Compression in Finite Fields and Torus-Based Cryptography
نویسندگان
چکیده
منابع مشابه
Compression in Finite Fields and Torus-Based Cryptography
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 ge...
متن کاملTorus-Based Cryptography
In a series of three lectures, we will introduce the main concepts behind torus-based cryptography. Algebraic tori were suggested in 2003 by K. Rubin and A. Silverberg for use in public-key cryptography. Torus-based cryptosystems are based on the Discrete Logarithm Problem in a subgroup of Fqn called the primitive subgroup. It is conjectured that the elements of the primitive subgroup can be re...
متن کاملTorus-Based Cryptography
We introduce the concept of torus-based cryptography, give a new public key system called CEILIDH, and compare it to other discrete log based systems including Lucas-based systems and XTR. Like those systems, we obtain small key sizes. While Lucas-based systems and XTR are essentially restricted to exponentiation, we are able to perform multiplication as well. We also disprove the open conjectu...
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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...
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We introduce a compact and efficient representation of elements of the algebraic torus. This allows us to design a new discretelog based public-key system achieving the optimal communication rate, partially answering the conjecture in [4]. For n the product of distinct primes, we construct efficient ElGamal signature and encryption schemes in a subgroup of F ∗ qn in which the number of bits exc...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2008
ISSN: 0097-5397,1095-7111
DOI: 10.1137/060676155