Quantum Safe Cryptographic Primitives Using Lattice Based Algorithms

From older times the varying security needs resulted in the design of various cryptographic primitives like encryptions, digital signatures, message digest, and digital certificate. The rapid digitization, online commerce, digital currency, cloud computing, Internet of things, and upcoming quantum computer threat moved researchers for finding provably secure cryptographic methods. According to Shor's algorithm given a sufficiently large quantum computer, conventional public-key cryptography techniques (like RSA and Elliptic-Curve Diffie-Hellman) based on the hardness of integer factorization and elliptic curve discrete logarithm problem will be solved in polynomial time. The data encrypted today using conventional method will no longer be forward secured. Thus, the need of hour is to develop and switch to quantum-secure cryptographic primitives to protect present and future communication.

The classical cryptosystem majorly involved three types of ciphers for encrypting information. The ciphers are substitution, transposition, and steganography. Tn a substitution cipher, the prevailing letters in the plaintext are substituted with other letters or numbers. The famous and oldest cipher based on substitution technique is Ceaser cipher. The German military during World War TT makes use of substitution techniques in the Enigma machine for encryption. The transposition cipher involves permutation of plaintext letters i.e. the position of letters is shuffled. Stenography is the method of hiding the message in an image, video, or any other media. The substitution and transposition form the basic building block of all the symmetric-key encryption schemes. Further multiple rounds of substitution and transposition provide a strong and hard cryptosystem.

As previously stated, cryptography was previously utilized to ensure merely the confidentiality of information transmitted through insecure networks. However, the digital revolution ushered in modern cryptography advancements in the areas of authentication, non- repudiation, and integrity. Digital signatures, digital certificates, hashing, and the message digest are all common primitives. These primitives also allowed modern-day technology such as online banking, credit cards, electronic commerce, and other digital tasks to be secure enough to attract the general public.

Identity-based encryption, location-based encryption, quantum-safe cryptography primitives, homomorphic encryption, blockchain, and cryptographic currencies (bitcoin, and ethereum) are some of the modern primitives