Basics of Homomorphic Encryption

Explore the basics of cryptography, the science of secure communication, covering encryption and decryption, symmetric and asymmetric cryptography, keys and algorithms, and core goals of confidentiality, integrity, authenticity, and non-repudiation.

Understand symmetric cryptography, using a secret key for encryption and decryption with block ciphers AES and DES, stream ciphers, and contrast it with asymmetric cryptography using public and private keys.

Explore how homomorphic encryption enables privacy-preserving computations on encrypted data. Assess its security foundations, performance overhead, and the range from partially to fully homomorphic schemes, including SSE and FSC.

Trace the development of homomorphic encryption from 1978 origins to Gentry's 2009 fully homomorphic breakthrough. Highlight key players and open-source libraries enabling secure data analysis and privacy preserving machine learning.

Explore how homomorphic encryption lets operations occur on ciphertexts without decrypting, focusing on homomorphic addition that yields the plaintext sum. Applications include secure voting and privacy preserving data aggregation.

Explore homomorphic multiplication on ciphertexts and how fully homomorphic encryption enables arithmetic on encrypted data for privacy-preserving analysis and secure outsourcing.

Explore partially homomorphic encryption, which supports addition or multiplication on encrypted data without decryption. Learn how Paillier enables secure data aggregation and Goldwasser-Micali enables secure multiplications.

Examine the advantages and disadvantages of partially homomorphic encryption, noting its efficiency and limited support for certain operations, while acknowledging that security relies on underlying mathematical assumptions and scheme guarantees.

Explore fully homomorphic encryption, enabling arbitrary computations on encrypted data with addition and multiplication, using bootstrapping to refresh noise, and enabling secure outsourcing, privacy-preserving analysis, and multi-party computation.

Learn how bootstrapping reduces noise in fully homomorphic encryption by decrypting and re-encrypting ciphertexts, enabling secure, repeated computations despite computational costs.

Encrypt data with homomorphic encryption to perform computations on ciphertext while preserving privacy. Decrypt results to reveal plaintext-equivalent outcomes for secure cloud computing, healthcare analytics, and encrypted data sharing.

Outsourced computation with homomorphic encryption lets providers run computations on encrypted data and return encrypted results for the data owner to decrypt, enabling secure data analytics and privacy-preserving machine learning.

Explore homomorphic encryption schemes such as RSA, Paillier, BFV, and CKKS, and gain hands-on with tools like Microsoft SEAL, Stencil, Palisade, HElib, SEAL-SIX, and TF Encrypted.

National Institute of Standards and Technology leads the standardization efforts for fully homomorphic encryption through the homomorphic encryption standardization project and the homomorphic encryption.org consortium, engaging industry, government, and academia.