Elliptic curves are the basis for a relative new class of public-key schemes. It is predicted that elliptic curves will replace many existing schemes in the near future. It is thus of great interest to develop algorithms which allow eecient implementations of elliptic curve crypto systems. This thesis deals with such algorithms. EEcient algorithms for elliptic curves can be classiied into low-l...

This work proposes a processor architecture for elliptic curves cryptosystems over fields GF (2 m). This is a scalable architecture in terms of area and speed that exploits the abilities of reconfigurable hardware to deliver optimized circuitry for different elliptic curves and finite fields. The main features of this architecture are the use of an optimized bit-parallel squarer, a digit-serial...

Many software implementations of public key cryptosystems have been concerned with efficiency. The advent of side channel attacks, such as timing and power analysis attacks, force us to reconsider the strategy of implementation of group arithmetic. This paper presents a study of software counter measures against side channel attacks for elliptic curve cryptosystems. We introduce two new counter...

Elliptic curves are the basis for a relative new class of public-key schemes. It is predicted that elliptic curves will replace many existing schemes in the near future. It is thus of great interest to develop algorithms which allow efficient implementations of elliptic curve crypto systems. This thesis deals with such algorithms. Efficient algorithms for elliptic curves can be classified into ...

Randomization techniques play an important role in the protection of cryptosystems against implementation attacks. This paper studies the case of elliptic curve cryptography and propose three novel randomization methods, for the elliptic curve point multiplication, which do not impact the overall performance. Our first method, dedicated to elliptic curves over prime fields, combines the advanta...

This contribution introduces a class of Galois eld used to achieve fast nite eld arithmetic which we call an Optimal Extension Field OEF This approach is well suited for implementation of public key cryptosystems based on elliptic and hyperelliptic curves Whereas previous reported optimizations focus on nite elds of the form GF p and GF m an OEF is the class of elds GF p for p a prime of specia...

Security issues play an important role in almost all modern communication and computer networks. The foundation of IT security are cryptographic systems, for example hyperelliptic curves cryptosystems (HECC). The advantage of HECC is that they allow encryption with shorter operands and at the same time, they provide the same level of security as other public-key cryptosystems, based on the inte...

Elliptic curve cryptosystems are more and more widespread in everyday-life applications. This trend should still gain momentum in coming years thanks to the exponential security enjoyed by these systems compared to the subexponential security of other systems such as RSA. For this reason, efficient elliptic curve arithmetic is still a hot topic for cryptographers. The core operation of elliptic...

Invalid curve attacks are a well-known class of attacks against implementations of elliptic curve cryptosystems, in which an adversary tricks the cryptographic device into carrying out scalar multiplication not on the expected secure curve, but on some other, weaker elliptic curve of his choosing. In their original form, however, these attacks only affect elliptic curve implementations using ad...

The scalar multiplication of elliptic curve based cryptosystems (ECC) is computed by repeatedly calling the addition formula that calculates the elliptic curve addition of two points. The addition formula involves several exceptional procedures so that implementers have to carefully consider their treatments. In this paper we study the exceptional procedure attack, which reveals the secret scal...