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
Power Analysis Breaks Elliptic Curve Cryptosystems even Secure against the Timing Attack
INDOCRYPT '00 Proceedings of the First International Conference on Progress in Cryptology
Securing Elliptic Curve Point Multiplication against Side-Channel Attacks
ISC '01 Proceedings of the 4th International Conference on Information Security
On the Performance of Signature Schemes Based on Elliptic Curves
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
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
Preventing SPA/DPA in ECC Systems Using the Jacobi Form
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
Universal Exponentiation Algorithm
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
Hessian Elliptic Curves and Side-Channel Attacks
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
Protections against Differential Analysis for Elliptic Curve Cryptography
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
ACISP '02 Proceedings of the 7th Australian Conference on Information Security and Privacy
Fast Elliptic Curve Multiplications with SIMD Operations
ICICS '02 Proceedings of the 4th International Conference on Information and Communications Security
Improved Elliptic Curve Multiplication Methods Resistant against Side Channel Attacks
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
ISC '02 Proceedings of the 5th International Conference on Information Security
A Second-Order DPA Attack Breaks a Window-Method Based Countermeasure against Side Channel Attacks
ISC '02 Proceedings of the 5th International Conference on Information Security
Exceptional Procedure Attackon Elliptic Curve Cryptosystems
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
On Montgomery-Like Representationsfor Elliptic Curves over GF(2k)
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
A Refined Power-Analysis Attack on Elliptic Curve Cryptosystems
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
Enhancing Simple Power-Analysis Attacks on Elliptic Curve Cryptosystems
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
The Montgomery Powering Ladder
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Address-Bit Differential Power Analysis of Cryptographic Schemes OK-ECDH and OK-ECDSA
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Fast algorithms for computing the eigenvalue in the Schoof-Elkies-Atkin algorithm
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Pipelined Computation of Scalar Multiplication in Elliptic Curve Cryptosystems (Extended Version)
IEEE Transactions on Computers
New Point Addition Formulae for ECC Applications
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
Highly Regular Right-to-Left Algorithms for Scalar Multiplication
CHES '07 Proceedings of the 9th international workshop on Cryptographic Hardware and Embedded Systems
Montgomery Ladder for All Genus 2 Curves in Characteristic 2
WAIFI '08 Proceedings of the 2nd international workshop on Arithmetic of Finite Fields
Recovering Secret Keys from Weak Side Channel Traces of Differing Lengths
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
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
Elliptic Curve Cryptography on FPGA for Low-Power Applications
ACM Transactions on Reconfigurable Technology and Systems (TRETS)
Implementation and analysis of stream ciphers based on the elliptic curves
Computers and Electrical Engineering
A Hardware Analysis of Twisted Edwards Curves for an Elliptic Curve Cryptosystem
ARC '09 Proceedings of the 5th International Workshop on Reconfigurable Computing: Architectures, Tools and Applications
Optimal Recovery of Secret Keys from Weak Side Channel Traces
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
Quantitative evaluation of side-channel security for elliptic curve cryptosystems
ASID'09 Proceedings of the 3rd international conference on Anti-Counterfeiting, security, and identification in communication
The Jacobi model of an elliptic curve and side-channel analysis
AAECC'03 Proceedings of the 15th international conference on Applied algebra, algebraic algorithms and error-correcting codes
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
Fast elliptic curve arithmetic and improved weil pairing evaluation
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
Solving discrete logarithms from partial knowledge of the key
INDOCRYPT'07 Proceedings of the cryptology 8th international conference on Progress in 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
Faster group operations on elliptic curves
AISC '09 Proceedings of the Seventh Australasian Conference on Information Security - Volume 98
Co-Z addition formulæ and binary ladders on elliptic curves
CHES'10 Proceedings of the 12th international conference on Cryptographic hardware and embedded systems
Coordinate blinding over large prime fields
CHES'10 Proceedings of the 12th international conference on Cryptographic hardware and embedded systems
Side-channel analysis of cryptographic software via early-terminating multiplications
ICISC'09 Proceedings of the 12th international conference on Information security and cryptology
An ECDSA pocessor for RFID athentication
RFIDSec'10 Proceedings of the 6th international conference on Radio frequency identification: security and privacy issues
Differential addition in generalized Edwards coordinates
IWSEC'10 Proceedings of the 5th international conference on Advances in information and computer security
Toric forms of elliptic curves and their arithmetic
Journal of Symbolic Computation
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
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
Generic cryptanalysis of combined countermeasures with randomized BSD representations
CARDIS'06 Proceedings of the 7th IFIP WG 8.8/11.2 international conference on Smart Card Research and Advanced Applications
Power analysis to ECC using differential power between multiplication and squaring
CARDIS'06 Proceedings of the 7th IFIP WG 8.8/11.2 international conference on Smart Card Research and Advanced Applications
Unified point addition formulæ and side-channel attacks
CHES'06 Proceedings of the 8th international conference on Cryptographic Hardware and Embedded Systems
Efficient simultaneous inversion in parallel and application to point multiplication in ECC
CISC'05 Proceedings of the First SKLOIS conference on Information Security and Cryptology
Signed MSB-set comb method for elliptic curve point multiplication
ISPEC'06 Proceedings of the Second international conference on Information Security Practice and Experience
EM analysis of rijndael and ECC on a wireless java-based PDA
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
Simple power analysis on fast modular reduction with NIST recommended elliptic curves
ICICS'05 Proceedings of the 7th international conference on Information and Communications Security
Efficient arithmetic on hessian curves
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Improving the randomized initial point countermeasure against DPA
ACNS'06 Proceedings of the 4th international conference on Applied Cryptography and Network Security
Evaluation metrics of physical non-invasive security
WISTP'10 Proceedings of the 4th IFIP WG 11.2 international conference on Information Security Theory and Practices: security and Privacy of Pervasive Systems and Smart Devices
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
On the automatic construction of indistinguishable operations
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
SPA resistant left-to-right integer recodings
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
An updated survey on secure ECC implementations: attacks, countermeasures and cost
Cryptography and Security
Fast and scalable parallel processing of scalar multiplication in elliptic curve cryptosystems
Security and Communication Networks
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
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Information Sciences: an International Journal
Elligator: elliptic-curve points indistinguishable from uniform random strings
Proceedings of the 2013 ACM SIGSAC conference on Computer & communications security
On the implementation of unified arithmetic on binary huff curves
CHES'13 Proceedings of the 15th international conference on Cryptographic Hardware and Embedded Systems
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Recent attacks show how an unskilled implementation of elliptic curve cryptosystems may reveal the involved secrets from a single execution of the algorithm. Most attacks exploit the property that addition and doubling on elliptic curves are different operations and so can be distinguished from side-channel analysis. Known countermeasures suggest to add dummy operations or to use specific parameterizations. This is at the expense of running time or interoperability.This paper shows how to rewrite the addition on the general Weierstra脽 form of elliptic curves so that the same formul忙 apply equally to add two different points or to double a point. It also shows how to generalize to the Weierstra脽 form a protection method previously applied to a specific form of elliptic curves due to Montgomery.The two proposed methods offer generic solutions for preventing sidechannel attacks. In particular, they apply to all the elliptic curves recommended by the standards.