Solving exponential diophantine equations using lattice Basis Reduction Algorithms

Weger, de Bmm Benne

doi:10.1016/0022-314x(87)90088-6

Cited by 70 publications

(59 citation statements)

References 12 publications

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“…Due to floating point errors this only provided an approximation to an LLL reduced basis. To obtain a fully reduced basis the version of De Weger [19] was then applied to the output basis from the Schnorr-Euchner algorithm.…”

Section: Resultsmentioning

confidence: 99%

Attacking DSA Under a Repeated Bits Assumption

Leadbitter

Page

Smart

2004

Lecture Notes in Computer Science

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Abstract.We discuss how to recover the private key for DSA style signature schemes if partial information about the ephemeral keys is revealed. The partial information we examine is of a second order nature that allows the attacker to know whether certain bits of the ephemeral key are equal, without actually knowing their values. Therefore, we extend the work of Howgrave-Graham, Smart, Nguyen and Shparlinski who, in contrast, examine the case where the attacker knows the actual value of such bits. We also discuss how such partial information leakage could occur in a real life scenario. Indeed, the type of leakage envisaged by our attack would appear to be feasible than that considered in the prior work.

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Section: Resultsmentioning

confidence: 99%

Attacking DSA Under a Repeated Bits Assumption

Leadbitter

Page

Smart

2004

Lecture Notes in Computer Science

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“…As far as the partial denominators of ß coincide with those of y, they coincide with the partial denominators of any number between ß and y (cf. [23]). When the partial denominators of ß and y fail to coincide, we use (29) to compute sharper approximants ß' and y : ß < ß' < a < y1 < y, and continue computations with ß', y'.…”

Section: Program Developmentsmentioning

confidence: 99%

Catalan’s equation 𝑥^{𝑝}-𝑦^{𝑞}=1 and related congruences

Aaltonen¹,

Inkeri²

1991

Math. Comp.

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Abstract.We investigate solutions of Catalan's equation x -yq = 1 in nonzero integers x, y, p, q . By use of class numbers and congruences pq = p (mod g ) we show the impossibility of the equation for a large number of prime exponents p , q . Both theoretical and computer results are included. We also study lower bounds on possible, hitherto unknown, solutions x, y > 2; we especially wish to communicate the bound x , y > 10

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“…Deze, Tijdeman and Wang used de Weger's lower bound for differences between two prime powers [9], which follows from lower bounds for linear forms in two logarithms and classical theory of continued fractions.…”

Section: Introduction In 1970 Senge and Straussmentioning

confidence: 99%