A public key cryptosystem and a signature scheme based on discrete logarithms
Proceedings of CRYPTO 84 on Advances in cryptology
A course in number theory and cryptography
A course in number theory and cryptography
Designing programs that check their work
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Discrete logarithms in GF(P) using the number field sieve
SIAM Journal on Discrete Mathematics
A formal treatment of remotely keyed encryption
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Discrete Logarithms: The Past and the Future
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A method for obtaining digital signatures and public-key cryptosystems
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Handbook of Applied Cryptography
Handbook of Applied Cryptography
Parameter Selection for Server-Aided RSA Computation Schemes
IEEE Transactions on Computers
Speeding Up Secret Computations with Insecure Auxiliary Devices
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Efficient Identification and Signatures for Smart Cards
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
A Subexponential Algorithm for Discrete Logarithms over All Finite Fields
CRYPTO '93 Proceedings of the 13th Annual International Cryptology Conference on Advances in Cryptology
More Flexible Exponentiation with Precomputation
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
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CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
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CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
On Verifiable Implicit Asking Protocols for RSA Computation
ASIACRYPT '92 Proceedings of the Workshop on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Secure Acceleration of DSS Signatures Using Insecure Server
ASIACRYPT '94 Proceedings of the 4th International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
High-Bandwidth Encryption with Low-Bandwidth Smartcards
Proceedings of the Third International Workshop on Fast Software Encryption
On the Security of Remotely Keyed Encryption
FSE '97 Proceedings of the 4th International Workshop on Fast Software Encryption
Discrete Logarithms: The Effectiveness of the Index Calculus Method
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
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EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques
Concealment and its applications to authenticated encryption
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
How to securely outsource cryptographic computations
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Cryptanalysis of RSA with private key d less than N0.292
IEEE Transactions on Information Theory
Grid's confidential outsourcing of string matching
SEPADS'07 Proceedings of the 6th WSEAS International Conference on Software Engineering, Parallel and Distributed Systems
Low-cost client puzzles based on modular exponentiation
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The Journal of Supercomputing
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Journal of Computer Security
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We present protocols for speeding up fixed-base variable-exponent exponentiation and variable-base fixed-exponent exponentiation using an untrusted computational resource. In the fixed-base protocols, the exponent may be blinded. In the variable-base protocols, the base may be blinded. The protocols are described for exponentiation in a cyclic group. We describe how to extend them to exponentiation modulo an integer where the modulus is the product of primes with single multiplicity. The protocols provide a speedup of $$\frac{3}{2}((\log k)-1)$$ over the square-and-multiply algorithm, where k is the bitlength of the exponent.One application of the protocols is to speed up exponentiation-based verification in discrete log-based signature and credential schemes. The protocols also allow signature verifiers to dynamically choose, for each message, the amount of work it would like to perform to verify the signature. This results in a work-security tradeoff. We introduce a fifth protocol to perform variable-base variable- exponent exponentiation, which also has this feature.Our model allows the trusted resource to perform computations in its idle time. The protocols facilitate the offloading of work to the offline stage, such that the work the trusted resource performs when it has to do an exponentiation is smaller. Our protocols are unconditionally secure.