Concurrent Error Detection in Multiplexer-Based Multipliers for Normal Basis of GF(2m) Using Double Parity Prediction Scheme

Journal of Signal Processing Systems (Impact Factor: 0.56). 02/2010; 58(2):233-246. DOI: 10.1007/s11265-009-0361-4
Source: DBLP

ABSTRACT Successful implementation of elliptic curve cryptographic systems primarily depends on the efficient and reliable arithmetic
circuits for finite fields with very large orders. Thus, the robust encryption/decryption algorithms are elegantly needed.
Multiplication would be the most important finite field arithmetic operation. It is much more complex compared to the finite
field addition. It is also frequently used in performing point operations in elliptic curve groups. The hardware implementation
of a multiplication operation may require millions of logic gates and may thus lead to erroneous outputs. To obtain reliable
cryptographic applications, a novel concurrent error detection (CED) architecture to detect erroneous outputs in multiplexer-based
normal basis (NB) multiplier over GF(2
) using the parity prediction scheme is proposed in this article. Although various NB multipliers, depending on aa2i = åj = 0m - 1 ti,j a2j \alpha \alpha^{{2^i }} = \sum\limits_{j = 0}^{m - 1} {t_{i,j} } \alpha^{{2^j }} , have different time and space complexities, NB multipliers will have the same structure if they use a parity prediction
function. By using the structure of the proposed CED NB multiplier, a CED scalable multiplier over composite fields with 100%
error detection rate is also presented.

1 Bookmark
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The finite field is widely used in error-correcting codes and cryptography. Among its important arithmetic operations, multiplication is identified as the most important and complicated. Therefore, a multiplier with concurrent error detection ability is elegantly needed. In this paper, a concurrent error detection scheme is presented for bit-parallel systolic dual basis multiplier over GF(2m) according to the Fenn’s multiplier in [7]. Although, the proposed method increases the space complexity overhead about 27% and the latency overhead about one extra clock cycle as compared to Fenn’s multiplier. Our analysis shows that all single stuck-at faults can be detected concurrently.
    Journal of Electronic Testing 01/2005; 21(5):539-549. · 0.43 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Because fault-based attacks on cryptosystems have been proven effective, fault diagnosis and tolerance in cryptography have started a new surge of research and development activity in the field of applied cryptography. Without magnitude comparisons, the Montgomery multiplication algorithm is very attractive and popular for Elliptic Curve Cryptosystems. This paper will design a Montgomery multiplier array with a bit-parallel architecture in GF (2 m ) with concurrent error detection capability to protect it against fault-based attacks. The robust Montgomery multiplier array with concurrent error detection requires only about 0.2% extra space overhead (if m = 512 is as an example) and requires four extra clock cycles compared to the original Montgomery multiplier array without concurrent error detection.
    IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences 02/2006; E89-A(2):566–574. · 0.23 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Since the Fq-linear spaces F m q and Fq m are isomorphic, an m-fold multisequence S over the finite field Fq with a given characteristic polynomial f ∈ Fq(x), can be identified with a single sequence S over Fqm with characteristic polynomial f . The linear complexity of S, which will be called the generalized joint linear complexity of S , can be significantly smaller than the conventional joint linear complexity of S. We determine the expected value and the variance of the generalized joint linear complexity of a random m- fold multisequence S with given minimal polynomial. The result on the expected value generalizes a previous result on periodic m- fold multisequences. Moreover we determine the expected drop of linear complexity of a random m-fold multisequence with given characteristic polynomial f , when one switches from conventional
    Handbook of Algebra 01/1996; 1:321-363.

Full-text (2 Sources)

Available from
Jun 4, 2014