Introduction to Cryptography
Cryptography is a young yet ancient discipline. It has been used to protect military and diplomatic communications for thousands of years. The earliest recorded communication cipher dates back to 400 BC. The ancient Greeks invented substitution ciphers. In 1881, the world’s first telephone secrecy patent emerged. The invention of the telegraph and radio made cryptography an unavoidable research topic in the field of communication.
From the early days of World War II when the German military used the “Enigma” cipher machine, to the Pacific War where the US military decrypted the Japanese Navy’s cipher machine, it can be said that cryptography plays a very important role in warfare. With the continuous development of the information age, the role of cryptography is no longer limited to military, political, and diplomatic aspects, but has quietly integrated into the daily lives of ordinary people, such as online banking, electronic shopping, and emails, all of which require cryptographic knowledge to protect personal information and privacy.
The development of cryptography can be roughly divided into three stages: ancient encryption methods (manual phase), classical ciphers (mechanical phase), and modern ciphers (computer phase).
Ancient encryption methods originated around 440 AD during the Greek wars with steganography. Later, in 400 BC, the Spartans invented the “Scytale” cipher. The cryptographic techniques of this period can be considered an art rather than a science, utilizing classical cryptographic systems primarily applied in military, political, and diplomatic contexts.
The encryption methods of classical ciphers generally involve letter substitution, using manual or mechanical transformations to achieve this. Classical cipher systems have initially reflected the embryonic form of modern cipher systems, being more complex than ancient encryption methods but with relatively minor variations. The earliest classical cipher systems mainly include monoalphabetic substitution ciphers and polyalphabetic substitution ciphers.
In 1949, Shannon published the paper “A Mathematical Theory of Communication” which established the theoretical foundation for private key cipher systems, marking the transition of cryptography into a science. The most complete non-technical work in this field is Kahn’s “The Codebreakers”. Since the 1960s, the proliferation of computers and communication systems has driven individuals’ demand for digital information protection and various security services. IBM’s Feistel began his work in the early 1970s, reaching a peak in 1977 when his research results were adopted as the US Federal Information Processing Standard for encrypting non-classified information, known as the Data Encryption Standard (DES), the most famous cipher system in history. However, with the development of computer hardware and the enhancement of computing power, DES has become insecure. In December 1998, the US decided to discontinue the use of DES. The National Institute of Standards and Technology (NIST) has now implemented a new encryption standard, AES, which uses the Belgian research product “Rijndael”. The cipher systems used in the above two stages are referred to as symmetric cipher systems, where the secret key for encryption and the secret key for decryption are the same. In the third stage of cryptographic development, asymmetric cipher systems—public key cryptography—emerged. The birth of public key cryptography opened up a broad path for the research and application of digital signatures. Currently, the research content of digital signatures is very rich, including ordinary signatures and special signatures. Special signatures include blind signatures, proxy signatures, group signatures, non-repudiable signatures, fair blind signatures, threshold signatures, and more. The advent of the computer and electronics era has given cryptographers unprecedented freedom; they can easily avoid the mistakes made during manual design with pencil and paper, and no longer face the high costs associated with mechanical cipher machines. In summary, using electronic computers allows for the design of more complex cipher systems.
