings of the 1st IFIP TC6 /WG8.8 /WG11.2 international conference on Information security theory and practices: smart cards, mobile and ubiquitous computing systems
CRT RSA algorithm protected against fault attacks
WISTP'07 Proceedings of the 1st IFIP TC6 /WG8.8 /WG11.2 international conference on Information security theory and practices: smart cards, mobile and ubiquitous computing systems
Safe-error attack on SPA-FA resistant exponentiations using a HW modular multiplier
ICISC'07 Proceedings of the 10th international conference on Information security and cryptology
Faster addition and doubling on elliptic curves
ASIACRYPT'07 Proceedings of the Advances in Crypotology 13th international conference on Theory and application of cryptology and information security
A generic method for secure Sbox implementation
WISA'07 Proceedings of the 8th international conference on Information security applications
SPA resistant elliptic curve cryptosystem using addition chains
International Journal of High Performance Systems Architecture
Finite field arithmetic for cryptography
IEEE Circuits and Systems Magazine
New fault attacks using Jacobi symbol and application to regular right-to-left algorithms
Information Processing Letters
An efficient implementation of montgomery powering ladder in reconfigurable hardware
SBCCI '10 Proceedings of the 23rd symposium on Integrated circuits and system design
ISWPC'10 Proceedings of the 5th IEEE international conference on Wireless pervasive computing
Proceedings of the 6th ACM workshop on QoS and security for wireless and mobile networks
A new CRT-RSA algorithm resistant to powerful fault attacks
WESS '10 Proceedings of the 5th Workshop on Embedded Systems Security
A high speed coprocessor for elliptic curve scalar multiplications over Fp
CHES'10 Proceedings of the 12th international conference on Cryptographic hardware and embedded systems
Co-Z addition formulæ and binary ladders on elliptic curves
CHES'10 Proceedings of the 12th international conference on Cryptographic hardware and embedded systems
Combined implementation attack resistant exponentiation
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
An ECDSA pocessor for RFID athentication
RFIDSec'10 Proceedings of the 6th international conference on Radio frequency identification: security and privacy issues
Horizontal correlation analysis on exponentiation
ICICS'10 Proceedings of the 12th international conference on Information and communications security
High speed flexible pairing cryptoprocessor on FPGA platform
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
International Journal of Reconfigurable Computing - Special issue on selected papers from the southern programmable logic conference (SPL2010)
An efficient CRT-RSA algorithm secure against power and fault attacks
Journal of Systems and Software
A cryptographic processor for low-resource devices: canning ECDSA and AES like sardines
WISTP'11 Proceedings of the 5th IFIP WG 11.2 international conference on Information security theory and practice: security and privacy of mobile devices in wireless communication
Arithmetic of split kummer surfaces: montgomery endomorphism of Edwards products
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
Memory-constrained implementations of elliptic curve cryptography in co-Z coordinate representation
AFRICACRYPT'11 Proceedings of the 4th international conference on Progress in cryptology in Africa
Fault attacks on the montgomery powering ladder
ICISC'10 Proceedings of the 13th international conference on Information security and cryptology
To infinity and beyond: combined attack on ECC using points of low order
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
On XTR and side-channel analysis
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
Compiler mitigations for time attacks on modern x86 processors
ACM Transactions on Architecture and Code Optimization (TACO) - HIPEAC Papers
Superscalar coprocessor for high-speed curve-based cryptography
CHES'06 Proceedings of the 8th international conference on Cryptographic Hardware and Embedded Systems
RFID-Tags for anti-counterfeiting
CT-RSA'06 Proceedings of the 2006 The Cryptographers' Track at the RSA conference on Topics in Cryptology
Sign change fault attacks on elliptic curve cryptosystems
FDTC'06 Proceedings of the Third international conference on Fault Diagnosis and Tolerance in Cryptography
Blinded fault resistant exponentiation
FDTC'06 Proceedings of the Third international conference on Fault Diagnosis and Tolerance in Cryptography
CT-RSA'05 Proceedings of the 2005 international conference on Topics in Cryptology
Predicting secret keys via branch prediction
CT-RSA'07 Proceedings of the 7th Cryptographers' track at the RSA conference on Topics in Cryptology
Atomicity improvement for elliptic curve scalar multiplication
CARDIS'10 Proceedings of the 9th IFIP WG 8.8/11.2 international conference on Smart Card Research and Advanced Application
SPA resistant left-to-right integer recodings
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
Relative doubling attack against montgomery ladder
ICISC'05 Proceedings of the 8th international conference on Information Security and Cryptology
An updated survey on secure ECC implementations: attacks, countermeasures and cost
Cryptography and Security
Elliptic curve cryptography on the WISP UHF RFID tag
RFIDSec'11 Proceedings of the 7th international conference on RFID Security and Privacy
Memory-efficient fault countermeasures
CARDIS'11 Proceedings of the 10th IFIP WG 8.8/11.2 international conference on Smart Card Research and Advanced Applications
A hardware processor supporting elliptic curve cryptography for less than 9 kGEs
CARDIS'11 Proceedings of the 10th IFIP WG 8.8/11.2 international conference on Smart Card Research and Advanced Applications
INDOCRYPT'11 Proceedings of the 12th international conference on Cryptology in India
Exploring the design space of prime field vs. binary field ECC-Hardware implementations
NordSec'11 Proceedings of the 16th Nordic conference on Information Security Technology for Applications
Improved fixed-base comb method for fast scalar multiplication
AFRICACRYPT'12 Proceedings of the 5th international conference on Cryptology in Africa
The importance of the final exponentiation in pairings when considering fault attacks
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Complete atomic blocks for elliptic curves in jacobian coordinates over prime fields
LATINCRYPT'12 Proceedings of the 2nd international conference on Cryptology and Information Security in Latin America
Horizontal and vertical side-channel attacks against secure RSA implementations
CT-RSA'13 Proceedings of the 13th international conference on Topics in Cryptology
Low-Cost countermeasure against RPA
CARDIS'12 Proceedings of the 11th international conference on Smart Card Research and Advanced Applications
Secure dual-core cryptoprocessor for pairings over Barreto-Naehrig curves on FPGA platform
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Amplitude demodulation-based EM analysis of different RSA implementations
DATE '12 Proceedings of the Conference on Design, Automation and Test in Europe
Attacks on implementations of cryptographic algorithms: side-channel and fault attacks
Proceedings of the 6th International Conference on Security of Information and Networks
Fault attacks on projective-to-affine coordinates conversion
COSADE'13 Proceedings of the 4th international conference on Constructive Side-Channel Analysis and Secure Design
Updated recommendations for blinded exponentiation vs. single trace analysis
COSADE'13 Proceedings of the 4th international conference on Constructive Side-Channel Analysis and Secure Design
On the implementation of unified arithmetic on binary huff curves
CHES'13 Proceedings of the 15th international conference on Cryptographic Hardware and Embedded Systems
| Hi-index | 0.01 |
This paper gives a comprehensive analysis of Montgomery powering ladder. Initially developed for fast scalar multiplication on elliptic curves, we extend the scope of Montgomery ladder to any exponentiation in an abelian group. Computationally, the Montgomery ladder has the triple advantage of presenting a Lucas chain structure, of being parallelized, and of sharing a common operand. Furthermore, contrary to the classical binary algorithms, it behaves very regularly, which makes it naturally protected against a large variety of implementation attacks.