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The impact of error dependencies on Ring/Mod-LWE/LWR based schemes
Lattice cryptography Ring-LWE Error Correcting Codes
2018/12/3
Current estimation techniques for the probability of decryption failures in Ring/Mod-LWE/LWR based schemes assume independence of the failures in individual bits of the transmitted message to calculat...
Most multi-party computation protocols allow secure computation of arithmetic circuits over a finite field, such as the integers modulo a prime. In the more natural setting of integer computations mod...
Computing Mod Without Mod
mod modulo modulus
2016/1/7
Encryption algorithms are designed to be difficult to break
without knowledge of the secrets or keys. To achieve this, the algorithms
require the keys to be large, with some algorithms having a reco...
Statistical Properties of Multiplication mod $2^n$
Modular multiplication Boolean function Joint probability distribution
2016/1/3
In this paper, we investigate some statistical properties of multiplication
mod 2n for cryptographic use. For this purpose, we introduce a family
of T-functions similar to modular multiplication, wh...
How to Factor N_1 and N_2 When p_1=p_2 mod 2^t
factoring Gaussian reduction algorithm lattice
2014/3/13
Let $N_1=p_1q_1$ and $N_2=p_2q_2$ be two different RSA moduli. Suppose that $p_1=p_2 \bmod 2^t$ for some $t$, and $q_1$ and $q_2$ are $\alpha$ bit primes. Then May and Ritzenhofen showed that $N_1$ an...
On r-th Root Extraction Algorithm in F_q For q=lr^s+1 (mod r^(s+1)) with 0 < l < r and Small s
r-th root algorithm finite field Adleman-Manders-Miller algorithm Cipolla-Lehmer algorithm
2013/4/18
We present an r-th root extraction algorithm over a finite field F_q. Our algorithm precomputes a primitive r^s-th root of unity where s is the largest positive integer satisfying r^s| q-1, and is app...
We present a square root algorithm in F_q which generalizes Atkins's square root algorithm for q=5(mod 8) and Kong et al.'s algorithm for q=9(mod 16) Our algorithm precomputes a primitive 2^s-th root ...
Randomized Secure Two-Party Computation for Modular Conversion, Zero Test, Comparison, MOD and Exponentiation
applications / secure two-party computation randomized algorithm efficiency
2012/3/23
When secure arithmetic is required, computation based on secure multiplication ($\MULT$) is much more efficient than computation based on secure boolean circuits. However, a typical application can al...
On Nonlinear Polynomial Selection and Geometric Progression (mod N) for Number Field Sieve
foundations / Polynomial Selection Number Field Sieve LLL Algorithm
2012/3/28
The general number field sieve (GNFS) is asymptotically the fastest known factoring algorithm. One of the most important steps of GNFS is to select a good polynomial pair. A standard way of polynomial...
On Nonlinear Polynomial Selection and Geometric Progression (mod N) for Number Field Sieve
Polynomial Selection Number Field Sieve LLL Algorithm
2011/6/9
The general number field sieve (GNFS) is asymptotically the fastest known factoring algorithm. One of the most important steps of GNFS is to select a good polynomial pair. A standard way of polynomial...
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