## CryptoDB

### Tomas Toft

#### Publications

Year
Venue
Title
2019
JOFC
The problem of generating an RSA composite in a distributed manner without leaking its factorization is particularly challenging and useful in many cryptographic protocols. Our first contribution is the first non-generic fully simulatable protocol for distributively generating an RSA composite with security against malicious behavior. Our second contribution is a complete Paillier (in: EUROCRYPT, pp 223–238, 1999) threshold encryption scheme in the two-party setting with security against malicious attacks. We further describe how to extend our protocols to the multiparty setting with dishonest majority. Our RSA key generation protocol is comprised of the following subprotocols: (i) a distributed protocol for generation of an RSA composite and (ii) a biprimality test for verifying the validity of the generated composite. Our Paillier threshold encryption scheme uses the RSA composite for the public key and is comprised of the following subprotocols: (i) a distributed generation of the corresponding secret key shares and (ii) a distributed decryption protocol for decrypting according to Paillier.
2015
EPRINT
2014
EPRINT
2014
JOFC
2011
PKC
2010
ASIACRYPT
2008
EPRINT
In this note, we briefly report on the first large-scale and practical application of multiparty computation, which took place in January 2008.
2006
TCC
2005
EPRINT
We show that if a set of players hold shares of a value $a\in Z_p$ for some prime $p$ (where the set of shares is written $[a]_p$), it is possible to compute, in constant round and with unconditional security, sharings of the bits of $a$, i.e.~compute sharings $[a_0]_p, \ldots, [a_{l-1}]_p$ such that $l = \lceil \log_2(p) \rceil$, $a_0, \ldots, a_{l-1} \in \{0,1\}$ and $a = \sum_{i=0}^{l-1} a_i 2^i$. Our protocol is secure against active adversaries and works for any linear secret sharing scheme with a multiplication protocol. This result immediately implies solutions to other long-standing open problems, such as constant-round and unconditionally secure protocols for comparing shared numbers and deciding whether a shared number is zero. The complexity of our protocol is $O(l \log(l))$ invocations of the multiplication protocol for the underlying secret sharing scheme, carried out in $O(1)$.

PKC 2012