Secure Trapdoor Hash Functions Based on Public-Key Cryptosystems

In this paper we systematically consider examples representative of the various families of public-key cryptosystems to see if it would be possible to incorporate them into trapdoor hash functions, and we attempt to evaluate the resulting strengths and weaknesses of the functions we are able to construct. We are motivated by the following question: Question 1.2 How likely is it that the discoverer of a heretofore unknown public-key cryptosystem could subvert it for use in a plausible secure trapdoor hash algorithm? In subsequent sections, our investigations will lead to a variety of constructions and bring to light the non-adaptability of public-key cryptosystems that are of a \low density. More importantly, we will be led to consider from a new point of view the effects of the unsigned addition, shift, exclusive-or and other logical bit string operators that are presently used in constructing secure hash algorithms: We will show how the use of publickey cryptosystems leads to \fragile secure hash algorithms, and we will argue that circular shift operators are largely responsible for the security of modern high-speed secure hash algorithms

A dynamical systems approach to the discrimination of the modes of operation of cryptographic systems

Evidence of signatures associated with cryptographic modes of operation is established. Motivated by some analogies between cryptographic and dynamical systems, in particular with chaos theory, we propose an algorithm based on Lyapunov exponents of discrete dynamical systems to estimate the divergence among ciphertexts as the encryption algorithm is applied iteratively. The results allow to distinguish among six modes of operation, namely ECB, CBC, OFB, CFB, CTR and PCBC using DES, IDEA, TEA and XTEA block ciphers of 64 bits, as well as AES, RC6, Twofish, Seed, Serpent and Camellia block ciphers of 128 bits. Furthermore, the proposed methodology enables a classification of modes of operation of cryptographic systems according to their strength.Comment: 14 pages, 10 figure

Progress on probabilistic encryption schemes

The purpose of this master\u27s project is to study different probabilistic cryptography schemes. The older probabilistic schemes, Goldwasser-Micali and Blum-Goldwasser, will only be covered briefly for a historical perspective. Several new and promising schemes have appeared in the last 7 years, generating interest. I will be examining the Paillier and Damgard-Jurik schemes in depth. This report explains the mathematics behind the schemes along with their inherent benefits, while also suggesting some potential uses. Details are given on how I optimized the algorithms, with special emphasis on using the Chinese Remainder Theorem (CRT) in the Damgard-Jurik algorithm as well as the other algorithms. One of the main benefits these schemes posses is the additively homomorphic property. I explain the homomorphic properties in the description of the schemes and give an overview of these properties in Appendix A. I create software based in the Java Cryptography Extension (JCE) that is used to do a comparative study. This includes a simple message passing program for encrypted text. I create my own implementations of Paillier, Damgard-Jurik, and a variation of Paillier\u27s scheme as a Provider using the JCE. These implementations use the CRT along with other methods to increase performance and create optimized algorithms. The implementations are plugged into the message passing program with an implementation of RSA from another Provider. A comparative study of the timings of these three schemes is done to show which one performs better in different circumstances. Conclusions are drawn based on the results of the tests and my final opinions are stated

Group theory in cryptography

This paper is a guide for the pure mathematician who would like to know more about cryptography based on group theory. The paper gives a brief overview of the subject, and provides pointers to good textbooks, key research papers and recent survey papers in the area.Comment: 25 pages References updated, and a few extra references added. Minor typographical changes. To appear in Proceedings of Groups St Andrews 2009 in Bath, U

A New Methodology to Find Private Key of RSA Based on Euler Totient Function

الهدف من هذه البحث هو تقديم منهجية جديدة للعثور على المفتاح الخاص لـ RSA  .القيمة الاولية الجديدة يتم إنشاؤها من معادلة جديدة لتسريع العملية. في الواقع ، بعد العثور على هذه القيمة ، يتم اختيار هجوم القوة القاسية لاكتشاف المفتاح الخاص. بالإضافة إلى ذلك ، بالنسبة إلى المعادلة المقترحة ، تم تعيين مضاعف دالة مؤشر أويلر لايجاد كلا من المفتاح العام والمفتاح الخاص على أنه 1. ومن ثم ، حصلنا على  أن المعادلة التي تقدر قيمة أولية جديدة مناسبة للمضاعف الصغير. النتائج التجريبية تبين أنه إذا تم تعيين جميع العوامل الأولية للمعامل أكبر من 3 وكان المضاعف 1 ، فإن المسافة بين القيمة الأولية والمفتاح الخاص تنخفض بنحو 66٪. من ناحية أخرى ، تقل المسافة عن 1٪ عندما يكون المضاعف أكبر من 66. لذلك ، لتجنب الهجوم باستخدام الطريقة المقترحة ، يجب اختيار المضاعف الأكبر من 66. علاوة على ذلك ، يتضح أنه إذا كان المفتاح العمومي يساوي 3 ، فإن المضاعف دائمًا يساوي 2.          The aim of this paper is to present a new methodology to find the private key of RSA. A new initial value which is generated from a new equation is selected to speed up the process. In fact, after this value is found, brute force attack is chosen to discover the private key. In addition, for a proposed equation, the multiplier of Euler totient function to find both of the public key and the private key is assigned as 1. Then, it implies that an equation that estimates a new initial value is suitable for the small multiplier. The experimental results show that if all prime factors of the modulus are assigned larger than 3 and the multiplier is 1, the distance between an initial value and the private key is decreased about 66%. On the other hand, the distance is decreased less than 1% when the multiplier is larger than 66. Therefore, to avoid attacking by using the proposed method, the multiplier which is larger than 66 should be chosen. Furthermore, it is shown that if the public key equals 3, the multiplier always equals 2

Toward trusted wireless sensor networks

This article presents the design and implementation of a trusted sensor node that provides Internet-grade security at low system cost. We describe trustedFleck, which uses a commodity Trusted Platform Module (TPM) chip to extend the capabilities of a standard wireless sensor node to provide security services such as message integrity, confidentiality, authenticity, and system integrity based on RSA public-key and XTEA-based symmetric-key cryptography. In addition trustedFleck provides secure storage of private keys and provides platform configuration registers (PCRs) to store system configurations and detect code tampering. We analyze system performance using metrics that are important for WSN applications such as computation time, memory size, energy consumption and cost. Our results show that trustedFleck significantly outperforms previous approaches (e.g., TinyECC) in terms of these metrics while providing stronger security levels. Finally, we describe a number of examples, built on trustedFleck, of symmetric key management, secure RPC, secure software update, and remote attestation

Study and Implementation of Cryptographic Algorithms

Cryptography has a long and fascinating history. Over the centuries, an elaborate set of protocols and mechanisms has been created to deal with information security issues when the information is conveyed by physical documents. Often the objectives of information security cannot solely be achieved through mathematical algorithms and protocols alone, but require procedural techniques and abidance of laws to achieve the desired result. For example, privacy of letters is provided by sealed envelopes delivered by an accepted mail service. The physical security of the envelope is, for practical necessity, limited and so laws are enacted which make it a criminal offense to open mail for which one is not authorized. It is sometimes the case that security is achieved not through the information itself but through the physical document recording it. For example, paper currency requires special inks and material to prevent counterfeiting