Secret sharing is a tool that has many applications in cryptography. The concept involves sharing a secret with a group of people or devices that can only be reconstructed when the majority of the group unifies and combines the individual share. Ignacio Cascudo of the Centrum Wiskunde & Informatica (CWI) in Amsterdam developed techniques that improve the performance of some of these applications. On July 24 he will defend his thesis ‘On asymptotically good strongly multiplicative linear secret sharing’.
A secure storage of a password on internet is a well known application example of secret sharing. Sharing a password on a group of computers requires access to the whole group of devices to retrieve the password. Cascudo focused in his research on using the concept of secret sharing for a larger number of users and at the same time apply it to cryptographical areas like multi-party computation. Techniques to address these issues separately existed already, but to address these problems simultaneously is a new research area that is only recently being studied.
In his thesis Cascudo studied algebraic properties that enable to apply secret sharing to cryptographical areas like multi-party computation in a setting of a large group of users. In multi-party computation several people make calculations, without revealing specific data that are part of the final calculation. For example in auctions this method is applied when calculating the highest bid, without revealing information on individual offers. The research makes it possible to obtain more efficient multi-party computation protocols when many users are involved.
Next to multi-party computation the techniques Cascudo developed can also applied to improve the efficiency of cryptographical protocols in more theoretical domains like zero knowledge and correlation extractors.
The research was conducted at the Centrum Wiskunde & Informatica (CWI); Supervisor is Prof.dr. R.J.F. Cramer . The PhD defence will take place at the University of Oviedo (Spain).
The Cryptology group of CWI investigates fundamental cryptographic problems from a broad scientific perspective, especially from mathematics, computer science and physics. Secret sharing is one of the research topics the group is studying.