4,698 research outputs found
Improved Memoryless RNS Forward Converter Based on the Periodicity of Residues
The residue number system (RNS) is suitable for DSP architectures because of its ability to perform fast carry-free arithmetic. However, this advantage is over-shadowed by the complexity involved in the conversion of numbers between binary and RNS representations. Although the reverse conversion (RNS to binary) is more complex, the forward transformation is not simple either. Most forward converters make use of look-up tables (memory). Recently, a memoryless forward converter architecture for arbitrary moduli sets was proposed by Premkumar in 2002. In this paper, we present an extension to that architecture which results in 44% less hardware for parallel conversion and achieves 43% improvement in speed for serial conversions. It makes use of the periodicity properties of residues obtained using modular exponentiation
Realizing arbitrary-precision modular multiplication with a fixed-precision multiplier datapath
Within the context of cryptographic hardware, the term scalability refers to the ability to process operands of any size, regardless of the precision of the underlying data path or registers. In this paper we present a simple yet effective technique for increasing the scalability of a fixed-precision Montgomery multiplier. Our idea is to extend the datapath of a Montgomery multiplier in such a way that it can also perform an ordinary multiplication of two n-bit operands (without modular reduction), yielding a 2n-bit result. This
conventional (nxn->2n)-bit multiplication is then used as a âsub-routineâ to realize arbitrary-precision Montgomery multiplication according to standard software algorithms such as Coarsely Integrated Operand Scanning (CIOS). We
show that performing a 2n-bit modular multiplication on an n-bit multiplier can be done in 5n clock cycles, whereby we assume that the n-bit modular multiplication takes n cycles. Extending a Montgomery multiplier for this extra
functionality requires just some minor modifications of the datapath and entails a slight increase in silicon area
Secure and Efficient RNS Approach for Elliptic Curve Cryptography
Scalar multiplication, the main operation in elliptic
curve cryptographic protocols, is vulnerable to side-channel
(SCA) and fault injection (FA) attacks. An efficient countermeasure
for scalar multiplication can be provided by using alternative
number systems like the Residue Number System (RNS). In RNS,
a number is represented as a set of smaller numbers, where each
one is the result of the modular reduction with a given moduli
basis. Under certain requirements, a number can be uniquely
transformed from the integers to the RNS domain (and vice
versa) and all arithmetic operations can be performed in RNS.
This representation provides an inherent SCA and FA resistance
to many attacks and can be further enhanced by RNS arithmetic
manipulation or more traditional algorithmic countermeasures.
In this paper, extending our previous work, we explore the
potentials of RNS as an SCA and FA countermeasure and provide
an description of RNS based SCA and FA resistance means. We
propose a secure and efficient Montgomery Power Ladder based
scalar multiplication algorithm on RNS and discuss its SCAFA
resistance. The proposed algorithm is implemented on an
ARM Cortex A7 processor and its SCA-FA resistance is evaluated
by collecting preliminary leakage trace results that validate our
initial assumptions
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Components for oversampled signal processors
Oversampled converters trade transmission bandwidth for
resolution. An idealized model gives an insight into the way in which signals are encoded and thus how they can be manipulated. Oversampling offers a form of signal processing that requires simple processing elements capable of exploiting the growing clock speeds available in integrated solutions. Simultaneously avoids the need for analog circuitry. This paper reviews common operations that can be performed on oversampled signals
Systematic redundant residue number system codes: analytical upper bound and iterative decoding performance over AWGN and Rayleigh channels
The novel family of redundant residue number system (RRNS) codes is studied. RRNS codes constitute maximumâminimum distance block codes, exhibiting identical distance properties to ReedâSolomon codes. Binary to RRNS symbol-mapping methods are proposed, in order to implement both systematic and nonsystematic RRNS codes. Furthermore, the upper-bound performance of systematic RRNS codes is investigated, when maximum-likelihood (ML) soft decoding is invoked. The classic Chase algorithm achieving near-ML soft decoding is introduced for the first time for RRNS codes, in order to decrease the complexity of the ML soft decoding. Furthermore, the modified Chase algorithm is employed to accept soft inputs, as well as to provide soft outputs, assisting in the turbo decoding of RRNS codes by using the soft-input/soft-output Chase algorithm. Index TermsâRedundant residue number system (RRNS), residue number system (RNS), turbo detection
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