A fast algorithm for computing multiplicative inverses in GF(2m) using normal bases
Information and Computation
Comparison of three modular reduction functions
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Private Information Retrieval Based on the Subgroup Membership Problem
ACISP '01 Proceedings of the 6th Australasian Conference on Information Security and Privacy
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Supersingular Abelian Varieties in Cryptology
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
IFIP/Sec '93 Proceedings of the IFIP TC11, Ninth International Conference on Information Security: Computer Security
Self-tallying Elections and Perfect Ballot Secrecy
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
Efficient Subgroup Exponentiation in Quadratic and Sixth Degree Extensions
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Replication is not needed: single database, computationally-private information retrieval
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Proceedings of the 11th ACM conference on Computer and communications security
Public-key cryptosystems based on composite degree residuosity classes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
A length-flexible threshold cryptosystem with applications
ACISP'03 Proceedings of the 8th Australasian conference on Information security and privacy
Exponentiation in Pairing-Friendly Groups Using Homomorphisms
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
A More Compact Representation of XTR Cryptosystem
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
On Cryptographic Schemes Based on Discrete Logarithms and Factoring
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
Double-Exponentiation in Factor-4 Groups and Its Applications
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
Toward acceleration of RSA using 3D graphics hardware
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
Efficient multiplication in finite field extensions of degree 5
AFRICACRYPT'11 Proceedings of the 4th international conference on Progress in cryptology in Africa
High security pairing-based cryptography revisited
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Further security analysis of XTR
ISPEC'06 Proceedings of the Second international conference on Information Security Practice and Experience
On the discrete logarithm problem on algebraic tori
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Faster squaring in the cyclotomic subgroup of sixth degree extensions
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
The function field sieve in the medium prime case
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
On the automatic construction of indistinguishable operations
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
Efficient multiplication over extension fields
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
Algorithms for Relatively Cyclotomic Primes
Fundamenta Informaticae
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At Crypto 2004, van Dijk and Woodruff introduced a new way of using the algebraic tori Tn in cryptography, and obtained an asymptotically optimal n/φ(n) savings in bandwidth and storage for a number of cryptographic applications. However, the computational requirements of compression and decompression in their scheme were impractical, and it was left open to reduce them to a practical level. We give a new method that compresses orders of magnitude faster than the original, while also speeding up the decompression and improving on the compression factor (by a constant term). Further, we give the first efficient implementation that uses T30, compare its performance to XTR, CEILIDH, and ECC, and present new applications. Our methods achieve better compression than XTR and CEILIDH for the compression of as few as two group elements. This allows us to apply our results to ElGamal encryption with a small message domain to obtain ciphertexts that are 10% smaller than in previous schemes.