A survey of fast exponentiation methods
Journal of Algorithms
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Checking Before Output May Not Be Enough Against Fault-Based Cryptanalysis
IEEE Transactions on Computers
Handbook of Applied Cryptography
Handbook of Applied Cryptography
A Countermeasure against One Physical Cryptanalysis May Benefit Another Attack
ICISC '01 Proceedings of the 4th International Conference Seoul on Information Security and Cryptology
Algorithms for Multi-exponentiation
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
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
Differential Fault Analysis of Secret Key Cryptosystems
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Breaking Public Key Cryptosystems on Tamper Resistant Devices in the Presence of Transient Faults
Proceedings of the 5th International Workshop on Security Protocols
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
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
Fault Attacks on RSA with CRT: Concrete Results and Practical Countermeasures
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
RSA Speedup with Chinese Remainder Theorem Immune against Hardware Fault Cryptanalysis
IEEE Transactions on Computers
A new CRT-RSA algorithm secure against bellcore attacks
Proceedings of the 10th ACM conference on Computer and communications security
Low-Cost Solutions for Preventing Simple Side-Channel Analysis: Side-Channel Atomicity
IEEE Transactions on Computers
Cryptanalysis of a provably secure CRT-RSA algorithm
Proceedings of the 11th ACM conference on Computer and communications security
On authenticated computing and RSA-based authentication
Proceedings of the 12th ACM conference on Computer and communications security
An RSA Implementation Resistant to Fault Attacks and to Simple Power Analysis
IEEE Transactions on Computers
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
Perturbating RSA Public Keys: An Improved Attack
CHES '08 Proceeding sof the 10th international workshop on Cryptographic Hardware and Embedded Systems
A Practical Fault Attack on Square and Multiply
FDTC '08 Proceedings of the 2008 5th Workshop on Fault Diagnosis and Tolerance in Cryptography
In(security) Against Fault Injection Attacks for CRT-RSA Implementations
FDTC '08 Proceedings of the 2008 5th Workshop on Fault Diagnosis and Tolerance in Cryptography
On the importance of checking cryptographic protocols for faults
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
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
Power analysis for secret recovering and reverse engineering of public key algorithms
SAC'07 Proceedings of the 14th international conference on Selected areas in cryptography
Why one should also secure RSA public key elements
CHES'06 Proceedings of the 8th international conference on Cryptographic Hardware and Embedded Systems
Attacking right-to-left modular exponentiation with timely random faults
FDTC'06 Proceedings of the Third international conference on Fault Diagnosis and Tolerance in Cryptography
Combined implementation attack resistant exponentiation
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
Modulus fault attacks against RSA-CRT signatures
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
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
Attacking RSA---CRT signatures with faults on montgomery multiplication
CHES'12 Proceedings of the 14th international conference on Cryptographic Hardware and Embedded Systems
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Fault Analysis is a powerful cryptanalytic technique that enables to break cryptographic implementations embedded in portable devices more efficiently than any other technique. For an RSA implemented with the Chinese Remainder Theorem method, one faulty execution suffices to factorize the public modulus and fully recover the private key. It is therefore mandatory to protect embedded implementations of RSA against fault analysis. This paper provides a new countermeasure against fault analysis for exponentiation and RSA. It consists in a self-secure exponentiation algorithm, namely an exponentiation algorithm that provides a direct way to check the result coherence. An RSA implemented with our solution hence avoids the use of an extended modulus (which slows down the computation) as in several other countermeasures. Moreover, our exponentiation algorithm involves 1.65 multiplications per bit of the exponent which is significantly less than the 2 required by other self-secure exponentiations.