Reflections on the Pentium Division Bug
IEEE Transactions on Computers
Economy-class ion-defying ICs in orbit
IEEE Spectrum
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Systolic Modular Multiplication
IEEE Transactions on Computers
A Systolic, Linear-Array Multiplier for a Class of Right-Shift Algorithms
IEEE Transactions on Computers
Moduli for Testing Implementations of the RSA Cryptosystem
ARITH '99 Proceedings of the 14th IEEE Symposium on Computer Arithmetic
Floating-Point Unit in Standard Cell Design with 116 Bit Wide Dataflow
ARITH '99 Proceedings of the 14th IEEE Symposium on Computer Arithmetic
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
Incorporating error detection in an RSA architecture
FDTC'06 Proceedings of the Third international conference on Fault Diagnosis and Tolerance in Cryptography
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An increasing mass market for cryptographic products leads to greater pressure on companies to fabricate chips which will recover from, and correct, sporadic errors resulting from design and fabrication faults, inadequate testing, smaller technology, ionising radiation, random noise, and so on. Where encryption is subject to such errors, large quantities of data can become totally corrupted or inaccessible unless fault detection is an integral part of the hardware arithmetic. Here realistically cheap methods are examined for checking the correctness of the arithmetic computations which are the basis of the RSA cryptosystem and Diffie-Hellman key exchange. As in ordinary integer multiplication, a modular residue checker function is used to detect errors and trigger re-computation when necessary. The mechanism will also detect most permanent faults. Some suggestions are made on how to correct infrequent errors without using additional hardware.