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Security and privacy represent crucial requirements in different scenarios as organizations and parties involved may not want to disclose their own private information to each other. Assuring adequate and verifiable security and privacy in these scenarios faces various challenges. One such challenge is whether proposed protocols can be used over public channels, like internet. Another possible issue is whether the complete final result of a protocol can be broadcasted to, or be received by all parties. Collusion attacks can pose another security challenge in multiparty settings. Finally, it may be desirable to design incremental versions of the protocols to improve security and efficiency. To address these problems we have designed new secure building blocks and privacy-preserving protocols, while considering their performance in terms of security and efficiency. Building blocks, and the resulting protocols which take advantage of these blocks can be implemented over public channels, have a balanced distribution of the final results, and are resistant to collusion attacks. These blocks are used to design novel privacy-preserving protocols for learning and data mining techniques.