Efficient Factoring Based on Partial Information
نویسندگان
چکیده
Rehovot 7 6 1 0 0 , I s r a e l Many r e c e n t l y p r o p o s e d c r y p t o s y s t e m s a r e based on t h e a s s u m p t i o n t h a t f a c t o r i n g l a r g e c o m p o s i t e i n t e g e r s i s c o m p u t a t i o n a l l y d i f f i c u l t. I n t h i s p a p e r w e e x a m i n e t h i s a s s u m p t i o n when t h e c r y p t a n a l y s t h a s " s i d e i n f o r m a t i o n " a v a i l a b l e. I n c r y p t o g r a p h i c a p p l i c a t i o n s , however, t h e c r y p t a n a l y s t may have a v a i l a b l e a d d i t i o n a l " s i d e i n f o r m a t i o n " above and beyond t h e number N i t s e l f. I n p r a c t i c e , o n e o f t h e p a r t i e s t y p i c a l l y knows P a n d Q a l r e a d y , and u s e s t h e s e f a c t o r s e x p l i c i t l y d u r i n g h i s c r y p t o g r a p h i c c o m p u …
منابع مشابه
Deterministically Factoring Sparse Polynomials into Multilinear Factors
We present the first efficient deterministic algorithm for factoring sparse polynomials that split into multilinear factors. Our result makes partial progress towards the resolution of the classical question posed by von zur Gathen and Kaltofen in [GK85] to devise an efficient deterministic algorithm for factoring (general) sparse polynomials. We achieve our goal by introducing essential factor...
متن کاملFactoring and recognition of read-once functions using cographs and normality and the readability of functions associated with partial k-trees
An approach for factoring general boolean functions was described in [15] which is based on graph partitioning algorithms. In this paper, we present a very fast algorithm for recognizing and factoring readonce functions which is needed as a dedicated factoring subroutine to handle the lower levels of that factoring process. The algorithm is based on algorithms for cograph recognition and on che...
متن کاملShort signature from factoring assumption in the standard model
Programmable hash functions (PHFs) is a new cryptographic primitive, which can mimic certain programmability properties of random oracles. Due to these properties, PHFs are very useful to construct short signatures in standard models. Based on (m,1)-PHF, we propose an efficient construction of short signature from factoring problem. Our signature doesn’t require the generation of primes at sign...
متن کاملDeterministically Factoring Sparse Polynomials into Multilinear Factors and Sums of Univariate Polynomials
We present the first efficient deterministic algorithm for factoring sparse polynomials that split into multilinear factors and sums of univariate polynomials. Our result makes partial progress towards the resolution of the classical question posed by von zur Gathen and Kaltofen in [6] to devise an efficient deterministic algorithm for factoring (general) sparse polynomials. We achieve our goal...
متن کاملEfficient Fail-Stop Signatures from the Factoring Assumption
In this paper, we revisit the construction of fail-stop signatures from the factoring assumption. These signatures were originally proposed to provide information-theoretic-based security against forgeries. In contrast to classical signature schemes, in which signers are protected through a computational conjecture, fail-stop signature schemes protect the signers in an information theoretic sen...
متن کاملFactoring multivariate polynomials via partial differential equations
A new method is presented for factorization of bivariate polynomials over any field of characteristic zero or of relatively large characteristic. It is based on a simple partial differential equation that gives a system of linear equations. Like Berlekamp’s and Niederreiter’s algorithms for factoring univariate polynomials, the dimension of the solution space of the linear system is equal to th...
متن کامل