Number Of Least Significant Bits Research Articles

Generalized PCM Coding of Images

Pulse-code modulation (PCM) with embedded quantization allows the rate of the PCM bitstream to be reduced by simply removing a fixed number of least significant bits from each codeword. Although this source coding technique is extremely simple, it has a poor coding efficiency. In this paper, we present a generalized PCM (GPCM) algorithm for images that simply removes bits from each codeword. In contrast to PCM, however, the number and the specific bits that a GPCM encoder removes in each codeword depends on its position in the bitstream and the statistics of the image. Since GPCM allows the encoding to be performed with different degrees of computational complexity, it can adapt to the computational resources that are available in each application. Experimental results show that GPCM outperforms PCM with a gain that depends on the rate, the computational complexity of the encoding, and the degree of inter-pixel correlation of the image.

On the Security of RSA with Primes Sharing Least-Significant Bits

We investigate the security of a variant of the RSA public-key cryptosystem called LSBS-RSA, in which the modulus primes share a large number of least-significant bits. We show that low public-exponent LSBS-RSA is inherently resistant to Partial Key Exposure (PKE) attacks in which least-significant bits of the secret exponent are revealed to the attacker, and in particular that the Boneh-Durfee-Frankel PKE attack [5] on low public-exponent RSA is less effective for LSBS-RSA systems than for standard RSA. On the other hand, we show that large public-exponent LSBS-RSA is more vulnerable to such attacks than standard RSA. An application to server-aided RSA signature generation is proposed.

Worst-case error analysis for the fast fourier transform

Tight worst-case error bounds are derived for the results of the fast Fourier transform (f.f.t.). The following f.f.t. algorithms are analysed: (i) standard method of complex multiplication without scaling (ii) standard method with prescaling (iii) standard method with stagewise scaling (iv) Buneman's method of complex multiplication without scaling (v) Buneman's method with prescaling (vi) Buneman's method with stagewise scaling. The results establish the maximum number of least-significant bits which can become noisy in the computed spectrum for a given number N of data points, a given accuracy in the arithmetic, and a given accuracy in the tabulated coefficients of the f.f.t. The results are compared with the r.m.s. errors obtained earlier from statistical considerations.2,3 The comparison indicates that the worst-case values cannot be extrapolated from the r.m.s. values, since their dependence on N is different.

Worst-case error analysis for the fast fourier transform

Tight worst-case error bounds are derived for the results of the fast Fourier transform (f.f.t.). The following f.f.t. algorithms are analysed:(i) standard method of complex multiplication without scaling(ii) standard method with prescaling(iii) standard method with stagewise scaling(iv) Buneman's method of complex multiplication without scaling(v) Buneman's method with prescaling(vi) Buneman's method with stagewise scaling.The results establish the maximum number of least-significant bits which can become noisy in the computed spectrum for a given number N of data points, a given accuracy in the arithmetic, and a given accuracy in the tabulated coefficients of the f.f.t. The results are compared with the r.m.s. errors obtained earlier from statistical considerations.2,3 The comparison indicates that the worst-case values cannot be extrapolated from the r.m.s. values, since their dependence on N is different.