Efficient identification and signatures for smart cards
CRYPTO '89 Proceedings on Advances in cryptology
A course in computational algebraic number theory
A course in computational algebraic number theory
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
A survey of fast exponentiation methods
Journal of Algorithms
Efficient Arithmetic on Koblitz Curves
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Cryptography: Theory and Practice
Cryptography: Theory and Practice
Handbook of Applied Cryptography
Handbook of Applied Cryptography
NTRU: A Ring-Based Public Key Cryptosystem
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Some baby-step giant-step algorithms for the low hamming weight discrete logarithm problem
Mathematics of Computation
Analysis of Low Hamming Weight Products
Discrete Applied Mathematics
Sliding Window Method for NTRU
ACNS '07 Proceedings of the 5th international conference on Applied Cryptography and Network Security
Algebraic Cryptanalysis of CTRU Cryptosystem
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Choosing NTRUEncrypt Parameters in Light of Combined Lattice Reduction and MITM Approaches
ACNS '09 Proceedings of the 7th International Conference on Applied Cryptography and Network Security
PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
Parameterized splitting systems for the discrete logarithm
IEEE Transactions on Information Theory
MaTRU: a new NTRU-Based cryptosystem
INDOCRYPT'05 Proceedings of the 6th international conference on Cryptology in India
Hard instances of the constrained discrete logarithm problem
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Choosing parameter sets for NTRUEncrypt with NAEP and SVES-3
CT-RSA'05 Proceedings of the 2005 international conference on Topics in Cryptology
CT-RSA'10 Proceedings of the 2010 international conference on Topics in Cryptology
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There are many cryptographic constructions in which one uses a random power or multiple of an element in a group or a ring. We describe a fast method to compute random powers and multiples in certain important situations including powers in the Galois field F2n, multiples on Koblitz elliptic curves, and multiples in NTRU convolution polynomial rings. The underlying idea is to form a random exponent or multiplier as a product of factors, each of which has low Hamming weight when expanded as a sum of powers of some fast operation.