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In 1995, Kuwakado, Koyama and Tsuruoka presented a new RSA-type scheme based on singular cubic curves y 2 ≡ x 3 +bx 2 (mod N) where N = pq is an RSA modulus. Then, in 2002, Elkamchouchi, Elshenawy and Shaban introduced an extension of the RSA scheme to the field of Gaussian integers using a modulus N = PQ where P and Q are Gaussian primes such that p = |P| and q = |Q| are ordinary primes. Later, in 2007, Castagnos proposed a scheme over quadratic field quotients with an RSA modulus N = pq. In the three schemes, the public exponent e is an integer satisfying the key equation ed -k(p 2 -1) (q 2 -1) = 1. In this paper, we apply the continued fraction method to launch an attack on the three schemes when the private exponent d is sufficiently small. Our attack can be considered as an extension of the famous Wiener attack on the RSA. Abstract. In 1995, Kuwakado, Koyama and Tsuruoka presented a new RSA-type scheme based on singular cubic curves y 2 ≡ x 3 + bx 2 (mod N ) where N = pq is an RSA modulus. Then, in 2002, Elkamchouchi, Elshenawy and Shaban introduced an extension of the RSA scheme to the field of Gaussian integers using a modulus N = P Q where P and Q are Gaussian primes such that p = |P | and q = |Q| are ordinary primes. Later, in 2007, Castagnos proposed a scheme over quadratic field quotients with an RSA modulus N = pq. In the three schemes, the public exponent e is an integer satisfying the key equation ed − k p 2 − 1 q 2 − 1 = 1. In this paper, we apply the continued fraction method to launch an attack on the three schemes when the private exponent d is sufficiently small. Our attack can be considered as an extension of the famous Wiener attack on the RSA.

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The rapid growth in Internet and communication technology has facilitated an escalation in the exchange of digital multimedia content. This has resulted in an increase in copyright infringement, which has led to a greater demand for more robust copyright protection mechanisms. Digital watermarking is a means of detecting ownership and illegal use of digital products. This paper presents an approach to watermarking images by embedding QR code information in a digital image.Abstract. The rapid growth in Internet and communication technology has facilitated an escalation in the exchange of digital multimedia content. This has resulted in an increase in copyright infringement, which has led to a greater demand for more robust copyright protection mechanisms. Digital watermarking is a means of detecting ownership and illegal use of digital products. This paper presents an approach to watermarking images by embedding QR code information in a digital image. The notion of the proposed scheme is to capitalize on the error correction mechanism that is inherent in the QR code structure, in order to increase the robustness of the watermark. By employing the QR code's error correction mechanism, watermark information contained within a watermarked image can potentially be decoded even if the image has been altered or distorted by an adversary. This paper studies the characteristics of the proposed scheme and presents experiment results examining the robustness and security of the QR code watermarking approach.