Cryptography is basically a science that involves the securing of information into unreadable form and access or understanding only by the right parties. It finds a very major role in modern digital security, with blockchains and cryptocurrencies especially, for the protection of transactions involving data and communications among parties.
In its essence, cryptography relies upon employing mathematical algorithms for encrypting-scrambling and decrypting-unscrambling data. There are primarily two kinds of cryptography: symmetric cryptography and asymmetric cryptography. Symmetric cryptography requires the same key for encryption and decryption; it thus requires sharing a secret key between sender and receiver. Asymmetric cryptography employs a key pair, like the public-private key. The public key can be shared without restrictions for encrypting the message, while the private key, which only the receiver knows, decrypts the message.
The other concepts it may involve are hashing, which transforms data into a fixed-length string, usually for purposes of verification in data integrity, and digital signatures authenticating the identity of a sender and ensuring that messages have not been tampered with.
More importantly, in blockchain systems, cryptography has become a preeminent defense-in-depth strategy as a means of ensuring transactional and wallet-level security, wherein only the rightful owner can authorize movements of funds. It also enables such consensus mechanisms as proof-of-work and proof-of-stake to enable trustless interactions sans intermediaries. Cryptography in this way provides a basis for privacy, security, and ultimately trust in the digital world.
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~ Nesaty