TY - JOUR
T1 - VSH and multiplicative modular relations between small primes with polynomial exponents
AU - Blake, Ian F.
AU - Luca, Florian
AU - Shparlinski, Igor E.
PY - 2014/6
Y1 - 2014/6
N2 - We study the frequency of the positive integers n that are products of two primes of the same order of magnitude and such that the congruence Π i = 1 k p i f i (n) ≡ 1 (mod n) holds with some fixed nonzero polynomials f 1 (X), ..., f k (X) Z [ X ], where p i denotes the i th prime. The question is motivated by collision finding in the so-called Very Smooth Hash function, introduced by Contini et al. (Lecture notes in computer science, vol. 4004. Springer, Berlin, pp 165-182, 2006).
AB - We study the frequency of the positive integers n that are products of two primes of the same order of magnitude and such that the congruence Π i = 1 k p i f i (n) ≡ 1 (mod n) holds with some fixed nonzero polynomials f 1 (X), ..., f k (X) Z [ X ], where p i denotes the i th prime. The question is motivated by collision finding in the so-called Very Smooth Hash function, introduced by Contini et al. (Lecture notes in computer science, vol. 4004. Springer, Berlin, pp 165-182, 2006).
KW - Hash function
KW - Multiplicative relations
KW - Polynomials
KW - Primes
UR - http://www.scopus.com/inward/record.url?scp=84903382888&partnerID=8YFLogxK
U2 - 10.1007/s00200-014-0219-2
DO - 10.1007/s00200-014-0219-2
M3 - Article
AN - SCOPUS:84903382888
SN - 0938-1279
VL - 25
SP - 181
EP - 188
JO - Applicable Algebra in Engineering, Communications and Computing
JF - Applicable Algebra in Engineering, Communications and Computing
IS - 3
ER -