Review on DNA Cryptography

Cryptography is the science that secures data and communication over the network by applying mathematics and logic to design strong encryption methods. In the modern era of e-business and e-commerce the protection of confidentiality, integrity and availability (CIA triad) of stored information as well as of transmitted data is very crucial. DNA molecules, having the capacity to store, process and transmit information, inspires the idea of DNA cryptography. This combination of the chemical characteristics of biological DNA sequences and classical cryptography ensures the non-vulnerable transmission of data. In this paper we have reviewed the present state of art of DNA cryptography.Comment: 31 pages, 12 figures, 6 table

Roadmap on optical security

Postprint (author's final draft

A Like ELGAMAL Cryptosystem But Resistant To Post-Quantum Attacks

The Modulo 1 Factoring Problem (M1FP) is an elegant mathematical problem which could be exploited to design safe cryptographic protocols and encryption schemes that resist to post quantum attacks. The ELGAMAL encryption scheme is a well-known and efficient public key algorithm designed by Taher ELGAMAL from discrete logarithm problem. It is always highly used in Internet security and many other applications after a large number of years. However, the imminent arrival of quantum computing threatens the security of ELGAMAL cryptosystem and impose to cryptologists to prepare a resilient algorithm to quantum computer-based attacks. In this paper we will present a like-ELGAMAL cryptosystem based on the M1FP NP-hard problem. This encryption scheme is very simple but efficient and supposed to be resistant to post quantum attacks

Goppa Codes and Their Use in the McEliece Cryptosystems

We explore the topic of Goppa codes and how they are used in the McEliece Cryptosystem. We first cover basic terminology that is needed to understand the rest of the paper. Then we explore the definition and limitations of a Goppa code along with how such codes can be used in a general cryptosystem. Then we go in depth on the McEliece Cryptosystem in particular and explain how the security of this method works

Synchronization of spatiotemporal semiconductor lasers and its application in color image encryption

Optical chaos is a topic of current research characterized by high-dimensional nonlinearity which is attributed to the delay-induced dynamics, high bandwidth and easy modular implementation of optical feedback. In light of these facts, which adds enough confusion and diffusion properties for secure communications, we explore the synchronization phenomena in spatiotemporal semiconductor laser systems. The novel system is used in a two-phase colored image encryption process. The high-dimensional chaotic attractor generated by the system produces a completely randomized chaotic time series, which is ideal in the secure encoding of messages. The scheme thus illustrated is a two-phase encryption method, which provides sufficiently high confusion and diffusion properties of chaotic cryptosystem employed with unique data sets of processed chaotic sequences. In this novel method of cryptography, the chaotic phase masks are represented as images using the chaotic sequences as the elements of the image. The scheme drastically permutes the positions of the picture elements. The next additional layer of security further alters the statistical information of the original image to a great extent along the three-color planes. The intermediate results during encryption demonstrate the infeasibility for an unauthorized user to decipher the cipher image. Exhaustive statistical tests conducted validate that the scheme is robust against noise and resistant to common attacks due to the double shield of encryption and the infinite dimensionality of the relevant system of partial differential equations.Comment: 20 pages, 11 figures; Article in press, Optics Communications (2011

Developments in multivariate post quantum cryptography.

Ever since Shor\u27s algorithm was introduced in 1994, cryptographers have been working to develop cryptosystems that can resist known quantum computer attacks. This push for quantum attack resistant schemes is known as post quantum cryptography. Specifically, my contributions to post quantum cryptography has been to the family of schemes known as Multivariate Public Key Cryptography (MPKC), which is a very attractive candidate for digital signature standardization in the post quantum collective for a wide variety of applications. In this document I will be providing all necessary background to fully understand MPKC and post quantum cryptography as a whole. Then, I will walk through the contributions I provided in my publications relating to differential security proofs for HFEv and HFEv−, key recovery attack for all parameters of HFEm, and my newly proposed multivariate encryption scheme, HFERP

