Handbook of Applied Cryptography
Handbook of Applied Cryptography
Low Cost Attacks on Tamper Resistant Devices
Proceedings of the 5th International Workshop on Security Protocols
Finding Small Roots of Univariate Modular Equations Revisited
Proceedings of the 6th IMA International Conference on Cryptography and Coding
Optical Fault Induction Attacks
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
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
Cryptanalysis of a provably secure CRT-RSA algorithm
Proceedings of the 11th ACM conference on Computer and communications security
A CRT-RSA Algorithm Secure against Hardware Fault Attacks
DASC '06 Proceedings of the 2nd IEEE International Symposium on Dependable, Autonomic and Secure Computing
Further Cryptanalysis of a CRT-RSA Algorithm at CCS 2003
NPC '07 Proceedings of the 2007 IFIP International Conference on Network and Parallel Computing Workshops
Finding a small root of a univariate modular equation
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Finding a small root of a bivariate integer equation; factoring with high bits known
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
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
Wagner’s attack on a secure CRT-RSA algorithm reconsidered
FDTC'06 Proceedings of the Third international conference on Fault Diagnosis and Tolerance in Cryptography
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It is well known that the Chinese Remainder Theorem (CRT) can greatly improve the performances of RSA cryptosystem in both running times and memory requirements. However, if the implementation of CRT-based RSA is careless, an attacker can reveal some secret information by exploiting hardware fault cryptanalysis. In this paper, we present some fault attacks on a type of CRT-RSA algorithms namely BOS type schemes including the original BOS scheme proposed by Blömer, Otto, and Seifert at CCS 2003 and its modified scheme proposed by Liu et al. at DASC 2006. We first demonstrate that if some special signed messages such as m = 0, ±1 are dealt carelessly, they can be exploited by an adversary to completely break the security of both the BOS scheme and Liu et al.'s scheme. Then we present a new permanent fault attack on the BOS scheme with a success probability about 25%. Lastly, we propose a polynomial time attack on Liu et al.'s CRT-RSA algorithm, which combines physical fault injection and lattice reduction techniques when the public exponent is short.