Compression in Finite Fields and Torus-Based Cryptography
نویسندگان
چکیده
We present efficient compression algorithms for subgroups of multiplicative groups of finite fields, we use our compression algorithms to construct efficient public key cryptosystems called T2 and CEILIDH, we disprove some conjectures, and we use the theory of algebraic tori to give a better understanding of our cryptosystems, the Lucas-based, XTR and Gong-Harn cryptosystems, and conjectured generalizations.
منابع مشابه
On Cryptographic Schemes Based on Discrete Logarithms and Factoring
At CRYPTO 2003, Rubin and Silverberg introduced the concept of torus-based cryptography over a finite field. We extend their setting to the ring of integers modulo N . We so obtain compact representations for cryptographic systems that base their security on the discrete logarithm problem and the factoring problem. This results in smaller key sizes and substantial savings in memory and bandwidt...
متن کاملEfficient implementation of low time complexity and pipelined bit-parallel polynomial basis multiplier over binary finite fields
This paper presents two efficient implementations of fast and pipelined bit-parallel polynomial basis multipliers over GF (2m) by irreducible pentanomials and trinomials. The architecture of the first multiplier is based on a parallel and independent computation of powers of the polynomial variable. In the second structure only even powers of the polynomial variable are used. The par...
متن کاملA More Compact Representation of XTR Cryptosystem
XTR is one of the most efficient public-key cryptosystems that allow us to compress the communication bandwidth of their ciphertext. The compact representation can be achieved by deploying a subgroup Fq2 of extension field Fq6 , so that the compression ratio of XTR cryptosystem is 1/3. On the other hand, Dijk et al. proposed an efficient public-key cryptosystem using a torus over Fq30 whose com...
متن کاملThe Function Field Sieve in the Medium Prime Case
In this paper, we study the application of the function field sieve algorithm for computing discrete logarithms over finite fields of the form Fqn when q is a medium-sized prime power. This approach is an alternative to a recent paper of Granger and Vercauteren for computing discrete logarithms in tori, using efficient torus representations. We show that when q is not too large, a very efficien...
متن کاملNormal Elliptic Bases and Torus-Based Cryptography
We consider representations of algebraic tori Tn(Fq) over finite fields. We make use of normal elliptic bases to show that, for infinitely many squarefree integers n and infinitely many values of q, we can encode m torus elements, to a small fixed overhead and to m φ(n)-tuples of Fq elements, in quasi-linear time in log q. This improves upon previously known algorithms, which all have a quasi-q...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Comput.
دوره 37 شماره
صفحات -
تاریخ انتشار 2008