Curves, codes, and cryptography

This thesis deals with two topics: elliptic-curve cryptography and code-based cryptography. In 2007 elliptic-curve cryptography received a boost from the introduction of a new way of representing elliptic curves. Edwards, generalizing an example from Euler and Gauss, presented an addition law for the curves x2 + y2 = c2(1 + x2y2) over non-binary fields. Edwards showed that every elliptic curve can be expressed in this form as long as the underlying field is algebraically closed. Bernstein and Lange found fast explicit formulas for addition and doubling in coordinates (X : Y : Z) representing (x, y) = (X/Z, Y/Z) on these curves, and showed that these explicit formulas save time in elliptic-curve cryptography. It is easy to see that all of these curves are isomorphic to curves x2 + y2 = 1 + dx2y2 which now are called "Edwards curves" and whose shape covers considerably more elliptic curves over a finite field than x2 + y2 = c2(1 + x2y2). In this thesis the Edwards addition law is generalized to cover all curves ax2 +y2 = 1+dx2y2 which now are called "twisted Edwards curves." The fast explicit formulas for addition and doubling presented here are almost as fast in the general case as they are for the special case a = 1. This generalization brings the speed of the Edwards addition law to every Montgomery curve. Tripling formulas for Edwards curves can be used for double-base scalar multiplication where a multiple of a point is computed using a series of additions, doublings, and triplings. The use of double-base chains for elliptic-curve scalar multiplication for elliptic curves in various shapes is investigated in this thesis. It turns out that not only are Edwards curves among the fastest curve shapes, but also that the speed of doublings on Edwards curves renders double bases obsolete for this curve shape. Elliptic curves in Edwards form and twisted Edwards form can be used to speed up the Elliptic-Curve Method for integer factorization (ECM). We show how to construct elliptic curves in Edwards form and twisted Edwards form with large torsion groups which are used by the EECM-MPFQ implementation of ECM. Code-based cryptography was invented by McEliece in 1978. The McEliece public-key cryptosystem uses as public key a hidden Goppa code over a finite field. Encryption in McEliece’s system is remarkably fast (a matrix-vector multiplication). This system is rarely used in implementations. The main complaint is that the public key is too large. The McEliece cryptosystem recently regained attention with the advent of post-quantum cryptography, a new field in cryptography which deals with public-key systems without (known) vulnerabilities to attacks by quantum computers. The McEliece cryptosystem is one of them. In this thesis we underline the strength of the McEliece cryptosystem by improving attacks against it and by coming up with smaller-key variants. McEliece proposed to use binary Goppa codes. For these codes the most effective attacks rely on information-set decoding. In this thesis we present an attack developed together with Daniel J. Bernstein and Tanja Lange which uses and improves Stern’s idea of collision decoding. This attack is faster by a factor of more than 150 than previous attacks, bringing it within reach of a moderate computer cluster. We were able to extract a plaintext from a ciphertext by decoding 50 errors in a [1024, 524] binary code. The attack should not be interpreted as destroying the McEliece cryptosystem. However, the attack demonstrates that the original parameters were chosen too small. Building on this work the collision-decoding algorithm is generalized in two directions. First, we generalize the improved collision-decoding algorithm for codes over arbitrary fields and give a precise analysis of the running time. We use the analysis to propose parameters for the McEliece cryptosystem with Goppa codes over fields such as F31. Second, collision decoding is generalized to ball-collision decoding in the case of binary linear codes. Ball-collision decoding is asymptotically faster than any previous attack against the McEliece cryptosystem. Another way to strengthen the system is to use codes with a larger error-correction capability. This thesis presents "wild Goppa codes" which contain the classical binary Goppa codes as a special case. We explain how to encrypt and decrypt messages in the McEliece cryptosystem when using wild Goppa codes. The size of the public key can be reduced by using wild Goppa codes over moderate fields which is explained by evaluating the security of the "Wild McEliece" cryptosystem against our generalized collision attack for codes over finite fields. Code-based cryptography not only deals with public-key cryptography: a code-based hash function "FSB"was submitted to NIST’s SHA-3 competition, a competition to establish a new standard for cryptographic hashing. Wagner’s generalized birthday attack is a generic attack which can be used to find collisions in the compression function of FSB. However, applying Wagner’s algorithm is a challenge in storage-restricted environments. The FSBday project showed how to successfully mount the generalized birthday attack on 8 nodes of the Coding and Cryptography Computer Cluster (CCCC) at Technische Universiteit Eindhoven to find collisions in the toy version FSB48 which is contained in the submission to NIST