Discrete Logarithm in GF(2809) with FFS

Barbulescu, Razvan; Bouvier, Cyril; Detrey, Jérémie; Gaudry, Pierrick; Jeljeli, Hamza; Thomé, Emmanuel; Videau, Marion; Zimmermann, Paul

doi:10.1007/978-3-642-54631-0_13

Cited by 17 publications

(15 citation statements)

References 20 publications

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“…This would require approximately 2 77 arithmetic operations on numbers of p bits, since we only need the value of logarithms modulo 2 p − 1. Comparing with the most recent data of the function field sieve [2], this L(1/3) algorithm remains more efficient in this range.…”

Section: Remarks On the Special Case Of F P K P And K Primementioning

confidence: 93%

A New Index Calculus Algorithm with Complexity $$L(1/4+o(1))$$ in Small Characteristic

Joux

2014

Lecture Notes in Computer Science

120

112

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Abstract. In this paper, we describe a new algorithm for discrete logarithms in small characteristic. This algorithm is based on index calculus and includes two new contributions. The first is a new method for generating multiplicative relations among elements of a small smoothness basis. The second is a new descent strategy that allows us to express the logarithm of an arbitrary finite field element in terms of the logarithm of elements from the smoothness basis. For a small characteristic finite field of size Q = p n , this algorithm achieves heuristic complexity LQ(1/4 + o(1)). For technical reasons, unless n is already a composite with factors of the right size, this is done by embedding FQ in a small extension FQe with e ≤ 2 log p n .

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Section: Remarks On the Special Case Of F P K P And K Primementioning

confidence: 93%

A New Index Calculus Algorithm with Complexity $$L(1/4+o(1))$$ in Small Characteristic

Joux

2014

Lecture Notes in Computer Science

120

112

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“…The ROW_FIXED cutting strategy split the loop in a fixed number of iterations (256 in this benchmarks) allowing the scheduler to efficiently balance the workload over the cores and the tasks are big enough to cover the management overhead. Table 2: Performance in Gfops of PALADIn compared to OpenMP and TBB "parallel for" for the CSR spmv operation of two sparses matrices arising in the discrete logarithm problem [2].…”

Section: Spmv Operationmentioning

confidence: 99%

Parallel algebraic linear algebra dedicated interface

Gautier

Roch

Sultan

et al. 2015

Proceedings of the 2015 International Workshop on Parallel Symbolic Computation

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This work deals with parallelism in linear algebra routines. We propose a domain specific language based on C/C++ macros, PALADIn (Parallel Algebraic Linear Algebra Dedicated Interface). This domain specific language allows the user to write C++ code and benefit from sequential and parallel executions on shared memory architectures. With a unique syntax, the user can switch between different parallel runtime systems such as OpenMP, TBB and xKaapi. This interface provides data and task parallelism. Depending on the runtime system, task parallelism can use explicit synchronizations or data-dependency based synchronizations. Also, this language provides different matrix cutting strategies according to one or two dimensions. Moreover, block algorithms, such as block iterative and recursive matrix multiplication, can involve splitting according to three dimensions. The latter is also a feature that is provided to the user. The PALADIn interface can be used in any C++ library for linear algebra computation and gets the best performance from the three supported parallel runtime systems.

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“…where for the first equality we use that Q ∈ E(F q ) and R ∈ E [2], and for the third equality we use that Q ∈ E[n − 2k] and R ∈ T n .…”

Section: An Equation For the Trace Zero Subgroupmentioning

confidence: 99%

Point compression for the trace zero subgroup over a small degree extension field

Gorla

Massierer

2014

Des. Codes Cryptogr.

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Using Semaev's summation polynomials, we derive a new equation for the Fqrational points of the trace zero variety of an elliptic curve defined over Fq. Using this equation, we produce an optimal-size representation for such points. Our representation is compatible with scalar multiplication. We give a point compression algorithm to compute the representation and a decompression algorithm to recover the original point (up to some small ambiguity). The algorithms are efficient for trace zero varieties coming from small degree extension fields. We give explicit equations and discuss in detail the practically relevant cases of cubic and quintic field extensions.

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Discrete Logarithm in GF(2809) with FFS

Cited by 17 publications

References 20 publications

A New Index Calculus Algorithm with Complexity $$L(1/4+o(1))$$ in Small Characteristic

A New Index Calculus Algorithm with Complexity $$L(1/4+o(1))$$ in Small Characteristic

Parallel algebraic linear algebra dedicated interface

Point compression for the trace zero subgroup over a small degree extension field

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