How to prove yourself: practical solutions to identification and signature problems
Proceedings on Advances in cryptology---CRYPTO '86
Fast Base Extension Using a Redundant Modulus in RNS
IEEE Transactions on Computers
Hardware Implementation of Montgomery's Modular Multiplication Algorithm
IEEE Transactions on Computers
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Systolic Modular Multiplication
IEEE Transactions on Computers
An Improvement of the Fiat-Shamir Identification and Signature Scheme
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
A Survey of Hardware Implementation of RSA (Abstract)
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Simplifying Quotient Determination in High-Radix Modular Multiplication
ARITH '95 Proceedings of the 12th Symposium on Computer Arithmetic
New Efficient Structure for a Modular Multiplier for RNS
IEEE Transactions on Computers
Fast modular exponentiation of large numbers with large exponents
Journal of Systems Architecture: the EUROMICRO Journal
Hardware architectures for public key cryptography
Integration, the VLSI Journal
How to fake an RSA signature by encoding modular root finding as a SAT problem
Discrete Applied Mathematics - The renesse issue on satisfiability
A Hardware Algorithm for Modular Multiplication/Division
IEEE Transactions on Computers
Hardware Complexity of Modular Multiplication and Exponentiation
IEEE Transactions on Computers
Efficient Modular Arithmetic in Adapted Modular Number System Using Lagrange Representation
ACISP '08 Proceedings of the 13th Australasian conference on Information Security and Privacy
WSEAS Transactions on Circuits and Systems
Cox-Rower architecture for fast parallel montgomery multiplication
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
A high speed coprocessor for elliptic curve scalar multiplications over Fp
CHES'10 Proceedings of the 12th international conference on Cryptographic hardware and embedded systems
Efficient modulo 2n±1 squarers
Integration, the VLSI Journal
FPGA implementation of pairings using residue number system and lazy reduction
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
Flexible design of a modular simultaneous exponentiation core for embedded platforms
ARC'13 Proceedings of the 9th international conference on Reconfigurable Computing: architectures, tools, and applications
Improving modular inversion in RNS using the plus-minus method
CHES'13 Proceedings of the 15th international conference on Cryptographic Hardware and Embedded Systems
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We present a new RNS modular multiplication for very large operands. The algorithm is based on Montgomery's method adapted to mixed radix, and is performed using a Residue Number System. By choosing the moduli of the RNS system reasonably large and implementing the system on a ring of fairly simple processors, an effect corresponding to a redundant high-radix implementation is achieved. The algorithm can be implemented to run in ${\cal O}(n)$ time on ${\cal O}(n)$ processors, where n is the number of moduli in the RNS system, and the unit of time is a simple residue operation, possibly by table look-up. Two different implementations are proposed, one based on processors attached to a broadcast bus, another on an oriented ring structure.