Quantum secret key encryption algorithm based on quantum discrete logarithm problem

Abstract

In this paper, we present a novel quantum secret key encryption algorithm based on quantum discrete logarithm problem (QDLP). QDLP is to find the exponent x from = å i x i C g mod p if C, åi i g and the prime p are given, where g gi modp i = for a generator g. According to our knowledge, QDLP cannot be solved by Shor’s quantum algorithm. Our algorithm assumes that the sender and the receiver share the secret key x. If the sender wants to send the message y to the receiver, the receiver first uses the secret key x to construct a quantum system å i x i i g mod p . Then, the receiver sends the quantum channel å i x i g mod p to the sender. After receiving å i x i g mod p , the sender uses the secret key x and the message y to generate ciphertext å i y i xg mod p . The receiver then construct a quantum system å i y i i xg mod p . According to the secret key x, the receiver can obtain final quantum system å i i gy mod p . Then, the receiver gets the value gy modp after measuring. Finally, the receiver can successfully recover the message y by using Shor’s quantum algorithm. Obviously, the quantum system will be broken after transferring messages. But, the secret key x can still be used repeatedly in our algorithm.