Statistically private oblivious transfer from CDH

A method for obliviously transferring either a first message or a second message to a receiver computer, the method comprising:

• determining, by the receiver computer, one or more first random numbers and one or more second random numbers;
• determining, by the receiver computer, one or more group elements;
• determining, by the receiver computer, based on the one or more first random numbers, one or more first random group elements;
• determining, by the receiver computer, based on the one or more second random numbers, one or more second random group elements;
• transmitting, by the receiver computer, to a sender computer, a first oblivious transfer message comprising the one or more group elements, the one or more first random group elements, and the one or more second random group elements, wherein the sender computer uses the one or more group elements, the one or more first random group elements, and the one or more second random group elements to determine a second oblivious transfer message comprising one or more sets of first public keys and one or more obfuscated messages, each set of first public keys comprising one or more public keys, wherein:
• the sender computer determines the one or more sets of first public keys and one or more sets of second public keys using one or more sets of secret keys, the one or more group elements and a generator, wherein each set of secret keys comprises one or more secret keys and wherein the one or more sets of second public keys each comprise one or more second public keys, and
• the sender computer determines the one or more sets of secret keys by randomly sampling the one or more sets of secret keys from an interval of integers defined by a prime number;
• receiving, by the receiver computer, from the sender computer, the second oblivious transfer message;
• determining, by the receiver computer, one or more first message computation values using the one or more sets of first public keys, the one or more first random numbers, and a hardcore predicate function;
• and
• de-obfuscating the one or more obfuscated messages using the one or more first message computation values, thereby determining an output message, wherein the output message comprises either the first message or the second message.

A method for obliviously transferring either a first message or a second message to a receiver computer, the method comprising:

• determining, by the receiver computer, one or more first random numbers and one or more second random numbers;
• determining, by the receiver computer, one or more group elements;
• determining, by the receiver computer, based on the one or more first random numbers, one or more first random group elements;
• determining, by the receiver computer, based on the one or more second random numbers, one or more second random group elements;
• transmitting, by the receiver computer, to a sender computer, a first oblivious transfer message comprising the one or more group elements, the one or more first random group elements, and the one or more second random group elements, wherein the sender computer uses the one or more group elements, the one or more first random group elements, and the one or more second random group elements to determine a second oblivious transfer message comprising one or more sets of first public keys and one or more obfuscated messages, each set of first public keys comprising one or more public keys;
• receiving, by the receiver computer from the sender computer, the second oblivious transfer message;
• determining, by the receiver computer, one or more first message computation values using the one or more sets of first public keys, the one or more first random numbers, and a hardcore predicate function;
• de-obfuscating the one or more obfuscated messages using the one or more first message computation values, thereby determining an output message, wherein the output message comprises either the first message or the second message;
• retrieving, by the receiver computer, a receiver choice bit;
• determining, by the receiver computer, one or more random receiver choice bits;
• determining, by the receiver computer, one or more indicator bits based on the receiver choice bit and the one or more random receiver choice bits;
• and
• transmitting a third oblivious transfer message comprising the one or more indicator bits to the sender computer, wherein the sender computer updates the first message and the second message based on the one or more indicator bits, thereby determining an updated first message and an updated second message.

A method for obliviously transferring either a first message or a second message to a receiver computer, the method comprising:

• receiving, by the receiver computer, from a sender computer, a first oblivious transfer message comprising one or more group elements and one or more sets of first public keys, wherein each set of first public keys comprises one or more first public keys;
• determining, by the receiver computer, one or more first message computation values using the one or more sets of first public keys, one or more first random numbers, and a hardcore predicate function;
• determining, by the receiver computer, one or more first random group elements using the one or more first random numbers and a generator;
• determining, by the receiver computer, one or more second random group elements using one or more second random numbers and the generator;
• determining, by the receiver computer, one or more indicator bits;
• transmitting, by the receiver computer, a second oblivious transfer message comprising the one or more first random group elements, the one or more second random group elements, and the one or more indicator bits to the sender computer, wherein the sender computer uses the one or more first random group elements, the one or more second random group elements, and the one or more indicator bits to determine one or more obfuscated messages;
• receiving, by the receiver computer, from the sender computer, a third oblivious transfer message comprising the one or more obfuscated messages;
• and
• de-obfuscating, by the receiver computer, the one or more obfuscated message using the one or more first message computation values, thereby determining an output message, wherein the output message comprises either the first message or the second message.