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| Abstract |
In this paper, we prove a closed formula for the degree of regularity of the family of HFE- (HFE Minus) multivariate public key cryptosystems over a finite field of size q. The degree of regularity of... the polynomial system derived from an HFE- system is less than or equal to ((q-1)(⌊log_q(D-1)⌋+a))/2+2 if q is even and r+a is odd, ((q-1)(⌊log_q(D-1)⌋+a+1))/2+2 otherwise. Here q is the base field size, D the degree of the HFE polynomial, r=⌊log_q(D-1)⌋+1 and a is the number of removed equations (Minus number). This allows us to present an estimate of the complexity of breaking the HFE Challenge 2: ・the complexity to break the HFE Challenge 2 directly using algebraic solvers is about 2^<97>.show more
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2012B-3