Advances in Applied Mathematics
A course in computational algebraic number theory
A course in computational algebraic number theory
A survey of fast exponentiation methods
Journal of Algorithms
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
Efficient elliptic curve exponentiation
ICICS '97 Proceedings of the First International Conference on Information and Communication Security
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
CM-Curves with Good Cryptographic Properties
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Efficient Multiplication on Certain Nonsupersingular Elliptic Curves
CRYPTO '92 Proceedings of the 12th 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
An Improved Algorithm for Arithmetic on a Family of Elliptic Curves
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Efficient Elliptic Curve Exponentiation Using Mixed Coordinates
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Resistance against Differential Power Analysis for Elliptic Curve Cryptosystems
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
CHES '00 Proceedings of the Second 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
ICISC '01 Proceedings of the 4th International Conference Seoul on Information Security and Cryptology
DPA Countermeasure Based on the "Masking Method"
ICISC '01 Proceedings of the 4th International Conference Seoul on Information Security and Cryptology
Improved Elliptic Curve Multiplication Methods Resistant against Side Channel Attacks
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
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
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
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
Preventing Differential Analysis in GLV Elliptic Curve Scalar Multiplication
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
DPA Countermeasures by Improving the Window Method
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Pipelined Computation of Scalar Multiplication in Elliptic Curve Cryptosystems (Extended Version)
IEEE Transactions on Computers
On Avoiding ZVP-Attacks Using Isogeny Volcanoes
Information Security Applications
Coordinate blinding over large prime fields
CHES'10 Proceedings of the 12th international conference on Cryptographic hardware and embedded systems
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
Efficient and secure elliptic curve point multiplication using double-base chains
ASIACRYPT'05 Proceedings of the 11th international conference on Theory and Application of Cryptology and Information Security
Efficient representations on koblitz curves with resistance to side channel attacks
ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
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
Sign change fault attacks on elliptic curve cryptosystems
FDTC'06 Proceedings of the Third international conference on Fault Diagnosis and Tolerance in Cryptography
Signed MSB-set comb method for elliptic curve point multiplication
ISPEC'06 Proceedings of the Second international conference on Information Security Practice and Experience
Novel efficient implementations of hyperelliptic curve cryptosystems using degenerate divisors
WISA'04 Proceedings of the 5th international conference on Information Security Applications
Countermeasures for preventing comb method against SCA attacks
ISPEC'05 Proceedings of the First international conference on Information Security Practice and Experience
Short memory scalar multiplication on koblitz curves
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
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
A general methodology for pipelining the point multiplication operation in curve based cryptography
ACNS'06 Proceedings of the 4th international conference on Applied Cryptography and Network Security
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
A DPA countermeasure by randomized frobenius decomposition
WISA'05 Proceedings of the 6th international conference on Information Security Applications
Efficient countermeasures for thwarting the SCA attacks on the frobenius based methods
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
An updated survey on secure ECC implementations: attacks, countermeasures and cost
Cryptography and Security
Same values power analysis using special points on elliptic curves
COSADE'12 Proceedings of the Third international conference on Constructive Side-Channel Analysis and Secure Design
Zero-value point attacks on kummer-based cryptosystem
ACNS'12 Proceedings of the 10th international conference on Applied Cryptography and Network Security
SPA countermeasure based on unsigned left-to-right recodings
ATC'07 Proceedings of the 4th international conference on Autonomic and Trusted Computing
ISC'07 Proceedings of the 10th international conference on Information Security
CHES'12 Proceedings of the 14th international conference on Cryptographic Hardware and Embedded Systems
Securing pairing-based cryptography on smartcards
International Journal of Information and Computer Security
Low-Cost countermeasure against RPA
CARDIS'12 Proceedings of the 11th international conference on Smart Card Research and Advanced Applications
Fault attacks on projective-to-affine coordinates conversion
COSADE'13 Proceedings of the 4th international conference on Constructive Side-Channel Analysis and Secure Design
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We propose several new methods to protect the scalar multiplication on an elliptic curve against Differential Analysis. The basic idea consists in transforming the curve through various random morphisms to provide a non-deterministic execution of the algorithm. The solutions we suggest complement and improve the state-of-the-art, but also provide a practical toolbox of efficient countermeasures. These should suit most of the needs for protecting implementations of crypto-algorithms based on elliptic curves.