Computer arithmetic: algorithms and hardware designs
Computer arithmetic: algorithms and hardware designs
Finite Field Multiplier Using Redundant Representation
IEEE Transactions on Computers
Faster Modular Multiplication by Operand Scaling
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Error Detection in Polynomial Basis Multipliers over Binary Extension Fields
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Optical Fault Induction Attacks
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Towards fault-tolerant cryptographic computations over finite fields
ACM Transactions on Embedded Computing Systems (TECS)
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
Sequential Circuit Design for Embedded Cryptographic Applications Resilient to Adversarial Faults
IEEE Transactions on Computers
Montgomery Residue Representation Fault-Tolerant Computation in GF(2k)
ACISP '08 Proceedings of the 13th Australasian conference on Information Security and Privacy
Novel PUF-Based Error Detection Methods in Finite State Machines
Information Security and Cryptology --- ICISC 2008
Coding Schemes for Arithmetic and Logic Operations - How Robust Are They?
Information Security Applications
Non-linear Error Detection for Finite State Machines
Information Security Applications
Fault-tolerant finite field computation in the public key cryptosystems
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
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 emerging threat: eve meets a robot
INTRUST'10 Proceedings of the Second international conference on Trusted Systems
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We present a new approach to fault tolerant public key cryptography based on redundant arithmetic in finite rings. Redundancy is achieved by embedding non-redundant field or ring elements into larger rings via suitable homomorphisms obtained from modulus scaling. Our approach is closely related to, but not limited by the exact definition of cyclic binary and arithmetic codes. We present a framework for system-designers that allows flexible trade-offs between circuit area and desired level of fault tolerance. Our method applies to arithmetic in prime fields and extension fields of characteristic 2 where it serves two mutually beneficial purposes: The redundancy of the larger ring can be used for error detection, while its modulus has a special low Hamming-weight form, lending itself particularly well to efficient modular reduction.