In this paper, an improved GEF fast addition algorithm is proposed. The proposed algorithm reduces time and memory space. In this algorithm, carry is calculated on the basis of arrival timing of the operand’s bits without overhead of sorting. Intermediate terms are generated from the most significant bit and the carry is generated from the least significant bit using the functions of efficient ...

This paper presents high-speed low-power small-area accumulator designs to be used in DDFS systems. To reduce the Numerically Controlled Oscillator (NCO) design complexity and size, only the most significant bits of the accumulator drive the phase to amplitude mapping block. Those bits need to be updated on every sampling clock, while the least significant bits of the accumulator are not visibl...

This paper presents three new attacks on the RSA cryptosystem. The first two attacks work when k RSA public keys (Ni, ei) are such that there exist k relations of the shape eix−yiφ(Ni) = zi or of the shape eixi − yφ(Ni) = zi where Ni = piqi, φ(Ni) = (pi − 1)(qi − 1) and the parameters x, xi, y, yi, zi are suitably small in terms of the prime factors of the moduli. We show that our attacks enabl...

To develop and check the Steganography based information’s by using Matlab this proposal investigates the detection of information hidden in digital media by both the least significant bit (LSB) matching and replacement scheme. Which can completely recover the original images without any distortion from the secret images by utilizing the parity features of the original images and defining two e...

We study the problem of integer factoring given implicit information of a special kind. The problem is as follows: let N1 = p1q1 and N2 = p2q2 be two RSA moduli of same bit-size, where q1,q2 are α-bit primes. We are given the implicit information that p1 and p2 share t most significant bits. We present a novel and rigorous lattice-based method that leads to the factorization of N1 and N2 in pol...

One of the most frequent operations in modern cryptosystems is a multi-scalar multiplication with two scalars. Common methods to compute it are the Shamir method and the Interleave method whereas their speed mainly depends on the (joint) Hamming weight of the scalars. To increase the speed, the scalars are usually deployed using some general representation which provides a lower (joint) Hamming...

We introduce the class MP of languages L which can be solved in polynomial time with the additional information of one bit from a #P function f . We prove that the polynomial hierarchy and the classes ModkP, k ≥ 2, are low for this class. We show that the middle bit of f(x) is as powerful as any other bit, and that a wide range of bits around the middle have the same power. By contrast, the O(l...

The FFT performs butterfly computations on pairs of data elements that differ in a single bit. The computations start from the most significant bit in the index space and proceeds monotonically to the least significant bit. In a binary cube, adjacent nodes differ in a single bit in their addresses. Thus, mapping data to nodes by a binary encoding of the indices is suitable for the FFT. We assum...

In [4], we introduced the alternating greedy expansion of integers, which turned out to be useful in several left-to-right algorihms in cryptography. In this paper, we collect known results about this alternating greedy expansion and complement it with other useful properties and algorithms. In the second part, we apply it to give an algorithm for computing a joint expansion of d integers of mi...

In this paper, we propose an MSD (most significant digit) multiplier based on an MSB (most significant bit) multiplier over GF(2). The proposed multiplier is based on connecting D (digit size)-bit bit-operations in series. In each digit operation in our proposed multiplier, the “left shift and reduction operation” is serially performed for each of D bits. Because registers for storing intermedi...